Ricardo Sanfelice
UC Santa Cruz

November 8, 2019
Hybrid systems model the behavior of dynamical systems in which the states can evolve continuously and, at isolate time instances, exhibit instantaneous jumps. Such systems arise when control algorithms that involve digital devices are applied to continuoustime systems, or when the intrinsic dynamics of the system itself has such hybrid behavior, for example, in mechanical systems with impacts, switching electrical circuits, spiking neurons, atc. 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 in a cyberphysical system. In this talk, we will introduce analysis and design tools for model predictive control (MPC) schemes for hybrid systems. We will present recently developed results on asymptotically stabilizing MPC for hybrid systems based on control Lyapunov functions. After a short overview of the state of the art on hybrid MPC, and a brief introduction to a powerful hybrid systems framework, we will present key concepts and analysis tools. After that, we will lay out the theoretical foundations of a general MPC framework for hybrid systems, with guaranteed stability and feasibility. In particular, we will characterize invariance properties of the feasible set and the terminal constraint sets, continuity of the value function, and use these results to establish asymptotic stability of the hybrid closedloop system. To conclude, we will illustrate the framework in several applications and summarize some of the open problems, in particular, those related to computational issues.

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0:00 Introduction
0:45 Hybrid Predictive Control for Manipulation
8:54 Model Predictive Control (MPC) Predict system behavior, select best decision
17:39 Hybrid MPC in the Literature
19:26 Modeling Hybrid Behavior
36:36 Stability of SampleandHold Control
39:16 Hybrid Basic Conditions (HBC)
40:27 Hybrid Equations (HyEQ) Toolbox The Hybrid Equations (HyEQ) Toolbox includes the following Simulink library for systems w/inputs and interconnections
40:55 Background on Model Predictive Control Most MPC strategies in the literature perform the following tasks Measure the current state of the system to control
46:35 Selecting the Prediction Horizon T
48:30 Example Implementation
50:18 Basic Conditions for Hybrid MPC
51:49 Stabilizing Ingredients for Hybrid MPC
55:09 MATLAB Implementation OPTI Toolbox
55:38 Hybrid Predictive Control for Tracking in Bipeds
56:25 Hybrid Predictive Control for Power Conversion
56:57 Hybrid Predictive Control for Motion Planning
57:18 Hybrid Predictive Control for Reactive Avoidance