Workshop on Feedback Control of Hybrid Systems

Pre-conference workshop at the 2016 IEEE Conference on Decision and Control, Las Vegas, NV

Feedback Control of Hybrid Systems

Prof. Ricardo G. Sanfelice (organizer and presenter)

Dr. Francesco FerranteJun Chai, Sean Phillips (presenters)

Computer Engineering, University of California, Santa Cruz

Course Overview

Hybrid dynamical systems, when broadly understood, encompass dynamical systems where states or dynamics can change continuously as well as instantaneously. Hybrid control systems arise when hybrid control algorithms — algorithms which involve logic, timers, clocks, and other digital devices — are applied to classical dynamical systems or systems that are themselves hybrid. Hybrid control may be used for improved performance and robustness properties compared to classical control, and hybrid dynamics may be unavoidable due to the interplay between digital and analog components of a system.

The proposed workshop has two main parts. The first part presents various modeling approaches to hybrid dynamics, focuses on a particular framework which combines differential equations with difference equations (or inclusions), and present key analysis tools. The ideas are illustrated in several applications. The second part presents control design methods for such rich class of hybrid dynamical systems, such as supervisory control, CLF-based control, invariance-based control, and passivity. A particular goal of the workshop is to reveal the key steps in carrying over such methodologies to the hybrid dynamics setting.

Each proposed module/lecture is designed to present key theoretical concepts as well as applications of hybrid control of current relevance. The workshop is based in part on the 2015 European Embedded Control Institute (EECI) International Graduate School on Control course that the organizer gave at Supelec, Paris, France in 2015, see

https://hybrid.soe.ucsc.edu/igsc-eeci-2015

its earlier version in 2014, see

https://hybrid.soe.ucsc.edu/teaching/igsc-eeci-2014

as well as recent articles by him and coauthors, see

https://hybrid.soe.ucsc.edu/biblio

Justification and Intended Audience

The workshop is intended to be a complete, even if brief, course on analysis and design of hybrid control systems. It will present recently developed results on robust asymptotic stability for hybrid systems (with Rafal Goebel and Andy Teel in [1] [2]) and recent advances on systematic design of control algorithms for nonlinear and hybrid systems [3], [4]. It 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; and researchers in dynamical systems in pursuit of relevant applications. The required background is basic familiarity with control theory for continuous-time and discrete-time linear and nonlinear systems. The lectures will be closely related to each other and are not meant to be independent research presentations. The workshop is planned for a full day.

Course Outline 

Part I

9:00 - 10:00 Introduction, examples, and modeling.

Speakers: Sanfelice (theory) and Ferrante (applications)

  • Theoretical topics: hybrid inclusions; solution concept, existence, and uniqueness. [1], [2]

  • Applications: hybrid automata [2], networked systems [5]. [6], [7], and cyber-physical systems [8].

10:00 - 11:30 Dynamical properties.

Speakers: Sanfelice (theory) and Phillips (applications)

  • Theoretical topics: continuous dependence of solutions, Lyapunov stability notion and sufficient conditions, invariance principles, and converse theorem. [1], [2],

  • Applications: synchronization of timers [9], [10] and state estimation over a network. [11], [12]

Coffee break within “Dynamical properties” 
 

Part II

11:30 - 12:00 Supervisory hybrid control. 

Speakers: Ferrante (theory and applications)

  • Theoretical topics: logic-based switching [13], uniting control [14], and throw-and-catch control [15].
  • Applications: aggressive control for aerial vehicles [16] and obstacle avoidance [17],

Lunch

1:00 - 1:55 CLF-based control.

Speakers: Sanfelice (theory) and Chai (applications)

  • Theoretical topics: control Lyapunov functions, stabilizability, Sontag-like universal formula for hybrid systems, selection theorems. [18], [19]
  • Applications: control for DC/DC conversion and for mechanical systems with impacts. [19], [20]

1:55 - 2:45 Invariance-based control.

Speakers: Chai (theory), and Phillips and Chai (applications)

  • Theoretical topics: invariance notions, viability, CLFs for invariance. [21], [22]
  • Applications: safety-based control for ground vehicles and control for DC/AC inversion. [23], [24]
 
Coffee Break

3:00 - 3:55 Passivity-based control.

Speakers: Sanfelice (theory) and Ferrante (applications)

  • Theoretical topics: passivity and dissipativity, storage function, connections to stability and detectability. [25][26]
  • Applications: control of power converters and mechanical systems with impacts. [23], [25], [20], [24]

3:55 - 4:50 Robustness.

