Model Embedded Control: A Method to Rapidly Synthesize Controllers in a Modeling Environment

Size: px
Start display at page:

Download "Model Embedded Control: A Method to Rapidly Synthesize Controllers in a Modeling Environment"

Transcription

1 Moel Embee Conrol: A Meho o Rapily Synhesize Conrollers in a Moeling Environmen Moel Embee Conrol: A Meho o Rapily Synhesize Conrollers in a Moeling Environmen E. D. Tae Michael Sasena Jesse Gohl Michael Tiller Hybri Powerrain Engineering, General Moors Corp. 187 Troy Tech Par, Troy, Michigan, 489 Emmesay, Inc, Five Mile Roa Plymouh, Michigan, Absrac One of he challenges in moeling complex sysems is he creaion of qualiy conrollers. In some projecs, he effor o evelop even a reasonable prooype conroller warfs he effor require o evelop a physical moel. For a limie class of problems, i is possible an racable o irecly synhesize a conroller from a mahemaical saemen of conrol objecives an a moel of he plan. To o his, a sysem moel is ecompose ino a conrols moel an a plan moel. The conrols moel is furher ecompose ino an opimizaion problem an a zero-ime plan moel. The zero-ime plan moel in he conroller is a copy or a reasonable represenaion of he real plan moel. I is use o evaluae he fuure impac of possible conrol acions. This ype of conroller is referre o as a Moel Embee Conroller (MEC) an can be use o realize conrollers esigne using Dynamic Programming (DP). To illusrae his approach, an approximaion o he problem of saring an engine is consiere. In his problem, an elecric machine wih a flywheel is connece o cran an slier wih a spring aache o he slier. The machine orque is consraine o a value which is insufficien o saically overcome he force of he spring. This consrain prevens he moor from achieving he esire spee from some iniial coniions if i only supplies maximal orque in he esire irecion of roaion. By using DP, a conrol sraegy ha achieves he esire spee from any iniial coniion is generae. This conroller is realize in he moel using MEC. The conroller for his example is creae by forming an opimizaion problem an calling an embee copy of he plan moel. Furhermore, his conroller is calibrae by conucing a large scale Design of Experimens (DOE). The experimens are processe o generae he calibraions for he conroller such ha i achieves is esign objecives when use for close loop conrol of he plan moel. I is well unersoo ha Moelica inclues many language feaures ha allow plan moels o be evelope quicly. As iscusse previously, he evelopmen of qualiy conrol sraegies generally remains a bolenec. In his paper we show how exising feaures along wih appropriae ool suppor an poenial language changes can mae a significan impac on he moel evelopmen process by supporing an auomae conrol synhesis process. Keywors: Conrol, Dynamic Programming, Moel Embee Conrol, Moel Base Conrol, Opimal Conrol 1 Inroucion The use of moeling is well esablishe in he evelopmen of complex proucs. Moern ools have significanly reuce he effor require o moel an une physical sysems. Acausal or opological moeling reuces he effor require o moel a sysem s physics. The use of opimizaion allows sysemaic uning of parameers o improve a esign. The combinaion of parameer opimizaion an The Moelica Associaion 493 Moelica 28, March 3 r 4 h, 28 1

2 E. Tae, M. Sasena, J. Gohl, M. Tiller rapi moeling allows a large se of poenial esigns o be quicly evaluae. However for sysems which inclue conrols, he evelopmen is, in general, a man-power inensive process subjec o large uncerainy in evelopmen ime an opimaliy. The opimizaion of boh conrols an esign mus be solve in many problems [1-3]. One way o aress his problem is o use numerical echniques o consruc conrollers. For cerain classes of problems, racable numerical echniques can be use o evelop an approximaely minimizing conroller [4]. A minimizing conroller is a conroller which achieves he bes possible performance from a sysem as measure agains an objecive. There may exis more han one conroller able o achieve his minimum, bu no conroller can perform beer han a minimizing conroller. For his wor, he erms minimizing conroller an opimal conroller are use inerchangeably. To consruc a minimizing conroller, an objec cos, J, is efine. This is a funcion which maps he sae an inpu rajecory of he sysem o a scalar: J C x, u. (1) Consier he special case of a plan escribe by orinary ifferenial equaions wih inpus ha are piecewise consan. These piecewise consan inpus are upae perioically a he ecision insances by a conroller a inervals of. The oal operaing cos is calculae as a sum over an infinie ime horizon. Furhermore, he sum of coss is iscoune by he erm which is greaer han zero an less han or equal o one. The oal cos is calculae by an aiive funcion ha operaes on he insananeous sae an he conrol inpus. This cos may ae a form similar o 1 J x c x, u. (2) The oal cos in (2) is a funcion of he iniial sae of he sysem. To simplify noaion, le he sae a he ecision insances be represene by con x x. (3) Le he iscree ime samples occur a. (4) Furhermore, le he coninuous-ime insananeous cos, c con, in (2) be represene in iscree ime noaion as an aiive cos over an inerval, 1 c x, u c x, u. (5) con Using he noaion evelope in (2) hrough (5), he coninuous-ime sysem s oal cos is expresse in iscree ime noaion as J x c x, u. (6) To simplify he coninuous-ime ynamics, le f x, u f, u, x. (7) Hence, x 1 f x, u. (8) An opimal conrol choice for each ime sep can be foun using he ynamic programming equaions, * u x arg min c x, u V f x, u. (9) u U x The funcion V x is nown as he value funcion. By using he ynamic programming (DP) equaions o fin he value funcion, a minimizing conroller is obaine. The DP equaions are V x min c x, u V f x, u, (1) where u U x U x u g x, u (11) efines he se of feasible acions, U x. For he case where he oal cos is consiere over an infinie horizon an u u x (see eq (9)), he * value funcion is he same as he oal cos funcion, J x V x. Equaion (1) can be solve hrough value ieraion, policy ieraion, or linear programming. See [5-23] for iscussion of soluion mehos. For iscussion of using DP o fin value funcions for auomoive conrol applicaion, see [24-29]. The formulaion of equaion (11) is chosen o simplify managemen of consrains hroughou he moel an o conform o a sanar form use in he opimizaion communiy, he negaive null form [3]. One problem wih solving (1) is ha when he sae space consiss of coninuous saes, V x is a funcion from one infinie se o anoher. Excep in special cases, his requires approximaion o solve. One common approach is o use linear bases o approximae he value funcion. Possible linear bases inclue he bases for muli-linear inerpolaion, he bases for barycenric inerpolaion, b-splines, an polynomials. See he appenices in [25] for a iscussion of linear bases for ynamic programming. In he case where V x is approximae by a linear basis, The Moelica Associaion 494 Moelica 28, March 3 r 4 h, 28 2

