Workshop on Model Predictive Control of Hybrid Dynamical Systems

Pre-conference workshop at the 2019 IEEE Conference on Decision and Control

Nice, France

December 10, 2019

 

Model Predictive Control

of Hybrid Dynamical Systems

 

Dr. Berk Altin1 (organizer and presenter)
Prof. Ricardo G. Sanfelice1 (organizer and presenter)
Prof. Francesco Ferrante2 (presenter)
 Dr. Mohamed A. Maghenem1 (presenter)   
Dr. Sean Phillips3 (presenter)
 
Department of Electrical and Computer Engineering, University of California, Santa Cruz
2 GIPSA Lab, Université Grenoble Alpes
Air Force Research Laboratory - Space Vehicles Directorate, Albuquerque, New Mexico
 

 

 

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Overview
Related Work
 

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Overview

Hybrid systems model the behavior of dynamical systems where the states can evolve continuously as well as instantaneously. Such systems arise when hybrid control algorithms — algorithms which involve logic, timers, clocks, and other digital devices — are applied to continuous-time systems, or due to the intrinsic dynamics (e.g., mechanical systems with impacts and switching electrical circuits). Hybrid control may be used for improved performance and robustness properties compared to conventional control, and hybrid dynamics may be unavoidable due to the interplay between digital and analog components of a system. This full day workshop is a brief but complete course on the analysis and design of model predictive control (MPC) algorithms for hybrid dynamical systems.

The workshop has three main parts. The first part presents an overview of the literature and state-of-the-art on hybrid MPC, and provides a short tutorial on a powerful hybrid modeling framework that encapsulates switched systems, hybrid automata, impulsive systems, and many other class of systems; see R. Goebel, R. G. Sanfelice, and A.R. Teel, "Hybrid dynamical systems", preprint available at PDF icon34.pdf. Key analysis tools corresponding to this framework, along with several advantages over other hybrid frameworks are demonstrated. This necessary background is then used to lay the theoretical foundations of a general MPC framework for hybrid dynamical systems, with guaranteed stability and feasibility. Numerical methods to solve the associated optimal control problem are presented. The ideas are illustrated in several applications, including networked systems, mechanical systems with impacts, power systems, and autonomous vehicles.

The second part presents a computationally tractable counterpart of the MPC framework in the first part. This particular MPC scheme relies on the time-discretization of the underlying continuous-time dynamics. Feasibility and stability properties of the nondiscretized hybrid MPC algorithm presented in the first part are extended to the discretized case. Computational methods to solve the optimal control problem, such as mixed integer nonlinear programming, are presented. As the discretization of hybrid dynamical systems is a nontrivial problem, appropriate discretization techniques are demonstrated. 

The third and final part of the workshop presents extensions in many directions of the results introduced earlier in the workshop.  In particular, we will present extensions of those results for robustness, estimation, output feedback, safety, learning, and optimal control.  The results are illustrated in the applications introduced earlier pertaining to mechanical systems with impacts, power systems, networked control systems, and autonomous vehicles. The workshop concludes with an in-depth discussion on open problems.

A particular goal of the workshop is to reveal the key steps in carrying over MPC methodologies to the hybrid dynamics setting. Each proposed module/lecture is designed to present key theoretical concepts as well as applications of current relevance.

The workshop is based in part on the recent articles by the organizers. Preprints of these articles are available at https://hybrid.soe.ucsc.edu/biblio.

 

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Intended Audience 

The workshop targets a broad audience in academia and industry, including graduate students, looking for an introduction to a new and active area of research and to some modern mathematical analysis tools; control practitioners interested in novel design techniques; researchers in dynamical systems in pursuit of relevant applications; and researchers in industry and labs applying hybrid predictive control methods to engineering systems. The required background is basic familiarity with continuous-time and discrete-time linear and nonlinear systems. The lectures are closely related to each other and not meant to be independent research presentations.

 

