A Data-rate Limited View of Adaptive Control

This paper addresses the problem of adaptively controlling a plant with unknown parameters using communication-limited feedback. Assuming known dynamics, expressions have recently been obtained for the minimum average feedback data rate required for asymptotic stabilisability. The main purpose of this work is to demonstrate that this minimum rate does not increase if the plant parameters are unknown, and the key elements of a stabilizing, minimum-rate policy are explicitly discussed. By regarding the uncertain plant as a higherdimensional, nonlinear plant with unknown initial condition, it is shown that this result agrees with the recent concept of local topological feedback entropy. Extensions to the case of uncertain nonlinear plants are discussed.