Exponentially Stable Combined Adaptive Control under Finite Excitation Condition

TL;DR

This paper introduces a combined adaptive control method for uncertain nonlinear systems that guarantees exponential stability under finite excitation conditions, removing the need for persistent excitation.

Contribution

It proposes a novel combined model reference adaptive control approach that ensures exponential stability without requiring persistent excitation, only finite excitation.

Findings

Exponential stability achieved under finite excitation.

Convergence rate independent of excitation level.

Validated through numerical simulations.

Abstract

The parameter convergence relies on a stringent persistent excitation (PE) condition in adaptive control. Several works have proposed a memory term in the last decade to translate the PE condition to a feasible finite excitation (FE) condition. This work proposes a combined model reference adaptive control for a class of uncertain nonlinear systems with an unknown control effectiveness vector. The closed-loop system is exponentially stable under the FE condition. The exponential rate of convergence is independent of the excitation level of the regressor vector and is lower-bounded in terms of the system parameters and user-designed gains. Numerical simulation is illustrated, validating the results obtained with the proposed adaptive control.