Hybrid Control Design

PhD Course at the University of Bologna

Hybrid Control Design

Prof. Ricardo G. Sanfelice

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 course 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 course 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.

Course Outline 

Week 1: Introduction, examples, and modeling. Slides here. Suggested reading and problems here.  Notes from all lectures are hereNotes about continuous-time nonlinear systems are here.

Week 2: Dynamical properties. Slides hereSuggested reading and problems here.  Notes from all lectures are here.

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

  • Applications: synchronization of timers [7] [8] [4] [9] and state estimation over a network [10] [5] [11].

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

Week 3: Supervisory control, uniting control, throw-catch, and event-triggered control. Slides here and hereSuggested reading and problems here.  Notes from all lectures are here.

  • Theoretical topics: logic-based switching [12], uniting control [13], throw-and-catch control [14], supervisory control [15], and event-triggered control [16].

  • Applications:  aggressive control for aerial vehicles [17], control of the pendubot [18], obstacle avoidance [19], control of robotic manipulators [12]

Week 4: Synergistic control, CLF-based control, Invariance-based control, and passivity-based control. Slides from lectures are here, here, and hereNotes from all lectures are here.
 
  • Theoretical topics: synergisit control [20] [21] [22], control Lyapunov functions, stabilizability, Sontag-like universal formula for hybrid systems, selection theorems [23], [24], [25], invariance and invariance-based control [26] [27], passivity-based control [28]

  • Applications:  control for DC/DC conversion and for mechanical systems with impacts. [29], [30]

Project topic suggestions
 
Applications: [23]  [31] [32] [33] [34] [35]  [36] [37]
 
Theory: [38] [39] [40] [19] [18] [41] [42] [43]  [5] 
 
Final exam report instructions are here.