3 Moel Embee Conrol: A Meho o Rapily Synhesize Conrollers in a Moeling Environmen where T V x x w, (12) x f1 x f2 x fn x. (13) An approximae soluion o (1) is foun by fining he weighs, w, which solve T T x w min c x, u f x, u w. (14) u U x See [5-7] for a iscussion of using linear bases o form he value funcion. I is imporan o unersan ha his conroller is an opimal conroller for he iscree ime case only, when he conroller upaes every secons. In oher uses, he conroller will generally be subopimal. Aiionally, any evelopmen algorihm base on his mehoology will suffer from he curse of imensionaliy [31]. In oher wors, he ime o fin an opimal conroller will increase geomerically wih he size of he plan sae space. As a poin of reference, using a single commercially available PC from 25, a five sae conroller was foun in less han weny four hours. 2 Conroller Developmen To use equaions (2) hrough (14) o evelop a conroller, i is necessary o have a plan moel which inclues he ynamics ( f ), cos funcion ( c ), an consrains ( g ) all couple o an inegraor which can be invoe as a funcion call by a Conrol Design Algorihm (CDA). In aiion, he se of saes for he plan moel an he se of conroller acions mus be specifie o he CDA. For his wor, a cusom wrapper was evelope ha allowe baches of saes an acions o be efficienly evaluae. Each evaluaion reurne he sae a he nex inerval, he cos of operaion for he inerval, an he consrain aciviy over he inerval. To unersan he srucure of he equaions involve in his wor, consier a sysem consising of a plan an a conroller. Wihou loss of generaliy, assume he plan ynamics are escribe by orinary ifferenial equaions x f x, u, (15) where f is a funcion ha escribes he plan ynamics. For noaional simpliciy consier a coninuous ime conroller. Le he conroller be a full sae feebac conroller implemene as a saic mapping, M, from he sae, x, o he acion se, u : u M x. (16) Assuming only a single global minimum exiss, he ynamic programming equaions in (9) can be irecly use for he saic mapping (16). The auonomous ynamics of his sysem are hen escribe by he following equaion x f x,arg min c x, u V f x, u (17) u U x This equaion is hen inegrae o solve for x, x c x s, u (18) f x s,arg min s u U x V f x s, u where x x (19) efines he iniial coniions. To evaluae f from (7), a nese inegraor, which is inepenen of he primary simulaion inegraor, is require. This nese inegraor execues in zero-ime from he perspecive of he primary inegraor. We refer o his as an embee or nese simulaion. Because he nese inegraor is use insie a numeric opimizaion, i will poenially be calle muliple imes a each primary inegraor evaluaion. If f in (18) is expane using (7), he plan ynamics funcion, f, from (15) occurs in wo locaions in x c x s, u f x s,arg min s u U x V f, u, x s where (2) x x (21) The nese copy of he plan ynamics equaions, f, is referre o as he embee or nese moel. In he case where he conroller is moele as upaing perioically, raher han coninuously, he soluion o he opimizaion problem is hel consan beween conroller upaes. The equaion srucure in (2) an he reuse of he plan ynamics funcion, f, offer he abiliy o quicly synhesize conrollers using numerical echniques. However, exising ools mae he implemenaion of his ype of moel problemaic. There are wo primary issues in implemenaion. The firs is execuion efficiency. Few commercial ools have been evelope wih he goal of efficienly solving his class of equaions. Seconly, several The Moelica Associaion 495 Moelica 28, March 3 r 4 h, 28 3

4 E. Tae, M. Sasena, J. Gohl, M. Tiller commercial moeling environmens mae he efiniion an reuse of he plan moel cumbersome, requiring significan effors uring evelopmen an mainenance. Forunaely, he feaures of Moelica mae he efiniion an reuse of a plan moel manageable. The examples ha follow have been evelope in Dymola, however his general approach has also been use wih Simulin an AMESim. To sysemaically generae a sysem wih an opimal conroller, a moel of he plan is generae. This plan moel is wrappe wih an applicaion programming inerface (API) so a conrol esign algorihm can eermine he sae space, he acion space, he sae a he nex ime sep, he consrain aciviy, an he cos for a given sae an acion. This ineracion beween he plan moel, he API an he conrol esign algorihm is illusrae in Figure 1. The CDA queries he API o eermine he srucure of he sae an acion space. Given his srucure an he configuraion of he CDA, a sequence of DOEs is execue. The DOE aa are use o fin a soluion o (1). For his wor, he value funcion was moele using muli-linear inerpolaion an a soluion o (14) was foun. To simplify coing, value ieraion was use [5, 6] o fin V x. Conrol Design Algorihm (CDA) V x Sae Space Acion Space x,u f x, u g x, u c x, u Figure 1 - Plan Moel API API o expose funcions Plan Moel Once he value funcion is generae, he sysem moel is forme by one of wo mehos. The firs meho is by generaing a looup able ha maps he sae variables o an acion as in (16). The process of generaing a value funcion, fining a mapping equivalen o (9), an realizing a conroller as a mapping (or looup able) is referre o as Inirec Moel Embee Conrol (IMEC). This meho is appropriae for some sysems. Anoher approach, which is more compuaionally expensive, is referre o as Direc Moel Embee Conrol (DMEC). For DMEC, he conroller is realize by forming an opimizaion saemen aroun an embee copy of he plan moel. This srucure is illusrae in Figure 2. x x, uˆ x, uˆ g x, uˆ f Conroller Opimizer API o expose funcions Embee Plan Moel c x, uˆ * u Plan Moel Figure 2 - Direc Moel Embee Conroller Srucure To realize a Direc Moel Embee Conroller (DMEC), wo pieces are ae o he sysem moel. The firs piece is an opimizer which solves (9). This opimizer can be as simple as a Design of Experimens (DOEs) which consiers a fixe se of acions, an selecs one which minimizes (9). For more sophisicaion, if he naure of he problem permis i, a graien-base opimizer can be employe [3, 32, 33]. If he naure of he problem oes no allow soluion using hese ypes of approaches, global solvers can be use [34-36]. Ieally, an opimizaion library shoul suppor boh graien an non-graien mehos for consraine opimizaion problems. As par of his projec, libraries for performing boh DOEs an graien-base opimizaions were implemene enirely in Moelica. However, here are currenly no comparable commercial or public omain libraries available. The secon piece require o implemen a DMEC is he abiliy o invoe a funcion which efficienly iniializes an simulaes, over a shor ime horizon, a se of moels which are copies of he plan moel wih moifie parameers. Because of he srucure of he problem, each ime he conroller execues, muliple embee simulaions will execue. Depening on he naure of he acion se, he number of embee simulaions may vary from as few as wo embee simulaions o several housan embee simulaions. 3 Example Simple Engine Sar To illusrae how hese conceps are use o buil a conroller, consier he problem of saring an inernal combusion engine using an elecric machine The Moelica Associaion 496 Moelica 28, March 3 r 4 h, 28 4

5 Moel Embee Conrol: A Meho o Rapily Synhesize Conrollers in a Moeling Environmen wih insufficien orque o guaranee he engine complees a revoluion from all possible saionary saring poins. If he iniial posiion of he engine is in a range of angles, he elecric machine will sall. To simplify he moeling, le us assume he engine can be approximae using a cran slier connece o a spring. The sysem moel, shown in Figure 3, consiss of an elecrical moor connece o he cran which connecs hrough he cran slier mechanism o a pison which is subjec o amping from fricion. Ineria is presen in he moor roor, cranshaf an pison. The elecric machine is subjec o consrains on minimum an maximum orque. Figure 3 - Engine Saring Moel The objecive of he conrol sysem is o ensure he engine will overcome he iniial compression orque from any iniial sae an minimize engine sar ime. The oal cos of operaion (wha is being minimize) is expresse mahemaically as he oal ime aen o achieve a spee greaer han or equal o five hunre RPM. Once his spee is achieve, he conroller is eacivae an anoher scheme is use o manage he engine. The oal cos of operaion for his sysem is consiere over an infinie ime horizon an is compue as, 5 rpm J x. (22) 1,oherwise The insananeous cos for his sysem is, 5 rpm c x. (23) 1,oherwise This ype of cos generaes a shores-pah conroller. The conroller will minimize he oal ime o achieve 5 rpm. The oal cos in (22) is uniscoune. Therefore he iscouning facor,, which is visible in (2) is assigne a value of one an omie from he expression. While i is clear ha he sysem has exacly wo saes, hey can be selece somewha arbirarily. For his example, he engine angle an engine spee were selece. Wih hese variables as he saes, he conroller is represene as a saic map from he engine angle an engine spee o he elecric machine orque. u M, (24) The feasible acion se is a single real number, he moor orque, boune by he consrains on moor orque an power. The se of feasible acions is efine by U x u 1 u 1, 1 u 1. (25) The value funcion was represene using mulilinear inerpolaion, see equaion (12). The plan moel was implemene in Moelica. The Conroller Design Algorihm (CDA) was implemene in MATLAB. The CDA invoe funcion calls o a cusom API, similar o Figure 1, applie o he plan moel in Dymola. The CDA solve for he weighs, w, in he value funcion (equaion (12)). This value funcion was use o generae an Inirec Moel Embee Conroller (IMEC) an a Direc Moel Embee Conroller (DMEC). The value funcion generae by he CDA is shown in Figure Engine Spee [rpm] Value funcion Figure 4 - Value funcion Engine Angle [eg] The IMEC was realize as a wo inpu looup able wih muli-linear inerpolaion on a regular gri. The gri poins in he able were foun by solving (9) using he value funcion generae by he CDA. This conroller was implemene using The Moelica Associaion 497 Moelica 28, March 3 r 4 h, 28 5

