IGSC-EECI (Hybrid) 2023

IGSC-EECI PhD Course at the Scuola IMT Studi Lucca

Hybrid Control Systems

Prof. Ricardo G. Sanfelice

Electrical and 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 

1. Introduction and examples.  [1], [2], [3]

2. Modeling. 

  • Theoretical topics: hybrid inclusions; solution concept, existence, and uniqueness [1], [2], [3]

  • Applications: hybrid automata [3], networked systems [4], [5], [6], and cyber-physical systems [7].

3. Dynamical properties. 

  • Theoretical topics: continuous dependence of solutions, Lyapunov stability notion and sufficient conditions, invariance principles, and converse theorem [2], [3].

  • Applications: synchronization of timers [8] [9] [5] [10] and state estimation over a network [11] [6] [12].

 4. Uniting control. 

  • Theoretical topics: logic-based switching [13], uniting control [14], throw-and-catch control [15], supervisory control [16], and event-triggered control [17].

  • Applications:  aggressive control for aerial vehicles [18], control of the pendubot [19], obstacle avoidance [20], control of robotic manipulators [13]

5. Event-triggered control.

  • Theoretical topics:  event-triggered control [17].

  • Applications:  network control.

6. Throw-catch control.

  • Theoretical topics:  throw-and-catch control [15]

  • Applications:  aggressive control for aerial vehicles [18], control of the pendubot [19], obstacle avoidance [20], control of robotic manipulators [13]

7. Synergistic control.

8. Supervisory control.

  • Theoretical topics:  supervisory control [16] [3] 

  • Applications:  aggressive control for aerial vehicles [18], control of the pendubot [19], obstacle avoidance [20], control of robotic manipulators [13]

9. Invariance-based control.

  • Theoretical topics: invariance and invariance-based control [24] [25]

  • Applications:  control for AC/DC conversion

10. Other topics

References

  1. [220] Hybrid Feedback Control, Sanfelice, R. G. , New Jersey, (2021)
  2. [65] Hybrid Dynamical Systems: Modeling, Stability, and Robustness, Goebel, R., Sanfelice R. G., and Teel A. R. , New Jersey, (2012)
  3. [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)
  4. [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)
  5. [140] A Hybrid Consensus Protocol for Pointwise Exponential Stability with Intermittent Information, Phillips, S., Li Y., and Sanfelice R. G. , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.146--151, (2016)
  6. [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)
  7. [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)
  8. [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)
  9. [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)
  10. [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)
  11. [114] Interconnected Observers for Robust Decentralized Estimation with Performance Guarantees and Optimized Connectivity Graph, Li, Y., and Sanfelice R. G. , IEEE Transactions on Control of Network Systems, Volume 3, Issue 1, p.1--11, (2016)
  12. [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)
  13. [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)
  14. [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)
  15. [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)
  16. [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)
  17. [158] Analysis and Design of Event-triggered Control Algorithms using Hybrid Systems Tools, Chai, J., Casau P., and Sanfelice R. G. , Proceedings of the 2017 IEEE Conference on Decision and Control, p.6057-6062, (2017)
  18. [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)
  19. [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)
  20. [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)
  21. [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)
  22. [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)
  23. [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)
  24. Citekey </span><span style="font-size: 1em;">120</span><span style="font-size: 1em;"> not found
  25. [141] Results on invariance-based feedback control for hybrid dynamical systems, Chai, J., and Sanfelice R. G. , Proceedings of the 55th IEEE Conference on Decision and Control, December, p.622--627, (2016)