Synthesizing controllers for hybrid systems

Abstract

A methodology for synthesizing control laws of hybrid systems is proposed using the hybrid automaton framework. The objective is to synthesize guards for making phase transitions to ensure that the system satisfies the global invariance over the whole state space. Classical analysis is used to derive a controller given the phases, transitions and global invariance of a hybrid system. The methodology seems to be general in the sense that control laws can be synthesized even if the hybrid system is modeled by an automaton more general than bounded-drift linear hybrid automaton model frequently discussed in the literature. The main requirement is that it should be possible to generate a closed form expression for state variables in every phase, as a function of time elapsed in that phase. Conditions on system parameters can be identified for which the control laws can be synthesized. Optimality criteria can be incorporated for selecting among different control strategies. The methodology is illustrated using three examples. This work is in contrast to most of the work on hybrid systems in which the focus has been on the analysis problem.

The work was partially supported by an NSF Indo-US grant INT-9416687. The first author was partially supported by an NSF grant nos. CCR-9303394, CCR-9308016, and CCR-9404930.