DYNAMICAL NETWORKS: structural analysis and synthesis

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1 A social networks synchronization DYNAMICAL NETWORKS: structural analysis and synthesis traffic management B C (bio)chemical processes water distribution networks biological systems, ecosystems production and distribution systems telecommunication / data communication networks PhD student: Giulia Giordano Supervisor: Prof. Franco Blanchini

2 A social networks biological systems, ecosystems 4 C 2 5 synchronization B (bio)chemical processes water distribution networks 1 production and distribution systems 3 traffic management Dynamical network: subsystems (each with its own dynamics) interconnected by "flows" / interactions telecommunication / data communication networks (hyper-)graph representation: nodes subsystems arcs flows

3 Compartmental systems... - positive systems - mass conservation constraints - flow: interaction between two compartments graph representation: nodes compartments arcs flows...generalised hyper-graph: flows can require interactions among more than two compartments

4 A twofold goal Structural Analysis Structural Control Synthesis - independent of parameters - based on the nature of interactions (graph topology) - explain robustness and characteristic behaviours - interactions decided based on local information (decentralized) - control / coordinate global system behaviour...especially meant for... biologically-inspired design: learn from nature Man-made Systems Natural Systems synthetic biology: engineer natural systems Applications to biochemical systems Network-decentralized control

5 Structural Analysis Applications to biochemical systems Structural Control Synthesis

6 Biological systems are extremely robust: fundamental properties are preserved despite huge uncertainties and parameter variations STRUCTURAL ANALYSIS explain behaviours based on the system inherent structure (...motifs...) structure graph Structural property: satisfied by all the systems of a family specified by a structure without numerical bounds

7 Numerical tests based on polyhedral Lyapunov functions to structurally assess stability boundedness Yes Yes No No F. Blanchini, G. Giordano, Piecewise-linear Lyapunov functions for structural stability of biochemical networks, Automatica

8 Structural graph-based classification of oscillatory/multistationary behaviours Candidate oscillator Candidate multistable F. Blanchini, E. Franco, G. Giordano, A structural classification of candidate oscillators and multistationary systems, Bull. Math. Biol.

9 Similar results hold for the interconnection of structurally stable monotone subsystems + SSMS SSMS + SSMS + SSMS Candidate oscillator SSMS SSMS Candidate multistable F. Blanchini, E. Franco, G. Giordano, Structural conditions for oscillations and multistationarity in aggregate monotone systems, submitted

10 Synthesis of biomolecular oscillators z1, z2, x3 z1 x1 x1, x2, z3 Negative feedback of two monotone subsystems r2, e1, q1 e1 e2 r1, e2, qz23 F. Blanchini, C. Cuba Samaniego, E. Franco, G. Giordano, Design of a molecular clock with RNA mediated regulation, IEEE CDC 2014

11 Structural steady-state analysis Output variation (at steady state) Input variation Increase Perfect adaptation Decrease Depends on parameters G. Giordano, C. Cuba Samaniego, E. Franco, F. Blanchini, Computing the Structural Influence Matrix for Biological Systems, submitted

12 Structural steady-state analysis Influence matrix: structural steady-state variation of variable i due to a persistent additive input applied to variable j Network from Shinar&Feinberg (2010) G. Giordano, C. Cuba Samaniego, E. Franco, F. Blanchini, Computing the Structural Influence Matrix for Biological Systems, submitted

13 Structural Analysis Structural Control Synthesis Network-decentralized control

14 subsystems huge number of subsystems control agents

15 Control strategy decided locally, to govern the dynamics of the whole system The feedback matrix has a structure given by the graph F. Blanchini, E. Franco, G. Giordano, Structured LMI Conditions for Stabilizing Network Decentralized Control, IEEE CDC13; Network-Decentralized Control Strategies for Stabilization, IEEE Trans. Autom. Contr.

