PhD Course at the University of Bologna
Hybrid Control Design
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, CLFbased control, invariancebased 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 2: Dynamical properties. Slides here. Suggested 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, throwcatch, and eventtriggered control. Slides here and here. Suggested reading and problems here. Notes from all lectures are here.

Theoretical topics: logicbased switching [12], uniting control [13], throwandcatch control [14], supervisory control [15], and eventtriggered control [16].

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

Theoretical topics: synergisit control [20] [21] [22], control Lyapunov functions, stabilizability, Sontaglike universal formula for hybrid systems, selection theorems [23], [24], [25], invariance and invariancebased control [26] [27], passivitybased control [28]

Applications: control for DC/DC conversion and for mechanical systems with impacts. [29], [30]
References
 [65] Hybrid Dynamical Systems: Modeling, Stability, and Robustness, , Issue NULL, New Jersey, (2012)
 [34] Hybrid dynamical systems, , IEEE Control Systems Magazine, April, Volume 29, Issue NULL, Number 2, p.2893, (2009)
 [138] ComputationallyAware Switching Criteria for Hybrid Model Predictive Control Of CyberPhysical Systems, , IEEE Transactions on Automation Science and Engineering, Volume 13, Issue 2, p.479490, (2016)
 [140] On Distributed Intermittent Consensus for FirstOrder Systems with Robustness, , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.146151, (2016)
 [136] State Estimation of Linear Systems in the Presence of Sporadic Measurements, , Automatica, November, Volume 73, p.101109, (2016)
 [105] Analysis and Design of CyberPhysical Systems: A Hybrid Control Systems Approach, , Cyber Physical Systems: From Theory to Practice, p.331, (2015)
 [93] A Framework for Modeling and Analysis of Robust Stability for Spiking Neurons, , Proceedings of the American Control Conference, June, Issue NULL, p.14141419, (2014)
 [112] Robust Asymptotic Stability of Desynchronization in ImpulseCoupled Oscillators, , IEEE Transactions on Control of Network Systems, June, Volume 3, Issue 2, p.127136, (2016)
 [150] On Asymptotic Synchronization of Interconnected Hybrid Systems with Applications, , Proceedings of the American Control Conference, p.22912296, (2017)
 [114] Interconnected Observers for Linear Systems to Improve Rate of Convergence and Robustness to Measurement Noise, , IEEE Transactions on Control of Network Systems, Volume 3, Issue 1, p.111, (2016)
 [139] On Distributed Observers for Linear Timeinvariant Systems Under Intermittent Information Constraints, , Proceedings of 10th IFAC Symposium on Nonlinear Control Systems, Issue NULL, p.654659, (2016)
 [13] A hybrid control strategy for robust contact detection and force regulation, , Proc. 26th American Control Conference, Issue NULL, p.1461–1466, (2007)
 [14] {H}ybrid {S}ystems: stability and control, , Proc. 26th Chinese Control Conference, Issue NULL, (2007)
 [15] Hybrid systems techniques for convergence of solutions to switched systems, , Proc. 46th IEEE Conference on Decision and Control, Issue NULL, p.92–96, (2007)
 [33] Supervising a family of hybrid controllers for robust global asymptotic stabilization, , Proc. 47th IEEE Conference on Decision and Control, Issue NULL, p.4700–4705, (2008)
 [158] Analysis and Design of Eventtriggered Control Algorithms using Hybrid Systems Tools, , Proceedings of the IEEE Conference on Decision and Control, p.60576062, (2017)
 [26] A Hybrid Control Framework for Robust Maneuverbased motion planning, , Proc. 27th American Control Conference, Issue NULL, p.2254–2259, (2008)
 [25] Robust global swingup of the pendubot via hybrid control, , Proc. 27th American Control Conference, Issue NULL, p.1424–1429, (2008)
 [17] A hybrid systems approach to trajectory tracking control for juggling systems, , Proc. 46th IEEE Conference on Decision and Control, Issue NULL, New Orleans, LA, p.5282–5287, (2007)