6 E. Tae, M. Sasena, J. Gohl, M. Tiller sanar Moelica componens. The acuaor commans for he IMEC conroller are shown in Figure 5 as a funcion of engine spee an angle Bes Conrol Choice - u* Engine Spee [rpm] Figure 5 - IMEC conrol able Engine Angle [eg] The DMEC was realize by wrapping a copy of he plan moel wih an API similar o he one use for he CDA. A DOE was use o search feasible acions. The resuling coe srucure is ienical o Figure 2. The opimal acion was chosen o minimize (9). For boh of hese conrollers, he problem of saring he engine from any iniial coniion was solve. The soluion involve he couner-inuiive approach of spinning he engine bacwars, hen reversing irecion o allow enough energy o be sore in he ineria o overcome he spring force. From a moel an a conrol objecive, an opimal conroller wih very complex behaviors was numerically generae in less han 1 minues on a single PC (3GHz, 2Gb RAM). Furhermore, a similar problem wih four saes was solve in less han hree hours. Of course he power of his approach can only be realize once a sufficien level of ool suppor is available so ha he ime require o se up he analysis is on he same orer as he soluion ime. Conrol Design Algorihm (CDA). The IMEC conroller was esigne by solving for he bes elecric machine orque for a se of engine angles an spees on a regular gri. For engine saes which occur off his gri, muli-linear inerpolaion was use o calculae he conrol acion. When he IMEC was use in an engine sar simulaion, if he opimal orque ransiione beween posiive an negaive, he inerpolaion cause a smooh change in he orque because of he coninuiy impose by inerpolaion. Alernaively, consier a Direc MEC. Because of he characerisics of he ynamic programming equaions an he value funcion, he opimal choices are eiher full posiive or full negaive orque. This resuls in an insananeous, nonconinuous change in orque. When ploe as in Figure 6, he ifference beween he conrol inpus an he sae evoluion of he sysem can be seen. The inerpolaion ue o he approximaion in he IMEC resuls in arifacs in he conrol acions an a sligh loss of performance in he sysem. Mahemaically his means ha more eail is require o resolve u * x, he funcion ha we are ulimaely rying o formulae, han o resolve V x. There are cases where an IMEC is superior o a DMEC approach (e.g. [26] illusraes jus such a case). In general, an IMEC implemenaion is superior when boh he acion se is coninuous an he opimal acions are coninuous. The DMEC approach is superior when eiher he acion se is iscree or he opimal acions are no coninuous wih respec o he sae. One example where DMEC is clearly superior is where he moor is conrolle by selecing he sae of a swich inverer. In his case, he acion se consiss of a finie se of choices for swich configuraion an he opimal acions are no coninuous wih respec o he sae. 3.1 Direc vs Inirec MEC Ieally, boh an IMEC an DMEC will resul in ienical behaviors. However, ifferences in approximaion schemes an inerpolaion can resuls in appreciable ifferences. In many cases, while Inirec MEC is simpler o realize in a moel, here are goo reasons o implemen a conroller wih he complexiy an compuaional cos of a Direc MEC. As an example, consier he previous problem. The value funcion, V(x), was foun using he Figure 6 - Comparison of IMEC an DMEC resuls The Moelica Associaion 498 Moelica 28, March 3 r 4 h, 28 6

7 Moel Embee Conrol: A Meho o Rapily Synhesize Conrollers in a Moeling Environmen 4 Implemenaion of opimizaion algorihms One of he challenges in Direc Moel Embee Conrol is he implemenaion of an opimizer. While his wor was performe using a Design of Experimens (DOE) o selec opimal acions, his approach becomes inracable when equaliy consrains an larger imensional acions ses are consiere. Towars he goal of supporing hese classes of problems, a graien-base opimizer was evelope. One of he goals in eveloping his opimizer was o fully implemen he opimizer in Moelica. By fully implemening in Moelica, all of he informaion use by he opimizer woul be accessible for spee improvemens by he compiler. Shoul naive suppor for moel embeing become available, all equaions associae wih a Direc MEC woul be accessible o he compiler for spee improvemen. Aiionally, since he embee simulaions in a DMEC can be compleely ecouple from each oher, simulaion ools coul easily exploi he coarse graine parallelism on muli-core CPUs by running several embee simulaions concurrenly when conucing searches in he opimizer (e.g. line searches an numerical graiens). The opimizer was evelope in Moelica o solve a consraine opimizaion problem which is generally sae in negaive null form [3] as min f s.. g h objecive inequaliies equaliies. (26) To implemen a graien opimizer, he opimizer funcionaliy was separae from he objecive funcion ( f objecive ), he inequaliy consrain funcions ( g inequaliies ), an he equaliy consrain funcions ( h equaliies ). The opimizer was esigne uner he assumpion ha he inequaliy consrain funcions are all in negaive null form: feasible inequaliy consrains are less han or equal o zero. The objecive funcion was assume o be a minimizaion objecive. Since Moelica oes no (ye) suppor he concep of mehos or passing of funcions as argumens, he opimizer was esigne o use saic inheriance. For his reason, he objecive an consrain funcions are replaceable funcions wihin an opimizer pacage. One feaure of his library, ha is no commonly available, is he abiliy o hanle funcions which are unefine over some region. The omain of he objecive an consrains may no be nown a priori. This occurs wih MEC applicaions because he objecive (e.g. equaion (9)) an consrain funcions (e.g. equaion (11)) are ypically evaluae using a solver. The solver may no fin a soluion. Hence, classical algorihms mus be moifie o recover from unefine evaluaions. Implemenaion of his capabiliy was problemaic because of he lac of numeric suppor for a real value which represens he concep of an unefine quaniy. Eiher a naive capabiliy similar o Malab s NaN, or operaor overloaing wih he abiliy o exen a class from real numbers woul have simplifie implemenaion. In his library, Moelica.Consans.inf was use o inicae ha a funcion call was unefine. However, he language specificaion oes no efine behavior for operaions (e.g. aiion, subracion, muliplicaion, ivision) on Moelica.Consans.inf. Therefore, all funcions an saemens which operae on variables ha migh be assigne a value of Moelica.Consans.inf require coniional expressions o ensure expece behavior. While his opimizaion library will no be publicly release, i is available for furher evelopmen. Conac he lea auhor for a copy. 5 Recommenaions While i is possible o realize boh IMEC an DMEC conrollers using Moelica 2.2, he aiion of a sanar opimizaion library an naive suppor for embee moel simulaion woul vasly simplify implemenaion an mainenance. Towars he goal of simplifying implemenaion of MEC, a recommene language improvemen is he aiion of a moel simulae funcion. The funcion woul accep argumens ha specify he moel o simulae, he parameer values o use in each simulaion, he oupus o reurn, an any solver specific seings. The solver shoul be able o be configure o solve boh iniializaion problems an simulaion problems. For efficiency in evaluaion, he funcion shoul suppor boh a scalar an vecor liss of parameers. In aiion o resuls which are associae wih he moel, here shoul be resuls associae wih he solver. These resuls shoul be sufficien o iagnose solver failures. A a minimum, hese shoul inclue he final ime in he evaluaion an an inicaion of wheher he simulaion successfully complee. A sample funcion efi- The Moelica Associaion 499 Moelica 28, March 3 r 4 h, 28 7

