Optimal Adaptive Cruise Control with Guaranteed String Stability

Transcription

1 Vehcle Syem ynamc pp /99/34-33$5. Swe & Zelnger Opmal Aape Crue Conrol wh uaranee Srng Sably CHI-YIN IAN an HUEI PEN SUMMAY A wo-leel Aape Crue Conrol ACC ynhe meho preene n h paper. A he upper leel ere ehcle acceleraon compue bae on ehcle range an range rae meauremen. A he lower ero leel an aape conrol algorhm egne o enure he ehcle follow he upper leel acceleraon comman accuraely. I hown ha he ero-leel ynamc can be nclue n he oerall egn an rng ably can be guaranee. In oher wor he propoe conrol egn prouce mnmum negae mpac on urrounng ehcle. he performance of he propoe ACC algorhm eamne by ung a mcrocopc mulaon program ACCSIM creae a he Unery of Mchgan. he archecure an bac funcon of ACCSIM are ecrbe n h paper. Smulaon reul uner fferen ACC peneraon rae an acuaor/engne banwh are repore.. INOUCION Aape Crue Conrol ACC yem were propoe a an enhancemen o clacal crue conrol yem for groun ehcle pee regulaon. ACC yem conrol he ehcle pee o follow a rer e alue when no lea ehcle n gh. When a lower leang ehcle preen he ACC conrolle ehcle wll follow he lea ehcle a a afe ance. ACC reearch fr began n he 96 [] an ha recee eergrowng aenon n he la ecae. her commercal mplemenaon no poble unl recenly wh gnfcan progree n enor acuaor an oher enablng echnologe. I ha been hown ha PI or araon prouce afacory conrol reul []. ACC algorhm of more comple form hae alo been propoe an analye [3] [4] [5]. wo large-cale fel e were alo performe recenly [8] [9] wh regular rer rng ACC ehcle on normal hghway. Prelmnary e reul hae hown ha hee mple ACC conrol algorhm wor relably n real raffc conon. rauae uen Aocae Profeor eparmen of Mechancal Engneerng an Apple Mechanc Unery of Mchgan; E-mal: [email protected]

2 34 c.-y. lang an h. peng A wo-leel approach commonly ue for ACC conrol egn. A he hgher leel ere force or acceleraon compue bae on ehcle range range rae an oher gnal. A he lower ero leel he hrole/brae are manpulae o follow he ere force or acceleraon comman cloely. I houl be noe ha h wo-leel egn concep alo common n auomae hghway reearch [] alhough n a lghly fferen form. h wo-leel approach wll be aope n h paper a well. A major conrbuon ha ffer h paper from preou reearch howeer ha he effec of ACC on urrounng ehcle wll be aree eplcly. In our wo-leel egn he upper leel conroller aree he performance of oher ehcle an he ACC egn wll hae guaranee rng ably. he rng ably problem ha been ue a early a 977 []. A plaoon of ehcle are a o be rng able f uner no oher ecaon he range error ecreae a hey propagae along he ehcle ream. In mahemacal erm f he ranfer funcon from he range error of a ehcle o ha of followng ehcle ha a magnue le han or equal o rng ably [5]. o achee rng ably wh conan ner-ehcle pacng ehcle-o-ehcle communcaon wa hown o be neceary []. Yanae an anellaopoulo [4] ue a mple prng-ma-amper yem o emonrae he ea of rng ably an how he rng-ably creron for conan me-heaway an arable me-heaway polce. Swaroop an Herc [5] howe ha f he couplng beween wo ehcle wea enough he conrolle yem rng able. h concluon mple ha here a rae-off beween raffc-frenlne an ehcle pee regulaon performance. Alhough he crera for guaranee rng-ably are well nown no ynhe meho ha been propoe. he choce of he conrol gan moly bae on ralan-error. In h paper we propoe an opmal conrol raegy whch can be ue o oban he gan of he upper-leel ACC conroller. he co funcon of h opmaon problem con of penaly for he range an range rae error erm for all he ehcle n he rng. herefore rng ably guaranee. h problem wa ole by applyng a me-pace ranformaon echnque propoe by en an Ahan []. In her uy he opmal conroller wa aume o ue he nformaon of all he ehcle n he rng. In oher wor hey ole a cenrale conrol problem. A ecenrale echnque wa eelope laer by. C. Chu [3] for couple ynamc yem. In h paper we apply he formulaon propoe by Chu o he ACC problem. he reul a ecenrale algorhm uable for ACC mplemenaon. In oher wor only local range an range rae gnal are neee for he conrol of nual ehcle. he performance of he conroller can be ajue by changng he penaly coeffcen of he co funcon ju le anar Q opmaon problem. In he pa ACC algorhm were ealuae eher ung a comple ehcle moel wh only wo ehcle a lea ehcle an a conrolle ehcle or a mplfe ehcle moel wh a rng of encal ehcle. In h reearch we propoe o ue a

