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

Abstract

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 ua(t) = −ŴT(t)σ(x(t)), where x(t) ∈ ℝn denotes the state vector of an uncertain dynamical system, σ:ℝn → ℝs denotes a known basis function, and Ŵ(t) ∈ ℝs×m denotes an estimation of the unknown weight matrix W ∈ ℝs×m 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.