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Tentative Course Outline

Part I
  • Introduction to Hybrid Dynamical Systems: Modeling and Examples
    • Hybrid inclusions: solution concept, existence and uniqueness, connections to other frameworks, asymptotic stability, (control) Lyapunov functions, invariance, and robustness
    • Applications: networked systems, power systems, mechanical systems with impacts, and autonomous vehicles
  • Background on Hybrid Model Predictive Control
    • Basic concepts: models, methods, and open questions
  • Overview of Model Predictive Control for Hybrid Systems
    • Main ingredients: prediction and reoptimization in the context of hybrid time domains, terminal cost and constraints
  • Model Predictive Control for Hybrid Dynamical Systems
    • Main results: forward/recursive feasibility; continuity, positive definiteness, and descent properties of the value function, Lyapunov stability analysis
    • Examples and applications revisited
Part II
  • Control Lyapunov Functions (CLF) and Forward Invariance
    • Main tools: CLF-based control synthesis, sufficient conditions for forward invariance, barrier functions and other certificates
  • Numerical Solutions and Discretization of Hybrid Systems and Hybrid Optimal Control
    • Simulation methods and dynamical properties, asymptotic analysis of discretization effects
  • Model Predictive Control for Discretized Hybrid Systems
    • Main ingredients: prediction and reoptimization in the context of hybrid time domains, terminal cost and constraints
  • Applications and Numerical Examples
Part III
  • Robustness
  • Optimal Control and Cost Evaluation Problems for Hybrid Systems
  • Extensions of Hybrid MPC
    • Estimation and output feedback
    • Incorporating data for online learning
    • Certifying invariance and safety with the value function
  • Open Problems and Concluding Remarks

 

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Instructors 

Berk Altın received his B.S. in Mechatronics from Sabancı University in 2011, Istanbul, Turkey in 2011. From 2011 to 2016, he attended the University of Michigan, Ann Arbor, as a Fulbright fellow, where he received the M.S. and Ph.D. degrees in Electrical Engineering: Systems, and the M.S. degree in Mathematics, in 2013, 2016 and 2016, respectively. He is currently employed as a postdoctoral researcher at the University of California, Santa Cruz, with the Hybrid Systems Laboratory. His primary research interests include hybrid systems, model predictive control, iterative learning control, repetitive processes, and multidimensional systems, with applications in cyber-physical systems, power systems, robotics, and additive manufacturing.

Ricardo G. Sanfelice received the B.S. degree in Electronics Engineering from the Universidad de Mar del Plata, Buenos Aires, Argentina, in 2001, and the M.S. and Ph.D. degrees in Electrical and Computer Engineering from the University of California, Santa Barbara, CA, USA, in 2004 and 2007, respectively. In 2007 and 2008, he held postdoctoral positions at the Laboratory for Information and Decision Systems at the Massachusetts Institute of Technology and at the Centre Automatique et Systemes at the Ecole de Mines de Paris. In 2009, he joined the faculty of the Department of Aerospace and Mechanical Engineering at the University of Arizona, Tucson, AZ, USA, where he was an Assistant Professor. In 2014, he joined the faculty of the Computer Engineering Department, University of California, Santa Cruz, CA, USA, where he is currently an Associate Professor. Prof. Sanfelice is the recipient of the 2013 SIAM Control and Systems Theory Prize, the National Science Foundation CAREER award, the Air Force Young Investigator Research Award, and the 2010 IEEE Control Systems Magazine Outstanding Paper Award. He is Associate Editor for Automatica and serves as Chair of the Hybrid Systems Technical Committee from the IEEE Control Systems Society. His research interests are in modeling, stability, robust control, observer design, and simulation of nonlinear and hybrid systems with applications to power systems, aerospace, and biology.

Francesco Ferrante is an assistant professor of Control Systems (maître de conférences) at the University of Grenoble Alpes and a member of the Grenoble Images Speech Signal and Control Laboratory. He received in 2010 a ''Laurea degree'' (BSc) in Control Engineering from University ''Sapienza'' in Rome, Italy and in 2012 a ''Laurea Magistrale'' degree (MSc) cum laude in Control Engineering from University ''Tor Vergata'' in Rome, Italy. During 2014, he held a visiting scholar position at the Department of Computer Engineering, University of California Santa Cruz. In 2015, he received a PhD degree in control theory from ''Institut supérieur de l'aéronautique et de l'espace'' (SUPAERO) Toulouse, France. From November 2015 to August 2016, he was a postdoctoral fellow at the Department of Electrical and Computer Engineering, Clemson University. From August 2015 to September 2016, he held a position as postdoctoral scientist at the Hybrid Systems Laboratory (HSL) at the University of California at Santa Cruz.

Mohamed Adlene Maghenem received his Control-Engineering Degree from the Polytechnical School of Algiers, Algeria, in 2013. He received his M.S. and Ph.D. degrees in Control from the University of Paris-Saclay, France, in 2014 and 2017, respectively.  He is currently a Postdoctoral Fellow at the Electrical and Computer Engineering Department at the University of California, Santa Cruz.  His research interests include: distributed coordination of multiagent systems with application to synchronization of oscillators and formation control of mechanical systems, control of nonholonomic and underactuated systems, singular perturbations, and safety verification in hybrid dynamical systems.