8 E. Tae, M. Sasena, J. Gohl, M. Tiller niion along wih an example invocaion are shown in Figure 7. funcion simulaemoel inpu Sring moelname; inpu Sring paramnames[:]; inpu Sring resulnames[:]; inpu Real paramvalues[:,size(paramnames,1)]; inpu SeingsRecor solverseings; oupu Real resuls[size(paramvalues,1), en simulaemoel; // example call size(resulnames,1)]; [angle, spee, exiconiion, exitime] = simulaemoel( moelname= Library.PlanMoel, paramnames{ w, hea, u }, resulnames= { w, hea, exiconiion, exitime }, paramvalues= [,, -1; 1,, -1; ; 2, 2*pi, 1], solverseings = ); SeingsRecor( soptime=1., fixesep=.1) Figure 7 - Moel evaluaion I is imporan o poin ou ha he goal is o be able o invoe such a funcion from wihin a running moel an no simply as a comman line analysis opion. As previously menione, he abiliy o irecly express such nese simulaion relaionships maes posing MEC problems much easier. If he MEC problem coul also irecly express he opimizaion problem associae wih MEC hen ools coul also bring he unerlying symbolic informaion o bear on efficien graien evaluaion as well. One remaining issue for DMEC problems is he iniializaion of sae variables in he embee moel. For DMEC problems we ypically wan he embee moel o sar a he curren sae of he paren simulaion. Sai anoher way, he curren values of he saes in he paren simulaion shoul be use as iniial coniions in he nese simulaion. Of course, i is possible using he funcion in Figure 7 o esablish such a mapping bu hopefully he language esign group will consier alernaives ha woul be less eious an error prone. 6 Conclusions I is racable o numerically synhesize near opimal (or approximaely minimal) conrollers for many sysems. While in mos cases he sae feebac require for he conrollers may mae hem impracical o eploy, hey can cerainly be use as prooype conrollers ha esablish performance limis for a given esign as well as provie insighs ino conrol laws for proucion conrollers. Furhermore, his approach can easily inegrae ino a combine plan-conroller opimizaion process. This can be one by maing he opimal conroller a funcion of he plan parameers. These opimal conrollers can be realize as looup ables (IMEC) or hrough he use of opimizaion an embee moels (DMEC). An algorihmic approach o conrols synhesis was presene. For his paper, he IMEC an DMEC approaches were applie o an engine saring problem o generae an opimal conroller in an auomae fashion. As his wor has shown, Moelica is a promising echnology for rapi prooyping of subsysem esigns an prooype conrollers. However, lac of suppor for moel embeing maes evelopmen an long erm mainenance problemaic because consierable wor mus be one o implemen his embeing. Lacing any language sanar, his wor will always be ool specific. Furhermore, implemenaion of conrollers which rely on opimizaion suffer from he lac of a sanar opimizaion library. While an opimizaion library was evelope for his wor, i isn pracical for mos users o mae such an invesmen. By aing boh language suppor o express he essenial aspecs of moel embeing an opimizaion iscusse in his paper, Moelica can evolve ino a powerful echnology for sysem evelopmen an opimizaion. References [1] H. K. Fahy,"Combine Plan an Conrol Opimaion: Theory, Sraegies, an Applicaions," Mechanical Engineering, Universiy of Michigan, Ann Arbor, 23. The Moelica Associaion 5 Moelica 28, March 3 r 4 h, 288

9 Moel Embee Conrol: A Meho o Rapily Synhesize Conrollers in a Moeling Environmen [2] H. K. Fahy, P. Y. Papalambros, A. G. Ulsoy, an D. Hrova, "Nese Plan/Conroller Opimizaion wih Applicaion o Combine Passive/Acive Auomoive Suspensions." [3] H. K. Fahy, J. A. Reyer, P. Y. Papalambros, an A. G. Ulsoy, "On he Coupling beween he Plan an Conroller Opimizaion Problems," in American Conrol Conference, Arlingon, Va, 21. [4] P. R. Kumar an P. Variaya, Sochasic Sysems: Esimaion, Ienificaion an Aapion. Englewoo Cliffs, New Jersey: Prenice Hall, [5] D. Berseas, Dynamic Programming an Opimal Conrol: Vol 2. Belmon, Mass: Ahena Scienific, [6] D. P. Berseas, Dynamic Programming an Opimal Conrol: Vol 1. Belmon, Mass: Ahena Scienific, [7] D. P. Berseas an J. N. Tsisilis, Neuro- Dynamic Programming. Belmon, Mass: Ahena Scienific, [8] M. A. Tric an S. E. Zin, "A Linear Programming Approach o Solving Sochasic Dynamic Programs," Carnegie Mellon Universiy [9] M. A. Tric an S. E. Zin, "Spline Approximaions o Value Funcions: A Linear Programming Approach," Macroeconomic Dynamics, pp , [1] D. P. e Farias an B. Van Roy, "The Linear Programming Approach o Approximae Dynamic Programming," Operaions Research, vol. 51, pp , November- December 23. [11] V. F. Farias an B. Van Roy, "Teris: Experimens wih he LP Approach o Approximae DP," 24. [12] D. P. e Farias,"The Linear Programming Approach o Approximae Dynamic Programming: Theory an Applicaion," Ph.D. Disseraion, Deparmen of Managemen Science an Engineering, Sanfor Universiy, Palo Alo, Ca, 22. [13] D. Dolgov an K. Labereaux, "Efficien Linear Approximaions o Sochasic Vehicular Collision-Avoiance Problems," in Proceeings of he Secon Inernaional Conference on Informaics in Conrol, Auomaion, an Roboics (ICINCO-5), 25. [14] G. J. Goron, "Sable Funcion Approximaion in Dynamic Programming," January [15] R. S. Suon an A. G. Baro, Reinforcemen Learning: An Inroucion. Cambrige, Mass: MIT Press, [16] R. Munos an A. Moore, "Barycenric Inerpolaors for Coninuous Space an Time Reinforcemen Learning," Avances in Neural Informaion Processing Sysems, vol. 11, pp , [17] R. Munos an A. Moore, "Variable Resoluion Discreizaion in Opimal Conrol," Machine Learning, vol. 1, pp. 1-24, [18] J. M. Lee an J. H. Lee, "Approximae Dynamic Programming Sraegies an Their Applicabiliy for Process Conrol: A Review an Fuure Direcions," Inernaional Journal of Conrol, Auomaion, an Sysems, vol. 2, pp , Sepember 24. [19] D. P. e Farias an B. Van Roy, "Approximae Value Ieraion wih Ranomize Policies," in 39h IEEE Conference on Decision an Conrol Suney, Ausralia, 2. [2] D. P. e Farias an B. Van Roy, "Approximae Value Ieraion an Temporal- Difference Learning," in IEEE 2 Aapive Sysems for Signal Processing, Communicaions an Conrol Symposium, 2, pp [21] B. Van Roy an J. N. Tsisilis, "Sable Linear Approximaions o Dynamic Programming for Sochasic Conrol Problems wih Local Transiions," Avances in Neural Informaion Processing Sysems, vol. 8, [22] P. W. Keller, S. Mannor, an D. Precup, "Auomaic Basis Funcion Consrucion for Approximae Dynamic Programming an Reinforcemen Learning." [23] V. C. P. Chen, D. Rupper, an C. A. Shoemaer, "Applying Experimenal Design an Regression Splines o High Dimensional Coninuous Sae Sochasic Dynamic Programming," Operaions Research, vol. 47, pp , January-February [24] C.-C. Lin, H. Peng, an J. W. Grizzle, "A Sochasic Conrol Sraegy for Hybri Elecric Vehicles," in Proceeings of he 24 American Conrol Conference, 24, pp vol. 5. [25] E. D. Tae,"Techniques of Hybri Elecic Vehicle Conroller Synhesis," Elecrical Engineering: Sysems, Universiy of Michigan, Ann Arbor, Michigan, 27. [26] E. Tae, J. Grizzle, an H. Peng, "Shores Pah Sochasic Conrol for Hybri Elecric Vehicles," Inernaion Journal of Robus an Nonlinear Conrol, 26. The Moelica Associaion 51 Moelica 28, March 3 r 4 h, 28 9

