Adaptive control of first-order nonlinear systems with reduced knowledge of the plant parameters

Abstract

This paper presents an adaptive control strategy for a class of first-order nonlinear systems of the form x/spl dot/=/spl theta//sub 1/*/sup T/f(x)+/spl theta//sub 2/*/sup T/g(x), where g(x) is a smooth function, whereas f(x) satisfies sectoricity conditions. /spl theta//sub 1/* and /spl theta//sub 2/* are constant parameter vectors. It is assumed that the system remains controllable for all values of x, but the sign of /spl theta//sub 2/*/sup T/g(x)(x) is unknown. The proposed adaptive scheme extends ideas previously presented the authors (1992) where the term premultiplying the input was supposed to be constant. The standard least-squares estimates of /spl theta//sub 2/* are modified using a hysteresis type switching algorithm that enables us to conclude on existence, uniqueness, boundedness and convergence of the solutions of the adaptive closed-loop system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>