Multiple models for decentralised adaptive control of discrete‐time systems

Abstract

AbstractThis paper investigates decentralised adaptive control of discrete‐time systems consisting of linear time‐invariant systems and a class of nonlinear systems. The parameters of the subsystems and the interconnection strengths between the subsystems are assumed unknown. Multiple adaptive prediction models with switching are used in this paper to address the relatively poor transient performance that typically results from a single prediction model. However, the application of this methodology requires indirect model reference discrete‐time adaptive control, and there appears to be very little focus in the literature on this. The principal contribution of this paper is to fill this void by arriving at proof of global stability of such decentralised adaptive systems using the theory of Lyapunov and properties of square‐summable sequences. The chosen representation of the system enables the same results to be directly applicable to both linear time‐invariant and linear‐in‐the‐parameters nonlinear subsystems. We consider two parametric update algorithms, one of which has a normalisation factor. Simulation studies included in this paper demonstrate the improvement in transient performance.