16 Node traffic splitting Internal node dynamics: stochastic Markov matrix Network-decentralized control: - robust (independent of Markov coefficients) - optimal: minimum norm (fairness) F. Blanchini, G. Giordano, P. L. Montessoro, Network decentralized robust congestion control with node traffic splitting, IEEE CDC 2014

17 PhD results: publications Journal papers * F. Blanchini, E. Franco, G. Giordano, Network-Decentralized Control Strategies for Stabilization, IEEE Trans. on Autom. Control, Feb * F. Blanchini, G. Giordano, Piecewise-linear Lyapunov Functions for Structural Stability of Biochemical Networks, Automatica, Oct * F. Blanchini, E. Franco, G. Giordano, A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems, Bulletin of Mathematical Biology, Oct Conference papers (peer reviewed) * F. Blanchini, G. Fenu, G. Giordano, F. A. Pellegrino, Inverse Kinematics by Means of Convex Programming: Some Developments, IEEE CASE, Gothenburg, August * F. Blanchini, D. Casagrande, G. Giordano, U. Viaro, Properties of Switching Dynamics Race Models, ECC, Linz, July * F. Blanchini, G. Giordano, Structural Stability of Biochemical Networks: Quadratic vs. Polyhedral Lyapunov Functions, ROCOND, Bratislava, July * F. Blanchini, G. Giordano, P. L. Montessoro, Network Decentralized Robust Congestion Control with Node Traffic Splitting, IEEE CDC, Los Angeles, December * F. Blanchini, C. Cuba Samaniego, E. Franco, G. Giordano, Design of a Molecular Clock with RNA mediated Regulation, IEEE CDC, Los Angeles, December * F. Blanchini, E. Franco, G. Giordano, Structured-LMI Conditions for Stabilizing NetworkDecentralized Control, IEEE CDC, Firenze, December 2013.

18 Gantt chart Activity // Month Attività Mese Analisi bibliografia Bibliography and e literature review letteratura Analisi teorica Analysis / / Numerical simulations Simulaz numeriche (1) (2) (5) (6) (3) (2) (4) (3) (4) (5) (4) (6) (7) (9) CDC (1) (3) ACC Articoli scientifici e Papers and conferences conferenze Attività formativa Scientific skills training scientifica Corsi formativi Transferable skills training complementari Prep PhDconferenze Conferencedi preparation dottorato Preparazione relazioni Annual report preparation annuali (1)(2) CDC Periodi all'estero Visits abroad Research activities (7) Training activities (10) (8) Doctoral activities PhD Thesis writing Stesura della tesi Milestones?? Visits abroad: (1) Supélec, FR, 7-10 April 2014; (2) INP Grenoble, FR, May 2014; (3) UC Riverside, CA, USA, December 2014; (4) Universität Stuttgart, DE, March-May Papers: (1) Proc. ACC 2013; (2) Proc. CDC 2013; (3) ACS Synthetic Biology; (4) Automatica + Bull Math Biol; (5) Proc. CDC 2014; (6) IEEE Trans Autom Contr; (7) Proc. ROCOND + Proc. ECC Training: (1) Photovoltaics: Principles and Devices; (2) Analisi Numerica IV; (3) Metodi topologici per la ricerca di punti fissi; (4) Scuola Nazionale di Dottorato SIDRA 2013; (5) Interdisciplinary PhD Spring School; (6) Corso di Deontologia e Pratica Professionale; (7) Lyapunov methods for robustness of control systems, PhD School, Grenoble; (8) Il ruolo del ricercatore in Europa; (9) Seminars in Stuttgart; (10) Set theoretic Fault Tolerant Control, Summer School, Grenoble Journal/Conference paper Presentation & Poster Annual report PhD thesis

19 PhD Thesis: Contents (tentative) DYNAMICAL NETWORKS: STRUCTURAL ANALYSIS AND SYNTHESIS Abstract 1 Introduction 2 Structural Properties I Background on Dynamical Networks II Structural Analysis of Dynamical Networks 3 Structural Stability and Boundedness 4 Structural Classification of Oscillatory and Multistationary Systems 5 Structural Steady-State Analysis and Influence Matrix 6 How Structural Analysis Can Aid the Synthesis of Biochemical Systems 6.1 Design of Biomolecular Oscillators 6.2 Rate Regulation in Artificial Gene Networks III Structural Control Synthesis for Dynamical Networks 7 Network-Decentralized Control Strategies for Stabilization 8 Network-Decentralized Congestion Control with Node Traffic Splitting 8.1 A Robust Decentralized Control for Channel-Sharing Communication 9 Compartmental Flow Control: Decentralization, Robustness and Optimality *** 10 Conclusions and Outlook IV Appendix Bibliography

20 Conclusions Now there is a PhD thesis to write......and still a lot of interesting work to do! GRAZIE!

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