3 opmal aape crue conrol 35 mcrocopc mulaor whch mae poble o uy he effec of he mo mporan urbance lane change. In h mulaon program he ehcle longunal ynamc mple bu a comple lane change behaor nclue. A wo-lane cloe-crcu hghway conruce n whch auonomou lane change wll occur. he fac ha we are mulang nual ehcle enable u o uy afey an raffc flow characerc more accuraely. he remaner of h paper organe a follow: rng ably analy of a plaoon of ehcle hown n Secon. In Secon 3 a ynhe meho for ACC conrol algorhm wh guaranee rng ably preene. ACCSIM a mcrocopc mulaon ool we eelope o ealuae arou ACC yem ecrbe n Secon 4. A ero-leel conrol egn alo preene o confrm ha he eroleel ynamc can be robuly regulae. epreenae mulaon reul are gen n Secon 5. Fnally concluon are rawn n Secon 6.. SIN SABIIY ANAYSIS OF A CONSAN-HEAWAY ACC POICY Coner a plaoon of encal ACC-conrolle ehcle runnng on he hghway n a rng ee Fg.. h plaoon a o be rng able f he ranfer funcon from he range error of a ehcle o ha of followng ehcle ha a magnue le han or equal o one. For each ehcle efne : he poon of he h ehcle : he elocy of he h ehcle u : acceleraon comman of he h ehcle from he upper leel ACC : range gnal meaure by he h ehcle Fg.. Schemac agram of he ehcle rng. We coner a mple proporonal conrol algorhm where he only feebac gnal aalable are range an range rae gnal. Uner hee aumpon ha an ACC algorhm aop a conan-eparaon polcy.e. he ere range a conan ance he ehcle plaoon canno be rng able. In he followng we wll aume ha he conan-heaway polcy aope he ably of he ehcle rng analye... Ieal ehcle For a conan-heaway ACC he conrol objece o manan he ame pee a he preceng ehcle an eep he me heaway a a conan alue where he me

4 36 c.-y. lang an h. peng heaway h efne a h. For eal ehcle he acceleraon comman followe eacly.e. u. he conrol law for he h an - h ehcle are hu h h From Eq. an we hae h 3 herefore h 4 Srng ably can hu be guaranee f an only f ω ω ω j j whch can be afe f an only f h h >. h mple ha he feebac gan houl be large enough o enure rng ably. he me heaway alo play an mporan role. When lme n magnue by praccal reaon enor noe ec. a large me heaway houl be ue.. Vehcle wh ero-loop ynamc When he ero-loop ecrbe by a fr-orer lag yem a u a a τ he conrol law for wo conecue ehcle become [ ] h a τ 5 [ ] h a τ 6 herefore 3 h a τ 7 For rng ably an hae o afy one of he followng wo conran:

5 opmal aape crue conrol 37 h τ a or h h > h τ a h < τ a τa 8 3. OPIMA ACC AOIHM WIH UAANEE SIN SABIIY Aumng ha he ynamc of a ngle ehcle ecrbe by A Bu 9 where enoe he ae ecor of he h ehcle no ju he rael ance. he feebac gnal epen on he ae of more han one ehcle an hu n general coul hae he form y j j j For mple proporonal conrol bae on range an range rae gnal he conrol law become u h y An opmal conrol framewor can hen be formulae o mnme he range an range rae error for all he ehcle n he rng. he performance ne efne a: J [ q h q ru ] where he coeffcen q q an r can be elece for performance/effor rae-off. Eq. can be rewren a J Q j u u j 3 j j j he major echncal challenge hen o compue he conrol gan an gen he weghng coeffcen q q an r. 3.. Opmal ACC algorhm o ole he opmaon problem ecrbe aboe a blaeral ranformaon echnque [3] apple. h ranformaon efne a follow:

6 38 c.-y. lang an h. peng A } { A A Z 4 where a pace aance operaor an correpon o mong upream n he ehcle rng ee Fg.. An nere ranformaon alo efne: A A A π 5 where he pah of negraon he un crcle n he comple plane. Noce ha he nere -ranformaon wll be enoe a n he remaner of h paper. Conerng Eq.9- an 3 no he oman we hae u B A 6 y u 7 y 8 u u Q J 9 From Eq.6-8 we hae ] [ B A. efne A B hen gen by nal conon from ep he performance ne 9 can hen be wren a ep ep M r J where Q M. Aumng ha he nal ae of he ehcle are ranomly rbue an nal-ae nepenen opmaon problem can hen be efne whch mnme a lghly fferen co funcon: ep ep ˆ M r J whch afe by he opmal gan * only f we hae J J J * * * ˆ ˆ ˆ. Eq. can be wren a

7 opmal aape crue conrol 39 ˆ P r M r J where wo era marce are efne: ep ep M P an ep ep. he neceary conon for opmaon hen ˆ M r M r J or P B P B 3 herefore r P B P B 4 where he marce P an are ole from he followng algebrac equaon: M P P 5 n I 6 he opmal gan can be calculae numercally from Eq.3-6. Alhough he rng ably conon no eplcly aree n he propoe conrol formulaon nrecly guaranee n he co funcon formulaon. In he followng heorem we wll proe ha when he opmal conrol gan * e hey wll guaranee rng ably.

8 3 c.-y. lang an h. peng heorem For eal ero-loop ynamc.e. A B [ ] an h he opmal conrol parameer * whch mnme he performance ne Ĵ n Eq. wll reul n a rng able ACC egn. Proof: he ae epenen on nal conon accorng o ep. For any boune nal conon he neceary an uffcen conon for o reman boune ha he mar [ ep ] houl be boune for all an ha approache ero a for all. In oher wor all he egen-alue of houl hae negae real par for all pon on he un crcle. Snce A B he characerc h equa- on of λ h λ. I can be een ha he neceary an uffcen conon for λ o hae negae real par for h all pon >. h conon eacly he ame a he rng h h ably conon hown n Secon.. In oher wor when > h [ ep ] boune Ĵ hu boune. herefore he opmal conrol parameer * whch mnme he performance ne J ˆ wll prouce a rng able egn. 3.. Ieal ehcle When he ero-loop perfec.e. he ehcle acceleraon follow he acceleraon comman from he upper leel eacly we hae A B [ ] q qh Q q qh q Q q Q qh qh q qh q Q > r an. Eample opmal ACC egn reul are hown below. Fgure how he conour plo of he performance ne Ĵ for q q r an h. 4. he ol lne a he lower lef corner how he rng ably creron h >. Fgure 3 how he opmal conrol gan h