 [49] Synergistic {L}yapunov functions and backstepping hybrid feedbacks, , Proc. 30th American Control Conference, Issue NULL, p.3203–3208, (2011)
 [54] Further results on synergistic {L}yapunov functions and hybrid feedback design through backstepping, , Proc. Joint Conference on Decision and Control and European Control Conference, Issue NULL, p.7428–7433, (2011)
 [135] Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions, , Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, April, p.235244 , (2016)
 [75] On the existence of control {L}yapunov functions and statefeedback laws for hybrid systems, , IEEE Transactions on Automatic Control, December, Volume 58, Issue NULL, Number 12, p.3242–3248, (2013)
 [85] Pointwise Minimumnorm Control Laws for Hybrid Systems, , Proceedings of the IEEE Conference on Decision and Control, Issue NULL, p.2665–2670, (2013)
 [135] Robust Asymptotic Stabilization of Hybrid Systems using Control Lyapunov Functions, , Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, April, p.235244 , (2016)
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 [141] Results on Feedback Design for Forward Invariance of Sets in Hybrid Dynamical Systems, , Proceedings of the 55th IEEE Conference on Decision and Control, December, p.622627, (2016)
 [69] Passivitybased Control for Hybrid Systems with Applications to Mechanical Systems Exhibiting Impacts, , Automatica, May, Volume 49, Number 5, p.1104–1116, (2013)
 [19] Hybrid {MPC}: Openminded but not Easily Swayed, , Assessment and Future Directions of Nonlinear Model Predictive Control, Volume Lecture Notes in Control and Information Sciences 358, Issue NULL, p.17–34, (2007)
 [91] A Robust Hybrid Control Algorithm for a SinglePhase DC/AC Inverter with Variable Input Voltage, , Proceedings of the 2014 American Control Conference, Issue NULL, p.14201425, (2014)
 [108] Observerbased Control Design for Linear Systems in the Presence of Limited Measurement Streams and Intermittent Input Access, , Proceedings of the American Control Conference, June, p.46894694, (2015)
 [111] A Finitetime Convergent Observer with Robustness to Piecewiseconstant Measurement Noise, , Automatica, July, Volume 57, Issue NULL, p.222230, (2015)
 [137] Distance function design and Lyapunov techniques for the stability of hybrid trajectories, , Automatica, November, Volume 73, p.3846 , (2016)
 [145] Incremental Graphical Asymptotic Stability for Hybrid Dynamical Systems, , Feedback Stabilization of Controlled Dynamical Systems  Lecture Notes in Control and Information Sciences , March, Volume 473, p.231262, (2017)
 [147] On an Invariance Principle for DifferentialAlgebraic Equations with Jumps and its Application to Switched DifferentialAlgebraic Equations, , Mathematics of Control Signal and Systems, Volume 185, (2017)
 [177] Robust Stability of Hybrid Limit Cycles With Multiple Jumps in Hybrid Dynamical Systems, , IEEE Transactions on Automatic Control, Volume 63, Number 4, p.12201226, (2018)
 [178] Pointwise Asymptotic Stability in a Hybrid System and WellPosed Behavior Beyond Zeno, , SIAM Journal on Control and Optimization, Volume 56, Issue 2, p.1358–1385, (2018)
 [7] Robust hybrid controllers for continuoustime systems with applications to obstacle avoidance and regulation to disconnected set of points, , Proc. 25th American Control Conference, Issue NULL, p.3352–3357, (2006)
 [11] A ``throwandcatch" hybrid control strategy for robust global stabilization of nonlinear systems, , Proc. 26th American Control Conference, Issue NULL, p.3470–3475, (2007)
 [12] Robust source seeking hybrid controllers for autonomous vehicles, , Proc. 26th American Control Conference, Issue NULL, p.1185–1190, (2007)
 [38] Robust Global Asymptotic Attitude Stabilization of a Rigid Body by Quaternionbased Hybrid Feedback, , Proc. 46th Conference on Decision and Control, Issue NULL, p.2522–2527, (2009)
 [79] Juggling On A Bouncing Ball Apparatus Via Hybrid Control, , Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems, Issue NULL, p.1848–1853, (2013)
 [82] Hybrid Control of the Boost Converter: {R}obust Global Stabilization, , Proceedings of the IEEE Conference on Decision and Control, Issue NULL, p.3635–3640, (2013)