10 E. Tae, M. Sasena, J. Gohl, M. Tiller [27] I. Kolmanovsy, I. Siverguina, an B. Lygoe, "Opimizaion of Powerrain Operaing Policy for Feasibiliy Assessmen an Calibraion: Sochasic Dynamic Programming Approach," in Proceeings of he American Conrol Conference, Anchorage, AK, 22, pp [28] J.-M. Kang, I. Kolmanovsy, an J. W. Grizzle, "Approximae Dynamic Programming Soluions for Lean Burn Engine Aferreamen," in Proceeings of he 38h Conference on Decision & Conrol, Phoenix, Arizona, 1999, pp [29] C.-C. Lin, H. Peng, J. W. Grizzle, an J.-M. Kang, "Power Managemen Sraegy for a Parallel Hybri Elecric Truc," IEEE Transacions on Conrol Sysems Technology, vol. 11, pp , November 23. [3] P. Y. Papalambros an D. J. Wile, Principles of Opimal Design: Moels an Compuaion, 2 e. New Yor, New Yor: Cambrige Universiy Press, 2. [31] J. Rus, "Using Ranomizaion o Brea he Curse of Dimensionaliy," [32] S. Boy an L. Venenberghe, Convex Opimizaion. New Yor, N.Y.: Cambrige Universiy Press, 24. [33] P. E. Gill, W. Murray, an M. H. Wrigh, Pracical Opimizaion. New Yor, N.Y.: Acaemic Press, [34] D. R. Jones, C. D. Periunen, an B. E. Sucman, "Lipschizian Opimizaion wihou he Lipschiz Consan," Journal of Opimizaion Theory an Applicaions, vol. 79, pp , [35] A. J. Booer, J. Dennis, J. E., P. D. Fran, D. B. Serafini, V. Torczon, an M. W. Trosse, "A Rigorous Framewor for Opimizaion of Expensive Funcions by Surrogaes." [36] M. J. Sasena,"Flexibiliy an Efficiency Enhancemens for Consraine Global Design Opimizaion wih Kriging Approximaions," Mechanical Engineering, Universiy of Michigan, Ann Arbor, 22. The Moelica Associaion 52 Moelica 28, March 3 r 4 h, 28 1

Stock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783

Stock Trading with Recurrent Reinforcement Learning (RRL) CS229 Application Project Gabriel Molina, SUID 5055783 Sock raing wih Recurren Reinforcemen Learning (RRL) CS9 Applicaion Projec Gabriel Molina, SUID 555783 I. INRODUCION One relaively new approach o financial raing is o use machine learning algorihms o preic

More information

Performance Center Overview. Performance Center Overview 1

Performance Center Overview. Performance Center Overview 1 Performance Cener Overview Performance Cener Overview 1 ODJFS Performance Cener ce Cener New Performance Cener Model Performance Cener Projec Meeings Performance Cener Execuive Meeings Performance Cener

More information

Multiprocessor Systems-on-Chips

Multiprocessor Systems-on-Chips Par of: Muliprocessor Sysems-on-Chips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,

More information

Distributing Human Resources among Software Development Projects 1

Distributing Human Resources among Software Development Projects 1 Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources

More information

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary

Random Walk in 1-D. 3 possible paths x vs n. -5 For our random walk, we assume the probabilities p,q do not depend on time (n) - stationary Random Walk in -D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes

More information

Task is a schedulable entity, i.e., a thread

Task is a schedulable entity, i.e., a thread Real-Time Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T: - s: saring poin - e: processing ime of T - d: deadline of T - p: period of T Periodic ask T

More information

The Application of Multi Shifts and Break Windows in Employees Scheduling

The Application of Multi Shifts and Break Windows in Employees Scheduling The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance

More information

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1

Single-machine Scheduling with Periodic Maintenance and both Preemptive and. Non-preemptive jobs in Remanufacturing System 1 Absrac number: 05-0407 Single-machine Scheduling wih Periodic Mainenance and boh Preempive and Non-preempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy

More information

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE

PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees

More information

Chapter 1.6 Financial Management

Chapter 1.6 Financial Management Chaper 1.6 Financial Managemen Par I: Objecive ype quesions and answers 1. Simple pay back period is equal o: a) Raio of Firs cos/ne yearly savings b) Raio of Annual gross cash flow/capial cos n c) = (1

More information

Chapter 7. Response of First-Order RL and RC Circuits

Chapter 7. Response of First-Order RL and RC Circuits Chaper 7. esponse of Firs-Order L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural

More information

Analysis of Non-Stationary Time Series using Wavelet Decomposition

Analysis of Non-Stationary Time Series using Wavelet Decomposition Naure an Science ;8() Analysis of Non-Saionary Time Series using Wavele Decomposiion Lineesh M C *, C Jessy John Deparmen of Mahemaics, Naional Insiue of Technology Calicu, NIT Campus P O 673 6, Calicu,

More information

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS

ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,

More information

Strategic Optimization of a Transportation Distribution Network

Strategic Optimization of a Transportation Distribution Network Sraegic Opimizaion of a Transporaion Disribuion Nework K. John Sophabmixay, Sco J. Mason, Manuel D. Rossei Deparmen of Indusrial Engineering Universiy of Arkansas 4207 Bell Engineering Cener Fayeeville,

More information

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)

cooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins) Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer

More information

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar

Analogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 0-7-380-7 Ifeachor

More information

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS

TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.

More information

Quality Assurance in Software Development

Quality Assurance in Software Development Insiue for Sofware Technology Qualiy Assurance in Sofware Developmen Qualiässicherung in der Sofwareenwicklung A.o.Univ.-Prof. Dipl.-Ing. Dr. Bernhard Aichernig Insiue for Sofware Technology Graz Universiy

More information

DC-DC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System

DC-DC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System DC-DC Boos Converer wih Consan Oupu Volage for Grid Conneced Phoovolaic Applicaion Sysem Pui-Weng Chan, Syafrudin Masri Universii Sains Malaysia E-mail: edmond_chan85@homail.com, syaf@eng.usm.my Absrac

More information

TOOL OUTSOURCING RISK RESEARCH BASED ON BP NEURAL NETWORK

TOOL OUTSOURCING RISK RESEARCH BASED ON BP NEURAL NETWORK Inernaional Journal of Innovaive Managemen, Informaion & Producion ISME Inernaionalc2011 ISSN 2185-5439 Volume 2, Number 1, June 2011 PP. 57-67 TOOL OUTSOURCING RISK RESEARCH BASED ON BP NEURAL NETWORK

More information

Option Put-Call Parity Relations When the Underlying Security Pays Dividends

Option Put-Call Parity Relations When the Underlying Security Pays Dividends Inernaional Journal of Business and conomics, 26, Vol. 5, No. 3, 225-23 Opion Pu-all Pariy Relaions When he Underlying Securiy Pays Dividends Weiyu Guo Deparmen of Finance, Universiy of Nebraska Omaha,

