Safe implementations of supervisory commands

Abstract

This paper compares two different types of control strategies used to safely implement supervisory commands of hybrid dynamical systems. Both approaches considered in this paper switch between members of a family of control agents to ensure that constraints on the plant state are not violated at any time. The first approach is motivated by a hybrid system architecture outlined in [7] and uses a Fliess functional series of the plant's output to form a system of linear inequalities characterizing safe control inputs. Control signals are determined by solving a sequence of linear programs. The second approach is a model reference control approach to bybrid systems introduced in [8] and uses a known safe dynamical reference model to characterize the desired plant behavior. The controller is determined by representing the resulting error dynamics as a linear parameter varying system and applying linear robust control techniques to enforce a bounded amplitude performance level. The fundamental results underlying each of the methods are derived; both approaches are compared with regard to their complexity, performance, and sensitivity to modeling uncertainty. A numerical example is included for illustration.

The authors gratefully acknowledge the partial financial support of the Army Research Office (DAAH04-95-1-0600, DAAH04-96-1-0134).