9 opmal aape crue conrol 3 for a e of 36 fferen q q combnaon on he plane. he opmal algorhm alway prouce rng-able conrol gan a he heorem ha prece. Fg.. Conour plo of he performance Ine eal ehcle. Fg. 3. Opmal conrol parameer plo eal ehcle Vehcle wh ero-loop ynamc When he ero-loop mperfec he opmal ACC egn nee o ae he eroloop ynamc no coneraon. We coner he cae when he ero-loop a ynamc can be appromae by a fr-orer lag.e. where a a τ a he ehcle acceleraon an a he acceleraon comman from he upper-leel. In h cae hree ae arable nee o be efne for each ehcle.e. [ ] a. he ae an npu marce are A an τ a B. he Q marce of he performance ne nee o be nflae n e τ a from o 33 by ang ero elemen. he opmaon problem oherwe encal o he eal-ehcle cae. Eample opmal ACC egn reul are hown below. he me conan τ a of he ub-loop ynamc aume o be. econ. Fgure 4 how he conour plo of he performance ne Ĵ for q q r an h.4. he ol lne a he lower lef an upper lef corner how he rng ably creron hown n Eq.8. Fgure 5 how he opmal conrol gan for a e of 49 fferen q q combnaon on he plane. Agan he opmal algorhm alway prouce rng-able conrol gan. Uner mlar penaly

10 3 c.-y. lang an h. peng weghng can be noce ha he conrol gan are alway maller han hoe of he eal-ehcle cae. Fg. 4. Conour plo of he performance ne wh ub-loop ynamc. Fg. 5. Opmal conrol parameer plo wh ub-loop ynamc. 4. UOFM ACC SIMUAO A PC bae mulaon program ACCSIM Aape Crue Conrol SIMulaor ha been eelope a he Unery of Mchgan o uy he effec of ACC on he ho ehcle a well a urrounng ehcle. h achee by conrucng a mulaor wh mulple ehcle. Varable uch a poon pee acceleraon an lane locaon of all he ehcle are mulae. he effec of ACC on afey fuel conumpon an hroughpu hu can all be negae a he ehcle leel. he mulae hghway aume o be a wo-lane hghway of m long wh no on-off ramp. he hghway cloe-loop n naure o ha f he ACC algorhm reul n rng nably effec wll be amplfe an become more ble. he mulaon program e no four par: rer moel ehcle/enor moel ACC moel an he neracon moel ee Fg. 6. he rer moel con of a lane change moel for all ehcle an a car-followng moel only for manually conrolle ehcle. he parameer of he rer moel are obane from fel e aa [6]. eal of h moel can be foun n [6]. he ehcle/rer are nale a he begnnng of he mulaon wh a e of arbue parameer uch a conrol ype manual. ACC acceleraon leel ere pee ere heaway ec. When he ehcle conrolle by ACC he ACC algorhm ecrbe n he preou econ ue. he neracon moel calculae he placemen pee an lane locaon of all ehcle an con of a collecon of algebrac an negraon roune. In he followng he ehcle ynamc moel ecrbe n eal.

11 opmal aape crue conrol 33 Vehcle neracon. an lane calculaon rer moel Senor moel Vehcle an rer probably rbuon Vehcle moel ACC Algorhm raphcal Uer Inerface a b Fg. 6. ACCSIM--a: archecure b: creen ho. 4.. Vehcle moel he longunal ehcle moel aope from a wor by Sommerlle [7]. Fgure 7 how he Smuln bloc agram of he ehcle moel. Major ub-moel are ecrbe n eal below. Engne moel A ac loo-up able ue o relae he engne ae hrole angle an engne pee wh combuon orque n N-m. near nerpolaon ue beween aa pon. h engne map wa obane epermenally an he reul were repore n [7]. Afer he engne oupu orque obane he engne pee calculae from hea hrole Angle Engne Moel We p W orque Conerer Moel ranmon Moel _ran Vehcle ynamc Moel a Fg. 7. Bloc agram of he ehcle moel. where θ h ω e ω ω e e ωe θh a ωe p ωe ω 7 J e hrole angle engne pee orque conerer urbne pee