Sean Phillips is a Research Mechanical Engineer at the Air Force Research Laboratory (AFRL) in the Space Vehicles Directorate, Kirtland Air Force Base, New Mexico. He received his Ph.D in the Department of Computer Engineering at the University of California, Santa Cruz, in 2018. He received his B.S. and M.S. in Mechanical Engineering from the University of Arizona in 2011 and 2013, respectively. In 2009, he joined the Hybrid Dynamics and Controls Lab where he received a NASA Space Grant in 2010. In 2010, he received an Undergraduate Research Grant from the University of Arizona Honors College. He first joined AFRL through the Space Scholars Internship Program in Albuquerque, New Mexico, for the summers of 2011, 2012 and 2017. In 2014, he joined the Hybrid Systems Laboratory at the University of California, Santa Cruz. In 2017, he received the Jack Baskin and Peggy Downes-Baskin Fellowship for his research on coordination of autonomous networked systems from the Baskin School of Engineering at the University of California, Santa Cruz.

 

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Related Work

[1] R. Goebel, R. G. Sanfelice, and A.R. Teel, "Hybrid dynamical systems", IEEE Control Systems Magazine, vol. 29, no. 2, pp. 28-93, April, 2009. PDF icon34.pdf

[2]R. Goebel, R. G. Sanfelice, and A. R. Teel, Hybrid Dynamical Systems: Modeling, Stability, and Robustness, New Jersey, Princeton University Press, 2012. PDF icon65.pdf

[3] B. Altin, P. Ojaghi, and R. G. Sanfelice, "A Model Predictive Control Framework for Hybrid Dynamical Systems", NMPC, vol. 51, pp. 128-133, 08/2018. PDF icon179.pdf

[4] B. Altin, and R. G. Sanfelice "Asymptotically Stabilizing Model Predictive Control for Hybrid Dynamical Systems", in American Control Conference, 2019.

[5] R. G. Sanfelice, "Hybrid Predictive Control", Handbook of Model Predictive Control, Edition 1, Basel, Birkhäuser , pp. pp. 199-220, 2018. PDF icon154.pdf

[6] F. Ferrante, R. G. Sanfelice, "Cost Evaluation for Hybrid Inclusions: A Lyapunov Approach", 57th IEEE Conference on Decision and Control, Miami, FL, 2018, pp. 855-860. PDF icon181.pdf

[7] T. A. F. Theunisse, J. Chai, R. G. Sanfelice, and M. Heemels, "Robust Global Stabilization of the DC-DC Boost Converter via Hybrid Control", IEEE Transactions on Circuits and Systems I, vol. 62, pp. 1052--1061, April, 2015. PDF icon110.pdf

[8] B. Short, and R. G. Sanfelice, "A Hybrid Predictive Control Approach to Trajectory Tracking for a Fully Actuated Biped", Proceedings of the American Control Conference, pp. 3526-3531, 2018. PDF icon172.pdf

[9] S. Phillips, and R. G. Sanfelice, "Robust Distributed Synchronization of Networked Linear Systems with Intermittent Information", to appear in Automatica, 2019.

[10] R. G. Sanfelice, "On the existence of control Lyapunov functions and state-feedback laws for hybrid systems", IEEE Transactions on Automatic Control, vol. 58, no. 12, pp. 3242–3248, December, 2013. PDF icon75.pdf

[11] J. Chai, and R. G. Sanfelice, "Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)",  IEEE Transactions on Automatic Control, 2019. PDF icon185.pdf

[12] M. Maghenem and R. G. Sanfelice, "Characterizations of Safety in Hybrid Inclusions Via Barrier Functions", in Proceedings of the 22Nd ACM International Conference on Hybrid Systems: Computation and Control, HSCC '19, (New York, NY, USA), pp. 109-118, ACM, 2019.

[13] R. G. Sanfelice, D. A. Copp, and P. Nanez, "A Toolbox for Simulation of Hybrid Systems in Matlab/Simulink: Hybrid Equations (HyEQ) Toolbox", Proceedings of Hybrid Systems: Computation and Control Conference, pp. 101–106, 2013. PDF icon74.pdf

[14] P. Ojaghi, B. Altin, and R. G. Sanfelice “On a Stabilizing Model Predictive Control Framework for Discretized Hybrid Dynamical Systems”, to appear in IEEE Conference on Decision and Control, 2019.

 

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Registration

To register, click here. Details can be found at the following website: https://cdc2019.ieeecss.org/workshops.php

 

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Contact Information

For further information, contact Berk Altın (berkaltin@ucsc.edu) or Ricardo G. Sanfelice (ricardo@ucsc.edu).

 

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