Inherent robustness in the adaptive control of a large class of systems

Abstract

Recently it has been shown how to carry out adaptive control for a linear time‐invariant (LTI) plant so that the effect of the initial condition decays exponentially to zero and so that the input‐output behavior enjoys a convolution bound. This, in turn, has been leveraged to prove, in several special cases, that the closed‐loop system is robust in the sense that both of these properties are maintained in the presence of a small amount of parameter time‐variation and unmodelled dynamics. This paper shows that this robustness property is true for a general adaptive controller with the right properties: if we are able to prove exponential stability and a convolution bound for the case of fixed plant parameters, then robustness comes for free. We also apply the results to solutions to various adaptive control problems in the literature.