Speakers: Sanfelice (theory), and Phillips and Chai (applications)

  • Theoretical topics: hybrid basic conditions, additive perturbations, unmodeled dynamics, computation errors, delays. [1], [27]

  • Applications: most applications will be revisited, in particular, synchronization over networks, power conversion, and aerial vehicle control. [6], [11], [28], [29], [30]

4:50 - 5:00 Closing remarks and future directions.
 
Speakers: Sanfelice 
 

4 Course Instructors

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 cole 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 a postdoctoral fellow at the Department of Computer Engineering, University of California, Santa Cruz. In 2010, he received a “Laurea degree” (BSc) in Control Engineering from University ”Sapienza” in Rome, Italy and in 2012 a “Laurea Magistrale” degree (MSc) 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 Ph.D. degree in control theory from Institut Superieur de l’Aeronautique et de l’Espace (SUPAERO), Toulouse, France. His research interests are in the general area of systems and control with a special focus on hybrid systems, observer design, and application of convex optimization to systems and control. Before joining Santa Cruz in September 2016, he was a postdoc at the Electrical and Computer Engineering Department in Clemson University.

Jun Chai received her B.S. and M.S. degrees in Mechanical Engineering from the University of Arizona in 2014. Since then, she has been a Ph.D. Candidate and a Research Assistant at the University of California, Santa Cruz in the Computer Engineering. Her research interests are in the area of hybrid control theory and applications using invariant-based control technique.

Sean Phillips is a Ph.D. Candidate in the Department of Computer Engineering at the University of California Santa Cruz. He received his B.S. degree in Mechanical Engineering from the University of Arizona in 2011 and continued to get his M.S. in Mechanical Engineering specializing in Dynamics and Controls in 2013. He started working with Dr. Sanfelice during his undergraduate where he helped set up the new Hybrid Dynamics and Controls Laboratory and had received a NASA Space Grant to work on a biological based path planning algorithm for micro air vehicles. During his graduate student career, he has been interested in using hybrid systems tools to develop stability results of synchronization and desynchronization in networks systems. 


