A variable structure gradient algorithm for adaptive control

A standard assumption in adaptive control is that the parameters being estimated are either constant or vary 'slowly' as a function of time. In this paper an adaptive control algorithm is presented which eliminates the need for the previous assumption provided that the systems being controlled belong to a specified class. The type of systems may be either linear or nonlinear. For this class of systems, the state space is separated into distinct subspaces. The parameters are then required to remain constant, or be slowly time varying, within the subspaces. Given a controller for the system, a Lyapunov analysis of the output error dynamics and the parameter error dynamics leads to a parameter adaptation algorithm with a variable structure. The stability and convergence of both the parameter error and the output tracking error are investigated. An analysis of SISO, full-state feedback, linear systems is used to motivate and illustrate the treatment of SISO feedback linearizable systems.