Construction of a robust adaptive regulator for time‐varying discrete time systems

Abstract

A robust adaptive regulator is constructed for single-inputlsingle-output discrete time systems modelled by a linear time-varying difference equation that includes an error term to incorporate model errors and/or disturbances. It is assumed that the parameters of the nominal model belong to a known bounded convex set and that the 'frozen time' nominal model is stabilizable for all possible parameter values. The estimation of the parameters of the nominal model is carried out using a standard gradient-type algorithm with a projection operation. An adaptive regulator is then constructed from the solution to a finite time Riccati equation. It is shown that the resulting closed-loop system is globally stable if the mean of the parameter time variations is sufficiently small and if the model error is sufficiently small, but where the disturbances applied to the plant may be arbitrarily large.