12 34 c.-y. lang an h. peng p J e e a loa orque from orque conerer pump o be ecrbe below engne nera engne combuon orque engne acceory an loa orque orque conerer moel he orque conerer proe mooh couplng beween he engne an he ranmon. he pump e of he orque conerer connece o he engne an he urbne e connece o he ranmon. he behaor of he orque conerer moele by a e of quarac equaon relang ω urbne pee an ω p pump pee o urbne an pump orque. p m n ω ω p m p n ω ω ω ω p m3 p n3 ω ω 8 he orque conerer can operae n one of hree moe: conerer moe couplng moe an oerrun moe. he moe an alue of he parameer m m m 3 n n an n 3 are eermne by he pee rao ω S : ω p S < S. S >. : Conerer moe : Couplng moe : Oerrun moe ranmon moel he ranmon reponble for ranferrng engne orque o he ren wheel. I gear rao eermne by he ehcle pee an engne/loa ae. he gearhf n h moel bae on ymmerc lnear hf lne ecrbe below: hf ω.77 θ hf ω.77 θ hf ω 4.6θ hf ω 7.85θ 9. 6 where ω he ranmon oupu pee ra/ec an θ he hrole angle n egree. Vehcle ynamc moel Vehcle pee calculae from he followng equaon bae on Newon econ law.

13 opmal aape crue conrol 35 where r M γ F rr b g ωe ω rγ rfrr b g 9 rm ehcle pee re rau ehcle ma oerall gear rao aeroynamc rag coeffcen orque from ranmon rollng reance force brang orque orque ue o roa nclnaon Smulaon reul of a ep-hrole acceleraon run wh all oher urbance npu e o ero are hown n Fgure 8. a Vehcle elocy repone b Engne pee repone Fg. 8. Smulaon reul of he ehcle repone uner 5 egree hrole angle. 4.. Sero-loop conrol egn A hown n econ 3 he hgher-leel ACC egn coner he behaor beween ehcle. A ero-leel conroller nee o be egne o ha he acceleraon comman followe cloely. Ieally he ero-loop conroller houl be egne o ha behaor no only fa bu alo conen. he ehcle moel hown n he preou econ ue for fnal mulaon. I howeer oo complcae for conrol egn purpoe. A mpler moel nee o be conruce. I a well-nown fac ha he relaonhp beween hrole angle an ehcle pee can be appromae by V where an τ ary wh ehcle pee V. Bae θ h /τ on h mplfe moel an aape PI conroller mplemene o compenae for he araon of he ehcle parameer an o achee eay-ae racng error. he bloc agram of he conrol ub-loop hown n Fgure 9.

14 36 c.-y. lang an h. peng ere Acceleraon / ere Spee PI Conroller hrole Angle Vehcle Moel Vehcle Spee Aapaon Algorhm S Emaon Fg. 9. Bloc agram of he ero-loop yem. he objece of he ero-loop conrol egn a a a equalen o τ a hae V V V. h goal achee by an aape PI conrol algorhm. he τ a ehcle parameer an τ are emae an he PI conrol gan are upae accorngly. A anar ecure ea-square S emaon meho ue o emae he parameer an τ. Becaue he ehcle parameer are mearyng he S meho wh a forgeng facor ue. Accorng o he rng ably analy reul preene n econ. for an ACC yem wh a ere me heaway of.4 ec he ero-loop me conan τ a mu be le han.7 ec for rng ably. We egne he ero-loop conroller o ha τ a. ec. he ero-loop yem hown n Fgure 9 n fac a econ-orer yem. We place a pole a -/τ a -5. an he oher faer pole a -/τ a o ha he oerall repone omnae by he lower pole -/τ a. he S aape algorhm mplemene n cree me wh a amplng rae of mec. he mulaon reul of he ub-loop conroller racng ep change of acceleraon comman wh magnue of..3.5 an.7 m/^ a four fferen ehcle pee are hown n Fgure. I can be een ha he ehcle pee repone are all ery cloe o he ere fr-orer form an he me conan for he 6 cae are all beween.9 ec an.3 ec. In oher wor he ub-loop conroller no only achee he ere ynamc behaor conen acro a we range of operang conon. Fg.. Smulaon reul of he ub-loop conroller uner ep repone.