References

  1. [65] Hybrid Dynamical Systems: Modeling, Stability, and Robustness, Goebel, R., Sanfelice R. G., and Teel A. R. , Issue NULL, New Jersey, (2012)
  2. [34] Hybrid dynamical systems, Goebel, R., Sanfelice R. G., and Teel A.R. , IEEE Control Systems Magazine, April, Volume 29, Issue NULL, Number 2, p.28-93, (2009)
  3. [99] Asymptotic Properties of Solutions to Set Dynamical Systems, Sanfelice, R. G. , Proceedings of the Conference on Decision and Control, December, Issue NULL, p.2287--2292, (2014)
  4. [77] Control of Hybrid Dynamical Systems: An Overview of Recent Advances, Sanfelice, R. G. , Hybrid Systems with Constraints, April, Issue NULL, p.146–177, (2013)
  5. [138] Computationally-Aware Switching Criteria for Hybrid Model Predictive Control Of Cyber-Physical Systems, Zhang, K., Sprinkle J., and Sanfelice R. G. , IEEE Transactions on Automation Science and Engineering, Volume 13, Issue 2, p.479--490, (2016)
  6. [140] On Distributed Intermittent Consensus for First-Order Systems with Robustness, Phillips, S., Li Y., and Sanfelice R. G. , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.146--151, (2016)
  7. [136] State Estimation of Linear Systems in the Presence of Sporadic Measurements, Ferrante, F., Gouaisbaut F., Sanfelice R. G., and Tarbouriech S. , In Automatica, November, Volume 73, p.101--109, (2016)
  8. [105] Analysis and Design of Cyber-Physical Systems: A Hybrid Control Systems Approach, Sanfelice, R. G. , Cyber Physical Systems: From Theory to Practice, (2015)
  9. [93] A Framework for Modeling and Analysis of Robust Stability for Spiking Neurons, Phillips, S., and Sanfelice R. G. , Proceedings of the 2014 American Control Conference, June, Issue NULL, p.1414-1419, (2014)
  10. [63] Switching System Model for Pinpoint Lunar Landing Guidance Using a Hybrid Control Strategy, Wibben, D. R., Furfaro R., and Sanfelice R. G. , Proceedings of the AIAA Guidance, Navigation, and Control Conference, Issue NULL, (2012)
  11. [139] On Distributed Observers for Linear Time-invariant Systems Under Intermittent Information Constraints, Li, Y., Phillips S., and Sanfelice R. G. , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.666--671, (2016)
  12. [114] Interconnected Observers for Linear Systems to Improve Rate of Convergence and Robustness to Measurement Noise, Li, Y., and Sanfelice R. G. , To appear in IEEE Transactions on Control of Network Systems, Issue NULL, (2015)
  13. [33] Supervising a family of hybrid controllers for robust global asymptotic stabilization, Sanfelice, R. G., Teel A. R., and Goebel R. , Proc. 47th IEEE Conference on Decision and Control, Issue NULL, p.4700–4705, (2008)
  14. [70] Robust Supervisory Control for Uniting Two Output-Feedback Hybrid Controllers with Different Objectives, Sanfelice, R. G., and Prieur C. , Automatica, July, Volume 49, Issue NULL, Number 7, p.1958–1969, (2013)
  15. [11] A ``throw-and-catch" hybrid control strategy for robust global stabilization of nonlinear systems, Sanfelice, R. G., and Teel A. R. , Proc. 26th American Control Conference, Issue NULL, p.3470–3475, (2007)
  16. [126] Robust Global Trajectory Tracking for Underactuated VTOL Aerial Vehicles using Inner-Outer Loop Control Paradigms, Naldi, R., Furci M., Sanfelice R. G., and Marconi L. , IEEE Transactions on Automatic Control, January, Volume 62, Number 1, p.97--112, (2017)
  17. [7] Robust hybrid controllers for continuous-time systems with applications to obstacle avoidance and regulation to disconnected set of points, Sanfelice, R. G., Messina M. J., Tuna S. E., and Teel A. R. , Proc. 25th American Control Conference, Issue NULL, p.3352–3357, (2006)
  18. [75] On the existence of control {L}yapunov functions and state-feedback laws for hybrid systems, Sanfelice, R. G. , IEEE Transactions on Automatic Control, December, Volume 58, Issue NULL, Number 12, p.3242–3248, (2013)
  19. [85] Pointwise Minimum-norm Control Laws for Hybrid Systems, Sanfelice, R. G. , Proceedings of the IEEE Conference on Decision and Control, Issue NULL, p.2665–2670, (2013)
  20. [110] Robust Global Stabilization of the DC-DC Boost Converter via Hybrid Control, Theunisse, T. A. F., Chai J., Sanfelice R. G., and Heemels M. , IEEE Transactions on Circuits and Systems I, April, Volume 62, Issue 4, p.1052--1061, (2015)
  21. [120] On Notions and Sufficient Conditions for Forward Invariance of Sets for Hybrid Dynamical Systems, Chai, J., and Sanfelice R.G. , Proceedings of the 54th IEEE Conference on Decision and Control, December, p.2869-2874, (2015)
  22. [141] Results on Feedback Design for Forward Invariance of Sets in Hybrid Dynamical Systems, Chai, J., and Sanfelice R. G. , Proceedings of the 55th IEEE Conference on Decision and Control, December, p.622--627, (2016)
  23. [91] A Robust Hybrid Control Algorithm for a Single-Phase DC/AC Inverter with Variable Input Voltage, Chai, J., and Sanfelice R. G. , Proceedings of the 2014 American Control Conference, Issue NULL, p.1420-1425, (2014)
  24. [117] Hybrid Feedback Control Methods for Robust and Global Power Conversion, Chai, J., and Sanfelice R. G. , Proceedings of the 5th Analysis and Design of Hybrid Systems, October, p.298-303, (2015)
  25. [69] Passivity-based Control for Hybrid Systems with Applications to Mechanical Systems Exhibiting Impacts, Naldi, R., and Sanfelice R. G. , Automatica, May, Volume 49, Number 5, p.1104–1116, (2013)
  26. [92] Sufficient Conditions for Passivity and Stability of Interconnections of Hybrid Systems using Sums of Storage Functions, Naldi, R., and Sanfelice R. G. , Proceedings of the 2014 American Control Conference, Issue NULL, p.1432-1437, (2014)
  27. [20] Robust Hybrid Control Systems, Sanfelice, R. G. , PhD. Thesis, Issue NULL, (2007)
  28. [113] Robust Global Trajectory Tracking for a Class of Underactuated Vehicles, Casau, P., Sanfelice R. G., Cunha R., Cabecinhas D., and Silvestre C. , Automatica, August, Volume 58, Issue NULL, p.90-98, (2015)
  29. [40] Dynamical Properties of Hybrid Systems Simulators, Sanfelice, R. G., and Teel A. R. , Automatica, Volume 46, Issue NULL, Number 2, p.239–248, (2010)
  30. [134] Computationally Tractable Implementations of Pointwise Minimum Norm State-Feedback Laws for Hybrid Systems, Sanfelice, R. G. , In Proceedings of American Control Conference, p.4257--4262, (2016)