Supervisory Control of Dynamical Systems With Uncertain Time Delays

Abstract

A study of controlling dynamical systems with uncertain and varying time delays is presented in this paper. The uncertain time delay is assumed to fall in a range with known upper and lower bounds. We apply the supervisory control algorithm to deal with uncertainties in the time delay. An index is defined for each of the predetermined controls for a discrete set of time delays sampled from the range. Based on this index, a hysteretic switching rule selects a control from the predetermined controls with optimal feedback gains. Each predetermined control must be stable for any time delay in the range. Two control design methods are discussed, namely, the mapping method and a higher order approach. Examples of linear systems are used to demonstrate the theoretical work.