Parameter Update Laws for Adaptive Control with Affine Equality Parameter Constraints

TL;DR

This paper develops and analyzes constrained parameter update laws for adaptive control systems with affine equality constraints, ensuring parameter estimates adhere to constraints while maintaining stability and tracking performance.

Contribution

It introduces two new update laws based on gradient and concurrent learning methods, reformulating the constrained optimization as an unconstrained problem for adaptive control.

Findings

The proposed laws maintain parameter constraints during adaptation.

The CL-based law achieves convergence to true parameters.

The gradient-based law ensures asymptotic tracking performance.

Abstract

In this paper, constrained parameter update laws for adaptive control with convex equality constraint on the parameters are developed, one based on a gradient only update and the other incorporating concurrent learning (CL) update. The update laws are derived by solving a constrained optimization problem with affine equality constraints. This constrained problem is reformulated as an equivalent unconstrained problem in a new variable, thereby eliminating the equality constraints. The resulting update law is integrated with an adaptive trajectory tracking controller, enabling online learning of the unknown system parameters. Lyapunov stability of the closed-loop system with the equality-constrained parameter update law is established. The effectiveness of the proposed equality-constrained adaptive control law is demonstrated through simulations, validating its ability to maintain constraints on the parameter estimates, achieving convergence to the true parameters for CL-based update law, and achieving asymptotic and exponential tracking performance for constrained gradient and constrained CL-based update laws, respectively.