Hierarchical Control for a Class of Uncertain Piecewise Linear Hybrid Dynamical Systems

In this paper, we consider the hierarchical control problem for a class of uncertain hybrid dynamical systems. The continuous dynamics of this class of uncertain hybrid systems are described by linear difference state equations, whose right side functions are unknown but lie within some convex hulls of known functions. Our control objective is for the closed loop system to exhibit a desired behavior under the dynamic uncertainty, continuous disturbances and uncontrollable events. One of the main questions is the existence of appropriate controllers. We will focus on this question here, and present a novel methodology for the analysis of uncertain piecewise linear hybrid dynamical systems (PLHDS) based on backward reachability analysis. For this purpose, we derive the predecessor operator for this class of uncertain PLHDS. Then both static control specifications such as safety and reachability, and dynamic control specifications are considered. A temperature control system is used for illustration.