Exponential Stability for Adaptive Control of a Class of First-Order Nonlinear Systems

Abstract

In adaptive control it is typically proven that a weak asymptotic form of stability holds; furthermore, at best it is proven that a bounded noise yields a bounded state. Recently, however, it has been proven in a variety of scenarios that it is possible to carry out adaptive control for a linear-time invariant (LTI) discrete-time plant so that the closed-loop system enjoys exponential stability, a bounded gain on the noise, as well as a convolution bound on the effect of the exogenous inputs; the key idea is to carry out parameter estimation by using the ideal projection algorithm in conjunction with restricting the parameter estimates to a convex set. In this paper we extend the approach to a class of first-order nonlinear systems.