Transient Performance Improvement in Reduced-Order Model Reference Adaptive Control Systems

The objective of model reference adaptive control systems is to drive the trajectories of an uncertain dynamical system to the trajectories of a given reference model capturing a desired closed-loop system performance. To this end, most adaptive control signals take the form u(a)(t) = -(W) over cap (T)(t)sigma-(x(t)), where x(t) is an element of R-n denotes the state vector of an uncertain dynamical xsystem, sigma : R-n -> R-s denotes a known basis function, and (W) over cap (t) is an element of R-sxm denotes an estimation of the unknown weight matrix W is an element of R-sxm satisfying sm update laws (here m denotes the number of control inputs). In this paper, we focus on a class of reduced-order, computationally less expensive, model reference adaptive control systems that are only predicated on a scalar update law. Specifically, our contribution is to utilize a command governor architecture in order to improve transient performance of this class of adaptive control systems. We prove the stability of the overall closed-loop system using Lyapunov stability theory and we also present an illustrative numerical example for demonstrating the efficacy of the proposed architecture. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.