Adaptive control for nonlinear systems with time-varying parameters and control coefficient

Abstract

This paper exploits the so-called congelation of variables method to design an adaptive controller for nonlinear systems with time-varying parameters. Two motivating examples describing scalar systems are discussed to illustrate the flexibility of the congelation of variables method to deal with the cases in which the time-varying parameters are coupled with the state and with the input, respectively. Interpretations from a passivity perspective are also provided. Then design procedures are derived for general nonlinear systems in parametric strict-feedback form, and it is shown that the state of the underlying system converges to the origin and all signals of the closed-loop system remain bounded. Simulations show that, in the presence of parameter variations, the performance of the proposed controller is superior to that of the classical adaptive controller designed for time-invariant systems.