More information

SKF Documented Solutions

SKF Documented Solutions SKF Documened Soluions Real world savings and we can prove i! How much can SKF save you? Le s do he numbers. The SKF Documened Soluions Program SKF is probably no he firs of your supplier parners o alk

More information

policies are investigated through the entire product life cycle of a remanufacturable product. Benefiting from the MDP analysis, the optimal or

policies are investigated through the entire product life cycle of a remanufacturable product. Benefiting from the MDP analysis, the optimal or ABSTRACT AHISKA, SEMRA SEBNEM. Invenory Opimizaion in a One Produc Recoverable Manufacuring Sysem. (Under he direcion of Dr. Russell E. King and Dr. Thom J. Hodgson.) Environmenal regulaions or he necessiy

More information

Small Menu Costs and Large Business Cycles: An Extension of Mankiw Model *

Small Menu Costs and Large Business Cycles: An Extension of Mankiw Model * Small enu Coss an Large Business Ccles: An Exension of ankiw oel * Hirana K Nah Deparmen of Economics an Inl. Business Sam Houson Sae Universi an ober Srecher Deparmen of General Business an Finance Sam

More information

Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds

Inventory Planning with Forecast Updates: Approximate Solutions and Cost Error Bounds OPERATIONS RESEARCH Vol. 54, No. 6, November December 2006, pp. 1079 1097 issn 0030-364X eissn 1526-5463 06 5406 1079 informs doi 10.1287/opre.1060.0338 2006 INFORMS Invenory Planning wih Forecas Updaes:

More information

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR

MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry

More information

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES

USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were

More information

CHARGE AND DISCHARGE OF A CAPACITOR

CHARGE AND DISCHARGE OF A CAPACITOR REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:

More information

B-Splines and NURBS Week 5, Lecture 9

B-Splines and NURBS Week 5, Lecture 9 CS 430/536 Compuer Graphics I B-Splines an NURBS Wee 5, Lecure 9 Davi Breen, William Regli an Maxim Peysahov Geomeric an Inelligen Compuing Laboraory Deparmen of Compuer Science Drexel Universiy hp://gicl.cs.rexel.eu

More information

PRECISE positioning/tracking control is being studied

PRECISE positioning/tracking control is being studied Design of High Accuracy Tracking Sysems wih H Preview Conrol Anonio Moran Cardenas, Javier G. Rázuri, Isis Bone, Rahim Rahmani, and David Sundgren Absrac Posiioning and racking conrol sysems are an imporan

More information

1.2 Goals for Animation Control

1.2 Goals for Animation Control A Direc Manipulaion Inerface for 3D Compuer Animaion Sco Sona Snibbe y Brown Universiy Deparmen of Compuer Science Providence, RI 02912, USA Absrac We presen a new se of inerface echniques for visualizing

More information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur Module 4 Single-phase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,

More information

RC, RL and RLC circuits

RC, RL and RLC circuits Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.

More information

Evolutionary building of stock trading experts in real-time systems

Evolutionary building of stock trading experts in real-time systems Evoluionary building of sock rading expers in real-ime sysems Jerzy J. Korczak Universié Louis Paseur Srasbourg, France Email: jjk@dp-info.u-srasbg.fr Absrac: This paper addresses he problem of consrucing

More information

Stochastic Optimal Control Problem for Life Insurance

Stochastic Optimal Control Problem for Life Insurance Sochasic Opimal Conrol Problem for Life Insurance s. Basukh 1, D. Nyamsuren 2 1 Deparmen of Economics and Economerics, Insiue of Finance and Economics, Ulaanbaaar, Mongolia 2 School of Mahemaics, Mongolian

More information

A Distributed Multiple-Target Identity Management Algorithm in Sensor Networks

A Distributed Multiple-Target Identity Management Algorithm in Sensor Networks A Disribued Muliple-Targe Ideniy Managemen Algorihm in Sensor Neworks Inseok Hwang, Kaushik Roy, Hamsa Balakrishnan, and Claire Tomlin Dep. of Aeronauics and Asronauics, Sanford Universiy, CA 94305 Elecrical

More information

Graduate Macro Theory II: Notes on Neoclassical Growth Model

Graduate Macro Theory II: Notes on Neoclassical Growth Model Graduae Macro Theory II: Noes on Neoclassical Growh Model Eric Sims Universiy of Nore Dame Spring 2011 1 Basic Neoclassical Growh Model The economy is populaed by a large number of infiniely lived agens.

More information

INCREASING RESPONSIBILITY TO CUSTOMERS THROUGH A DYNAMIC QUALITY ASSURANCE SYSTEM IN SOFTWARE DEVELOPMENT

INCREASING RESPONSIBILITY TO CUSTOMERS THROUGH A DYNAMIC QUALITY ASSURANCE SYSTEM IN SOFTWARE DEVELOPMENT AE Increasing Responsibiliy o Cusomers hrough a ynamic Qualiy Assurance Sysem in Sofware evelopmen ICREASIG RESOSIBILIY O CUSOMERS HROUGH A YAMIC QUALIY ASSURACE SYSEM I SOFWARE EVELOME Căălin Afrăsinei-Zevoianu

More information

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS

DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS DYNAMIC MODELS FOR VALUATION OF WRONGFUL DEATH PAYMENTS Hong Mao, Shanghai Second Polyechnic Universiy Krzyszof M. Osaszewski, Illinois Sae Universiy Youyu Zhang, Fudan Universiy ABSTRACT Liigaion, exper

More information

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS

SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS SELF-EVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD-20742 {wh2003, qinfen}@cfar.umd.edu

More information

Present Value Methodology

Present Value Methodology Presen Value Mehodology Econ 422 Invesmen, Capial & Finance Universiy of Washingon Eric Zivo Las updaed: April 11, 2010 Presen Value Concep Wealh in Fisher Model: W = Y 0 + Y 1 /(1+r) The consumer/producer

More information

Dynamic programming models and algorithms for the mutual fund cash balance problem

Dynamic programming models and algorithms for the mutual fund cash balance problem Submied o Managemen Science manuscrip Dynamic programming models and algorihms for he muual fund cash balance problem Juliana Nascimeno Deparmen of Operaions Research and Financial Engineering, Princeon

More information

PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM

PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM PATHWISE PROPERTIES AND PERFORMANCE BOUNDS FOR A PERISHABLE INVENTORY SYSTEM WILLIAM L. COOPER Deparmen of Mechanical Engineering, Universiy of Minnesoa, 111 Church Sree S.E., Minneapolis, MN 55455 billcoop@me.umn.edu

More information

Research on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment

Research on Inventory Sharing and Pricing Strategy of Multichannel Retailer with Channel Preference in Internet Environment Vol. 7, No. 6 (04), pp. 365-374 hp://dx.doi.org/0.457/ijhi.04.7.6.3 Research on Invenory Sharing and Pricing Sraegy of Mulichannel Reailer wih Channel Preference in Inerne Environmen Hanzong Li College

More information

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand

Market Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand 36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,

More information

Market Analysis and Models of Investment. Product Development and Whole Life Cycle Costing

Market Analysis and Models of Investment. Product Development and Whole Life Cycle Costing The Universiy of Liverpool School of Archiecure and Building Engineering WINDS PROJECT COURSE SYNTHESIS SECTION 3 UNIT 11 Marke Analysis and Models of Invesmen. Produc Developmen and Whole Life Cycle Cosing

More information

The Transport Equation

The Transport Equation The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be

More information

RC Circuit and Time Constant

RC Circuit and Time Constant ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisor-capacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he

More information

Real-time Particle Filters

Real-time Particle Filters Real-ime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 ckwok,fox @cs.washingon.edu, mmp@sa.washingon.edu Absrac

