ROBUST AND ADAPTIVE SUPERVISORY CONTROL OF DISCRETE-EVENT SYSTEMS

To control a system with model uncertainty, two approaches are available: 1) robust control that controls the system without actually resolving uncertainties; 2) adaptive control that invokes an identification scheme to resolve uncertainties and updates the control algorithm accordingly. In this note we discuss both robust and adaptive supervisory control in discrete event systems. We assume that the system G to be controlled is not known exactly. We only know that is belongs to a set or its ''lower'' and ''upper'' bounds. The task of robust supervision is to synthesize a supervisor that realizes a given desired behavior for alt possible G. We derive a necessary and sufficient condition for the existence of such a robustsupervisor. Based on this condition, a robust supervisory control and observation problem of synthesizing a robust supervisor whose behavior is both legal and acceptable is solved. We also discuss adaptive supervision. As the system progresses, the information on occurrences of events may help as to resolve or reduce uncertainties. This information can be used to improve the performance of the closed loop systems by introducing adaptive supervision.