A New Adaptive Suboptimal Controller for a Class of Linear Discrete-Time Systems with Unknown Bounded Disturbances

Abstract

This paper deals with adaptive suboptimal control of linear discrete-time, time-invariant, minimum phase, scalar systems in the presence of arbitrary bounded unmeasurable disturbances whose upper and lower bounds are a priori unknown. The distinguishing feature of the systems to be controlled is that there is no information concerning a priori knowledge of a bounded set to which the unknown parameters of these systems belong. Novelty of this paper is that, instead of unknown a priori membership set of parameters, the peculiar a posteriori membership sets are designed via the use of the measured signals. The adaptive suboptimal control algorithm utilizing this approach is proposed. The properties of the adaptive controller including the convergence of the adaptation procedure and also the ultimate boundedness of system's signals are established. To demonstrate an efficiency of this controller and support the theoretical study, simulation results are presented.