Design of piecewise linear hybrid dynamical systems using a control regulator approach

摘要

This paper presents a novel framework for hierarchical control of piecewise linear hybrid dynamical systems. The main characteristic of this class of hybrid systems is that the continuous dynamics are described by linear difference equations, the discrete dynamics by finite automata, and the interaction between the continuous and the discrete part is defined by piecewise linear maps. Control design is formulated as a regulator problem and algorithms for the synthesis of dynamical controllers are developed. Control specifications are modeled as finite automata. Both static specifications that do not change as time progresses and dynamic specifications that include sequencing of events and eventual execution of actions are considered. Control design is implemented using finite automata and linear programming techniques. Simulation results of a tank system are used to illustrate the approach.