15 opmal aape crue conrol SIMUAION ESUS he purpoe of h mulaon uy o negae he performance of ACC conrol algorhm uner arou peneraon rae an nfluence ynamc of he ero-loop on oerall ACC performance. he mulaon cenaro are a follow: on he m -lane e rac 5 ehcle are creae. S run were performe wh fferen ACC peneraon rae: % % 3% 5% 7% an 9%. he au of all he ehcle are recore for a pan of hour. he ehcle ere pee ere me heaway nenon facor an afey facor are nale accorng o he acal rbuon ecrbe n a preou paper [6]. ue o frequen lane changng ranen behaor.e. no plaoonng of he ACC yem become mporan. Fgure how he roo-mean-quare MS alue of he range error range rae error an acceleraon gnal of manual ehcle. ACC ehcle. I can be een ha ACC ehcle achee mare mproemen n range an range rae wh a gnfcanly reuce acceleraon leel. MS alue of range error MS alue of range rae MS alue of acceleraon m 5 ACC Manual oal m/ ACC Manual oal m/^.8.6 ACC Manual oal % % 3% 5% 7% 9% ACC peneaon rae 3 % % 3% 5% 7% 9% ACC peneraon rae. % % 3% 5% 7% 9% ACC peneraon rae Fg.. Smulaon reul of ACC. manual ehcle. Fgure how he cummulae percenage of me-o-collon C uner hree ACC peneraon rae: % 5% an 9%. Uner normal car-followng conon C houl approach nfny. he percenage of me he ehcle on he hghway hang a C le han ay 5 econ a goo ne of afey. I can be een ha when mo of he ehcle are conrolle by ACC he pobly of hang C<5 econ grealy reuce. C me o collon 3 5 Cum. frequency % 5 % 5% 9% econ Fg.. me-o-collon of all ehcle.

16 38 c.-y. lang an h. peng We ubequenly uy he effec of engn/acuaor lag on he performance of ACC. hree cae are mulae: a Ieal ehcle/orgnal conrol. In h cae he ero-leel ynamc are aume o be eal an he opmal conrol ACC reul n a conrol gan of. an.7. b eal ehcle/orgnal conrol. In he mulaon he ero-leel ynamc are nrouce. he ACC algorhm howeer ll ue he orgnal conrol gan. an.7. c eal ehcle/new conrol. In h cae he ACC conrol egn coner he ero-leel ynamc an hu reul n a new conrol gan ue echnque hown n Secon 3.3. he ero-leel ynamc aume o be ecrbe by whch. acheable by an aape conrol algorhm ee Secon 4. he MS alue of he range range rae an acceleraon gnal are a hown n able. I can be een ha able. Smulaon reul of hree cae uner ero-leel ynamc a a. 5 ehcle/ m/ lane 5% peneraon rae. MS of ange Error m MS of ange Error m/ MS of Accel. m/^ Cae a Ieal ehcle Orgnal conrol Cae b eal ehcle Orgnal conrol Cae c eal ehcle New conrol f ero-leel ynamc e bu are gnore n he ACC egn cae b he performance may eerorae gnfcanly. When he ACC egn coner eroleel ynamc cae c.83 an.6 he performance become que mlar o ha of he eal cae cae a. 6. CONCUSIONS In h paper a conrol ynhe meho wa preene for he egn of Aape Crue Conrol algorhm. h ynhe meho bae on opmal conrol heory apple o a pace-ranforme ehcle rng. ue o he fac ha he conrol gnal opme he range an range rae error of all he ehcle n he rng rng ably guaranee. he reule upper-leel ACC conrol algorhm generae

