Defense: Analysis and Design of Control Algorithms for Forward Invariance of Hybrid Systems

Speaker Name: 
Jun Chai
Speaker Title: 
PhD Candidate
Speaker Organization: 
Computer Engineering
Start Time: 
Monday, April 16, 2018 - 2:00pm
End Time: 
Monday, April 16, 2018 - 3:00pm
Location: 
Baskin Engineering, Room 330
Organizer: 
Ricardo Sanfelice

Abstract:  The recent advancements in automation technology in everyday lives call for reliable algorithms to guarantee safe operation of autonomous systems; such as path planing in autonomous driving, energy generation and allocation in smart grids, cooperative control in air traffic management and motion planning in human-robot collaboration. Such algorithms ought to ensure the complex systems to meet safety criteria under scenarios where uncertainties are taken into consideration. In this dissertation, tools to study the safety properties via robust forward invariance of sets for systems with unknown disturbances and hybrid dynamics are developed. In particular, the notion of robust forward invariance is proposed. This notion allows for a diverse type of solutions (with and without disturbances), including solutions that have persistent flow and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. For this new notion! , sufficient conditions for sets to enjoy such property are presented. These conditions involve the system data and the set to be rendered robust forward invariant. These conditions are exploited to derive conditions guaranteeing that sublevel sets of Lyapunov-like functions are robust forward invariant and, in turn, inspired a constructive way to design invariance-based control algorithms for a class of hybrid systems with control inputs and disturbances. More precisely, when there exists a Lyapunov-like function V satisfying certain conditions, existence of feedback laws that render sublevel sets of V robustly forward invariant for the closed-loop hybrid systems are presented. In addition, two selection theorems are proposed to design invariance-based controllers for the class of hybrid systems considered. Applications to power conversion systems, a constrained bouncing ball system and are given to illustrate major results.