An adaptive control algorithm for parameter adjustments

Abstract

This paper is concerned with making on-line adjustments in the adjustable parameters of a feedback control system in order to compensate for a deterioration of performance brought about by unknown variations in other system parameters. The algorithms to be discussed here are extensions and modifications of an algorithm reported in [1] and [2]. The basic control system containing known, adjustable and unknown parameters is assumed to be represented by the vector equations x = A(γ, ω)x + B(γ, ω)r (1) y = Cx The n-vector x(t) is the state of the over-all basic (feedback) control system, r(t) is a p-vector of arbitrary command and disturbance inputs, and y(t) is a q-vector of output variables. The coefficient matrices A and B in (1) are given functions of a vector γ = (γ1, .. γa) of adjustable controller parameters (adjustable amplifier gains, filter time constants and the like) and a vector ω = (ω1, .. ωb) of plant parameters. The value of ω is assumed to be unknown and may be slowly varying with time.