More information

Chabot College Physics Lab RC Circuits Scott Hildreth

Chabot College Physics Lab RC Circuits Scott Hildreth Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard

More information

THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS

THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS VII. THE FIRM'S INVESTMENT DECISION UNDER CERTAINTY: CAPITAL BUDGETING AND RANKING OF NEW INVESTMENT PROJECTS The mos imporan decisions for a firm's managemen are is invesmen decisions. While i is surely

More information

Individual Health Insurance April 30, 2008 Pages 167-170

Individual Health Insurance April 30, 2008 Pages 167-170 Individual Healh Insurance April 30, 2008 Pages 167-170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve

More information

Distributed Echo Cancellation in Multimedia Conferencing System

Distributed Echo Cancellation in Multimedia Conferencing System Disribued Echo Cancellaion in Mulimedia Conferencing Sysem Balan Sinniah 1, Sureswaran Ramadass 2 1 KDU College Sdn.Bhd, A Paramoun Corporaion Company, 32, Jalan Anson, 10400 Penang, Malaysia. sbalan@kdupg.edu.my

More information

Chapter 8: Regression with Lagged Explanatory Variables

Chapter 8: Regression with Lagged Explanatory Variables Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One

More information

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results:

GoRA. For more information on genetics and on Rheumatoid Arthritis: Genetics of Rheumatoid Arthritis. Published work referred to in the results: For more informaion on geneics and on Rheumaoid Arhriis: Published work referred o in he resuls: The geneics revoluion and he assaul on rheumaoid arhriis. A review by Michael Seldin, Crisopher Amos, Ryk

More information

Stochastic Recruitment: A Limited-Feedback Control Policy for Large Ensemble Systems

Stochastic Recruitment: A Limited-Feedback Control Policy for Large Ensemble Systems Sochasic Recruimen: A Limied-Feedback Conrol Policy for Large Ensemble Sysems Lael Odhner and Harry Asada Absrac This paper is abou sochasic recruimen, a conrol archiecure for cenrally conrolling he ensemble

More information

PolicyCore. Putting Innovation and Customer Service at the Core of Your Policy Administration and Underwriting

PolicyCore. Putting Innovation and Customer Service at the Core of Your Policy Administration and Underwriting PolicyCore Puing Innovaion and Cusomer Service a he Core of Your Policy Adminisraion and Underwriing As new echnologies emerge and cusomer expecaions escalae, P&C insurers are seeing opporuniies o grow

More information

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides

17 Laplace transform. Solving linear ODE with piecewise continuous right hand sides 7 Laplace ransform. Solving linear ODE wih piecewise coninuous righ hand sides In his lecure I will show how o apply he Laplace ransform o he ODE Ly = f wih piecewise coninuous f. Definiion. A funcion

More information

Gene Regulatory Network Discovery from Time-Series Gene Expression Data A Computational Intelligence Approach

Gene Regulatory Network Discovery from Time-Series Gene Expression Data A Computational Intelligence Approach Gene Regulaory Nework Discovery from Time-Series Gene Expression Daa A Compuaional Inelligence Approach Nikola K. Kasabov 1, Zeke S. H. Chan 1, Vishal Jain 1, Igor Sidorov 2 and Dimier S. Dimirov 2 1 Knowledge

More information

Heuristics for dimensioning large-scale MPLS networks

Heuristics for dimensioning large-scale MPLS networks Heurisics for dimensioning large-scale MPLS newors Carlos Borges 1, Amaro de Sousa 1, Rui Valadas 1 Depar. of Elecronics and Telecommunicaions Universiy of Aveiro, Insiue of Telecommunicaions pole of Aveiro

More information

Information Systems for Business Integration: ERP Systems

Information Systems for Business Integration: ERP Systems Informaion Sysems for Business Inegraion: ERP Sysems (December 3, 2012) BUS3500 - Abdou Illia, Fall 2012 1 LEARNING GOALS Explain he difference beween horizonal and verical business inegraion. Describe

More information

adaptive control; stochastic systems; certainty equivalence principle; long-term

adaptive control; stochastic systems; certainty equivalence principle; long-term COMMUICATIOS I IFORMATIO AD SYSTEMS c 2006 Inernaional Press Vol. 6, o. 4, pp. 299-320, 2006 003 ADAPTIVE COTROL OF LIEAR TIME IVARIAT SYSTEMS: THE BET O THE BEST PRICIPLE S. BITTATI AD M. C. CAMPI Absrac.

More information

System Performance Improvement By Server Virtualization

System Performance Improvement By Server Virtualization Sysem Performance Improvemen By Server Virualizaion Hioshi Ueno, Tomohide Hasegawa, and Keiichi Yoshihama Absrac Wih he advance of semiconducor echnology, microprocessors become highly inegraed and herefore

More information

A Robust Defense Scheme for the Detection of Distributed Denial of Service Attack through Web Proxy System

A Robust Defense Scheme for the Detection of Distributed Denial of Service Attack through Web Proxy System ISSN (Online) : 2319-8753 ISSN (Prin) : 2347-6710 Inernaional Journal o Innovaive Research in Science, Engineering an Technology Volume 3, Special Issue 3, March 2014 2014 Inernaional Conerence on Innovaions

More information

We addressed the problem of developing a model to simulate at a high level of detail the movements of over

We addressed the problem of developing a model to simulate at a high level of detail the movements of over Published online ahead of prin Augus 15, 28 Aricles in Advance, pp. 1 2 issn 41-1655 eissn 1526-5447 informs doi 1.1287/rsc.18.238 28 INFORMS An Approximae Dynamic Programming Algorihm for Large-Scale

More information

A Novel Approach to Improve Diverter Performance in Liquid Flow Calibration Facilities

A Novel Approach to Improve Diverter Performance in Liquid Flow Calibration Facilities A Novel Approach o Improve Diverer Performance in Liquid Flow Calibraion Faciliies R. Engel Physikalisch-Technische Bundesansal (PTB) Braunschweig, Germany U. Klages Universiy of Applied Sciences a Wolfenbüel,

More information

Distributed and Secure Computation of Convex Programs over a Network of Connected Processors

Distributed and Secure Computation of Convex Programs over a Network of Connected Processors DCDIS CONFERENCE GUELPH, ONTARIO, CANADA, JULY 2005 1 Disribued and Secure Compuaion of Convex Programs over a Newor of Conneced Processors Michael J. Neely Universiy of Souhern California hp://www-rcf.usc.edu/

More information

Q-SAC: Toward QoS Optimized Service Automatic Composition *

Q-SAC: Toward QoS Optimized Service Automatic Composition * Q-SAC: Toward QoS Opimized Service Auomaic Composiion * Hanhua Chen, Hai Jin, Xiaoming Ning, Zhipeng Lü Cluser and Grid Compuing Lab Huazhong Universiy of Science and Technology, Wuhan, 4374, China Email:

More information

Signal Processing and Linear Systems I

Signal Processing and Linear Systems I Sanford Universiy Summer 214-215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 14-15, Gibbons

More information

Inductance and Transient Circuits

Inductance and Transient Circuits Chaper H Inducance and Transien Circuis Blinn College - Physics 2426 - Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual

More information

Monte Carlo Observer for a Stochastic Model of Bioreactors

Monte Carlo Observer for a Stochastic Model of Bioreactors Mone Carlo Observer for a Sochasic Model of Bioreacors Marc Joannides, Irène Larramendy Valverde, and Vivien Rossi 2 Insiu de Mahémaiques e Modélisaion de Monpellier (I3M UMR 549 CNRS Place Eugène Baaillon

More information

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments

BALANCE OF PAYMENTS. First quarter 2008. Balance of payments BALANCE OF PAYMENTS DATE: 2008-05-30 PUBLISHER: Balance of Paymens and Financial Markes (BFM) Lena Finn + 46 8 506 944 09, lena.finn@scb.se Camilla Bergeling +46 8 506 942 06, camilla.bergeling@scb.se

More information

Hybrid System Design for Singularityless Task Level Robot Controllers *

Hybrid System Design for Singularityless Task Level Robot Controllers * Proceedings of he 2000 IEEE Inernaional Conference on Roboics & Auomaion San Francisco, CA April 2000 Hybrid Sysem Design for Singulariyless Task Level Robo Conrollers * Jindong Tan and Ning Xi Deparmen

More information

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005

Measuring macroeconomic volatility Applications to export revenue data, 1970-2005 FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970-005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a

More information

Activity-Based Scheduling of IT Changes

Activity-Based Scheduling of IT Changes Aciviy-Based Scheduling of IT Changes David Trasour, Maher Rahmoun Claudio Barolini Trused Sysems Laboraory HP Laboraories Brisol HPL-2007-03 July 3, 2007* ITIL, change managemen, scheduling Change managemen

More information

Can Individual Investors Use Technical Trading Rules to Beat the Asian Markets?