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. [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)
  4. [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)
  5. [136] State Estimation of Linear Systems in the Presence of Sporadic Measurements, Ferrante, F., Gouaisbaut F., Sanfelice R. G., and Tarbouriech S. , Automatica, November, Volume 73, p.101--109, (2016)
  6. [105] Analysis and Design of Cyber-Physical Systems: A Hybrid Control Systems Approach, Sanfelice, R. G. , Cyber Physical Systems: From Theory to Practice, p.3--31, (2015)
  7. [93] A Framework for Modeling and Analysis of Robust Stability for Spiking Neurons, Phillips, S., and Sanfelice R. G. , Proceedings of the American Control Conference, June, Issue NULL, p.1414-1419, (2014)
  8. [112] Robust Asymptotic Stability of Desynchronization in Impulse-Coupled Oscillators, Phillips, S., and Sanfelice R. G. , IEEE Transactions on Control of Network Systems, June, Volume 3, Issue 2, p.127--136, (2016)
  9. [150] On Asymptotic Synchronization of Interconnected Hybrid Systems with Applications, Phillips, S., and Sanfelice R. G. , Proceedings of the American Control Conference, p.2291--2296, (2017)
  10. [114] Interconnected Observers for Linear Systems to Improve Rate of Convergence and Robustness to Measurement Noise, Li, Y., and Sanfelice R. G. , IEEE Transactions on Control of Network Systems, Volume 3, Issue 1, p.1--11, (2016)
  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.654--659, (2016)
  12. [13] A hybrid control strategy for robust contact detection and force regulation, Carloni, R., Sanfelice R. G., Teel A. R., and Melchiorri C. , Proc. 26th American Control Conference, Issue NULL, p.1461–1466, (2007)
  13. [14] {H}ybrid {S}ystems: stability and control, Cai, C., Goebel R., Sanfelice R. G., and Teel A. R. , Proc. 26th Chinese Control Conference, Issue NULL, (2007)
  14. [15] Hybrid systems techniques for convergence of solutions to switched systems, Goebel, R., Sanfelice R. G., and Teel A.R. , Proc. 46th IEEE Conference on Decision and Control, Issue NULL, p.92–96, (2007)
  15. [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)
  16. [158] Analysis and Design of Event-triggered Control Algorithms using Hybrid Systems Tools, Chai, J., Casau P., and Sanfelice R. G. , Proceedings of the IEEE Conference on Decision and Control, p.6057-6062, (2017)
  17. [26] A Hybrid Control Framework for Robust Maneuver-based motion planning, Sanfelice, R. G., and Frazzoli E. , Proc. 27th American Control Conference, Issue NULL, p.2254–2259, (2008)
  18. [25] Robust global swing-up of the pendubot via hybrid control, O'Flaherty, R., Sanfelice R. G., and Teel A. R. , Proc. 27th American Control Conference, Issue NULL, p.1424–1429, (2008)
  19. [17] A hybrid systems approach to trajectory tracking control for juggling systems, Sanfelice, R. G., Teel A. R., and Sepulchre R. , Proc. 46th IEEE Conference on Decision and Control, Issue NULL, New Orleans, LA, p.5282–5287, (2007)
  20. [49] Synergistic {L}yapunov functions and backstepping hybrid feedbacks, Mayhew, C. G., Sanfelice R. G., and Teel A. R. , Proc. 30th American Control Conference, Issue NULL, p.3203–3208, (2011)
  21. [54] Further results on synergistic {L}yapunov functions and hybrid feedback design through backstepping, Mayhew, C. G., Sanfelice R. G., and Teel A. R. , Proc. Joint Conference on Decision and Control and European Control Conference, Issue NULL, p.7428–7433, (2011)
  22. [135] Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions, Sanfelice, R. G. , Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, April, p.235--244 , (2016)
  23. [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)
  24. [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)
  25. [135] Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions, Sanfelice, R. G. , Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, April, p.235--244 , (2016)
  26. Citekey </span><span style="font-size: 1em;">120</span><span style="font-size: 1em;"> not found
  27. [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)
  28. [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)
  29. [19] Hybrid {MPC}: Open-minded but not Easily Swayed, Tuna, S. E., Sanfelice R. G., Messina M. J., and Teel A. R. , Assessment and Future Directions of Nonlinear Model Predictive Control, Volume Lecture Notes in Control and Information Sciences 358, Issue NULL, p.17–34, (2007)
  30. [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)
  31. [108] Observer-based Control Design for Linear Systems in the Presence of Limited Measurement Streams and Intermittent Input Access, Ferrante, F., Gouaisbaut F., Sanfelice R. G., and Tarbouriech S. , Proceedings of the American Control Conference, June, p.4689-4694, (2015)
  32. [111] A Finite-time Convergent Observer with Robustness to Piecewise-constant Measurement Noise, Li, Y., and Sanfelice R. G. , Automatica, July, Volume 57, Issue NULL, p.222-230, (2015)
  33. [137] Distance function design and Lyapunov techniques for the stability of hybrid trajectories, Biemond, J. J. B., Heemels W. P. M. H., Sanfelice R. G., and van de Wouw N. , Automatica, November, Volume 73, p.38--46 , (2016)
  34. [145] Incremental Graphical Asymptotic Stability for Hybrid Dynamical Systems, Li, Y., and Sanfelice R. G. , Feedback Stabilization of Controlled Dynamical Systems - Lecture Notes in Control and Information Sciences , March, Volume 473, p.231--262, (2017)
  35. [147] On an Invariance Principle for Differential-Algebraic Equations with Jumps and its Application to Switched Differential-Algebraic Equations, Nanez, P., Sanfelice R. G., and Quijano N. , Mathematics of Control Signal and Systems, Volume 185, (2017)
  36. [177] Robust Stability of Hybrid Limit Cycles With Multiple Jumps in Hybrid Dynamical Systems, Lou, X., Li Y., and Sanfelice R. G. , IEEE Transactions on Automatic Control, Volume 63, Number 4, p.1220--1226, (2018)
  37. [178] Pointwise Asymptotic Stability in a Hybrid System and Well-Posed Behavior Beyond Zeno, Goebel, R., and Sanfelice R. G. , SIAM Journal on Control and Optimization, Volume 56, Issue 2, p.1358–1385, (2018)
  38. [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)
  39. [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)
  40. [12] Robust source seeking hybrid controllers for autonomous vehicles, Mayhew, C. G., Sanfelice R. G., and Teel A. R. , Proc. 26th American Control Conference, Issue NULL, p.1185–1190, (2007)
  41. [38] Robust Global Asymptotic Attitude Stabilization of a Rigid Body by Quaternion-based Hybrid Feedback, Mayhew, C. G., Sanfelice R. G., and Teel A. R. , Proc. 46th Conference on Decision and Control, Issue NULL, p.2522–2527, (2009)
  42. [79] Juggling On A Bouncing Ball Apparatus Via Hybrid Control, Tian, X., Koessler J. H., and Sanfelice R. G. , Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Issue NULL, p.1848–1853, (2013)
  43. [82] Hybrid Control of the Boost Converter: {R}obust Global Stabilization, Theunisse, T. A. F., Chai J., Sanfelice R. G., and Heemels W.P.M.H. , Proceedings of the IEEE Conference on Decision and Control, Issue NULL, p.3635–3640, (2013)