Composite Adaptive Control for Time-varying Systems with Dual Adaptation

TL;DR

This paper introduces a novel dual adaptation scheme for composite adaptive control of time-varying systems, achieving stability under milder conditions than traditional methods and recovering performance in time-invariant cases.

Contribution

A new dual adaptation mechanism for time-varying systems that ensures stability under initial excitation conditions, extending adaptive control capabilities.

Findings

Achieves UUB stability of the closed-loop system.

Recovers performance of IE-based controllers for time-invariant systems.

Uses a combination of projection and σ-modification algorithms.

Abstract

This paper proposes a composite adaptive control architecture using dual adaptation scheme for dynamical systems comprising time-varying uncertain parameters. While majority of the adaptive control schemes in literature address the case of constant parameters, recent research has conceptualized improved adaptive control techniques for time-varying systems with rigorous stability proofs. The proposed work is an effort towards a similar direction, where a novel dual adaptation mechanism is introduced to efficiently tackle the time-varying nature of the parameters. Projection and $\sigma$-modification algorithms are strategically combined using congelation of variables to claim a global result for the tracking error space. While the classical adaptive systems demand a restrictive condition of persistence of excitation (PE) for accurate parameter estimation, the proposed work relies on a milder condition, called initial excitation (IE) for the same. A rigorous Lyapunov stability analysis is carried out to establish uniformly ultimately bounded (UUB) stability of the closed-loop system. Further it is analytically shown that the proposed work can recover the performance of previously designed IE-based adaptive controller in case of time invariant systems.