Can Individual Investors Use Technical Trading Rules to Beat the Asian Markets? Can Individual Invesors Use Technical Trading Rules o Bea he Asian Markes? INTRODUCTION In radiional ess of he weak-form of he Efficien Markes Hypohesis, price reurn differences are found o be insufficien

More information

Analysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer

Analysis of Pricing and Efficiency Control Strategy between Internet Retailer and Conventional Retailer Recen Advances in Business Managemen and Markeing Analysis of Pricing and Efficiency Conrol Sraegy beween Inerne Reailer and Convenional Reailer HYUG RAE CHO 1, SUG MOO BAE and JOG HU PARK 3 Deparmen of

More information

ISABEL MARIA FERRAZ CORDEIRO ABSTRACT

ISABEL MARIA FERRAZ CORDEIRO ABSTRACT SOME NOTES ON THE AVERAGE DURATION OF AN INCOME PROTECTION CLAIM* BY ISABEL MARIA FERRAZ CORDEIRO ABSTRACT Coreiro (2002a) has presene a muliple sae moel for Income Proecion (formerly known as Permanen

More information

LEVENTE SZÁSZ An MRP-based integer programming model for capacity planning...3

LEVENTE SZÁSZ An MRP-based integer programming model for capacity planning...3 LEVENTE SZÁSZ An MRP-based ineger programming model for capaciy planning...3 MELINDA ANTAL Reurn o schooling in Hungary before and afer he ransiion years...23 LEHEL GYÖRFY ANNAMÁRIA BENYOVSZKI ÁGNES NAGY

More information

Multi-camera scheduling for video production

Multi-camera scheduling for video production Muli-camera scheduling for video producion Fahad Daniyal and Andrea Cavallaro Queen Mary Universiy of London Mile End Road, E 4S London, Unied Kingdom Email: {fahad.daniyal, andrea.cavallaro}@eecs.qmul.ac.uk

More information

The Grantor Retained Annuity Trust (GRAT)

The Grantor Retained Annuity Trust (GRAT) WEALTH ADVISORY Esae Planning Sraegies for closely-held, family businesses The Granor Reained Annuiy Trus (GRAT) An efficien wealh ransfer sraegy, paricularly in a low ineres rae environmen Family business

More information

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.

Duration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613. Graduae School of Business Adminisraion Universiy of Virginia UVA-F-38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised

More information

Journal Of Business & Economics Research September 2005 Volume 3, Number 9

Journal Of Business & Economics Research September 2005 Volume 3, Number 9 Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy Yi-Kang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo

More information

A Component-Based Navigation-Guidance-Control Architecture for Mobile Robots

A Component-Based Navigation-Guidance-Control Architecture for Mobile Robots A Componen-Based Navigaion-Guidance-Conrol Archiecure for Mobile Robos Nicolas Gobillo Charles Lesire David Doose Onera - The French Aerospace Lab, Toulouse, France firsname.lasname a onera.fr Absrac In

More information

GUIDE GOVERNING SMI RISK CONTROL INDICES

GUIDE GOVERNING SMI RISK CONTROL INDICES GUIDE GOVERNING SMI RISK CONTROL IND ICES SIX Swiss Exchange Ld 04/2012 i C O N T E N T S 1. Index srucure... 1 1.1 Concep... 1 1.2 General principles... 1 1.3 Index Commission... 1 1.4 Review of index

More information

Term Structure of Prices of Asian Options

Term Structure of Prices of Asian Options Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 1-1-1 Nojihigashi, Kusasu, Shiga 525-8577, Japan E-mail:

More information

The Belief Roadmap: Efficient Planning in Belief Space by Factoring the Covariance

The Belief Roadmap: Efficient Planning in Belief Space by Factoring the Covariance 1 The Belief Roadmap: Efficien Planning in Belief Space by Facoring he Covariance Samuel Prenice and Nicholas Roy Absrac When a mobile agen does no known is posiion perfecly, incorporaing he prediced uncerainy

More information

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.

Principal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya. Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one

More information

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test

Time Series Analysis Using SAS R Part I The Augmented Dickey-Fuller (ADF) Test ABSTRACT Time Series Analysis Using SAS R Par I The Augmened Dickey-Fuller (ADF) Tes By Ismail E. Mohamed The purpose of his series of aricles is o discuss SAS programming echniques specifically designed

More information

Capacitors and inductors

Capacitors and inductors Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear

More information

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework

SPEC model selection algorithm for ARCH models: an options pricing evaluation framework Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,

More information

4 Convolution. Recommended Problems. x2[n] 1 2[n]

4 Convolution. Recommended Problems. x2[n] 1 2[n] 4 Convoluion Recommended Problems P4.1 This problem is a simple example of he use of superposiion. Suppose ha a discree-ime linear sysem has oupus y[n] for he given inpus x[n] as shown in Figure P4.1-1.

More information

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits

Working Paper No. 482. Net Intergenerational Transfers from an Increase in Social Security Benefits Working Paper No. 482 Ne Inergeneraional Transfers from an Increase in Social Securiy Benefis By Li Gan Texas A&M and NBER Guan Gong Shanghai Universiy of Finance and Economics Michael Hurd RAND Corporaion

More information

Niche Market or Mass Market?

Niche Market or Mass Market? Niche Marke or Mass Marke? Maxim Ivanov y McMaser Universiy July 2009 Absrac The de niion of a niche or a mass marke is based on he ranking of wo variables: he monopoly price and he produc mean value.

More information

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements

11/6/2013. Chapter 14: Dynamic AD-AS. Introduction. Introduction. Keeping track of time. The model s elements Inroducion Chaper 14: Dynamic D-S dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuing-edge

More information

Chapter 6: Business Valuation (Income Approach)

Chapter 6: Business Valuation (Income Approach) Chaper 6: Business Valuaion (Income Approach) Cash flow deerminaion is one of he mos criical elemens o a business valuaion. Everyhing may be secondary. If cash flow is high, hen he value is high; if he

More information

Feasibility of Quantum Genetic Algorithm in Optimizing Construction Scheduling

Feasibility of Quantum Genetic Algorithm in Optimizing Construction Scheduling Feasibiliy of Quanum Geneic Algorihm in Opimizing Consrucion Scheduling Maser Thesis Baihui Song JUNE 2013 Commiee members: Prof.dr.ir. M.J.C.M. Herogh Dr. M. Blaauboer Dr. ir. H.K.M. van de Ruienbeek

More information

Making a Faster Cryptanalytic Time-Memory Trade-Off

Making a Faster Cryptanalytic Time-Memory Trade-Off Making a Faser Crypanalyic Time-Memory Trade-Off Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch

More information