17 opmal aape crue conrol 39 ere acceleraon comman whch hen followe by a ero-leel conroller. Smulaon were performe on a mcrocopc mulaor whch mmc a wo-lane hghway. I hown ha he ero-leel ynamc nee o be conere n he egn of upper-leel ACC o achee opmal performance. ACNOWEMEN h wor uppore by U.S. eparmen of ranporaon uner he conrac FH6-94-C-7-3 hrough he IS eearch Cener of Ecellence a he Unery of Mchgan. EFEENCES. ene W. an Ahan M. On he opmal error regulaon of a rng of mong ehcle IEEE ran. Auoma. Conr. ol. no. 3 July 966 pp Ioannou P. Xu Z. Ecer S. an Seja. Inellgen crue conrol: heory an epermen Proc. of he 3n Conference on econ an Conrol San Anono ecember 993 pp Ioannou P. e al. "Inellgen Crue Conrol: heory An Epermen" Proceeng of he 3n IEEE Conference on econ an Conrol San Anono X 993 IEEE 93CH pp Hapoglu C. Oguner U. an Sommerlle M. "ongunal Heaway Conrol Of Auonomou Vehcle" Proceeng of he 996 IEEE In. Conf. on Conrol Appl. IEEE 96CH pp Fancher P. Peng H. an Baree Z. "Comparon of hree Conrol Algorhm on Heaway Conrol for Heay ruc" Proceeng of he 995 IAVS Sympoum Ann Arbor MI 995a. 6. Fancher P.S. Baree Z. Sayer J.. Johnon.E. Ern.. Meffor M.. Foerng eelopmen Ealuaon an eploymen of Forwar Crah Aoance Syem FOCAS A Unery of Mchgan ranporaon eearch Inue echncal epor. 995b. 7. Fancher P.S. Baree Z. Sayer J.. MacAam C. Ern.. Meffor M.. Haugen J. Foerng eelopmen Ealuaon an eploymen of Forwar Crah Aoance Syem FOCAS A Unery of Mchgan ranporaon eearch Inue echncal epor number Fancher P. e al. e Characerng Performance of an Aape Crue Conrol Syem Proceeng of he 997 SAE Inernaonal Congre an Epoon Inellgen ranporaon Syem SAE SP-3 pp SAE paper# a. 9. Fancher P. e al. Inellgen Crue Conrol Fel Operaonal e Inerm epor echncal repor ep. of ran. O HS 88 6 Aug 997b.. McMahon.H. Narenran V.. Swaroop. Herc J.. Chang. S. an eln P. E. ongunal ehcle conroller for IVHS: heory an epermen Proc. of he 99 Amercan Conrol Conference Chcago 99 pp Caull. J. an arrar W.. Vehcle-follower longunal conrol for auomae ran ehcle J. of ynamc Syem Meauremen an Conrol ecember 977 pp Sheholelam S. an eoer C. A. ongunal conrol of a plaoon of ehcle Proc. of 99 Amercan Conrol Conference San ego 99 pp Chu. C. Opmal ecenrale regulaon for a rng of couple yem IEEE ran. Auoma. Conr. ol. 9 no. 3 June pp Yanae. anellaopoulo I. "A Smplfe Framewor for Srng Sably Analy n AHS" Proc. of he 3h IFAC Worl Congre Volume Q 996 pp.77-8.

18 33 c.-y. lang an h. peng 5. Swaroop. Herc J.. Srng Sably of Inerconnece Syem IEEE ran. Auoma. Conr. ol. 4 no. 3 March pp ang C. an Peng H. egn an Smulaon of A raffc-frenly Aape Crue Conrol Algorhm Proceeng of he 998 Inernaonal Mechancal Engneerng Congre an Epoon. 7. Sommerlle M. "Implemenaon of a ongunal Conroller for Ue on an Auomae Hghway Syem echncal epor 96-3 Cener for Inellgen ranporaon eearch he Oho Sae Unery Sprng 996.