Periodic Adaptive Control for First-Order Discrete-Time Plants

Abstract

In adaptive control the goal is to deal with systems that have unknown and/or time- varying parameters. An adaptive controller typically consists of an LTI compensator together with an identifier or a tuner which is used to adjust the compensator parameters. A common approach to tuning is to invoke the Certainty Equivalence Principle, where at each instance of time the estimated plant parameters are assumed to be correct and the controller gains are updated accordingly. In this work we consider the first order case. We use the Certainty Equivalence approach to periodically estimate the plant parameters and then update the control action in order to provide stability. The data from first two steps are used to estimate the system parameters for the next two steps; the approach works by using a nominal control law and adding a small perturbation to the gain. The controller is proven to be noise tolerant, and we are able to prove a linear-like bound on the closed-loop behavior.