Multiple Model Reference Adaptive Control with Blending for Non-Square Multivariable Systems

TL;DR

This paper introduces a multiple model reference adaptive control scheme with blending for non-square multivariable systems, ensuring stability and asymptotic tracking despite uncertainties.

Contribution

It develops a novel MMRAC with blending for non-square systems, including an online identification scheme and proven stability guarantees.

Findings

Guaranteed convergence of parameter estimates under persistence of excitation

Asymptotic state tracking to reference signals

Numerical simulations confirm stability and effectiveness

Abstract

In this paper we develop a multiple model reference adaptive controller (MMRAC) with blending. The systems under consideration are non-square, i.e., the number of inputs is not equal to the number of states; multi-input, linear, time-invariant with uncertain parameters that lie inside of a known, compact, and convex set. Moreover, the full state of the plant is available for feedback. A multiple model online identification scheme for the plant's state and input matrices is developed that guarantees the estimated parameters converge to the underlying plant model under the assumption of persistence of excitation. Using an exact matching condition, the parameter estimates are used in a control law such that the plant's states asymptotically track the reference signal generated by a state-space model reference. The control architecture is proven to provide boundedness of all closed-loop signals and to asymptotically drive the state tracking error to zero. Numerical simulations illustrate the stability and efficacy of the proposed MMRAC scheme.