Model-Free Dynamic Mode Adaptive Control for Data-Driven Control Synthesis

TL;DR

This paper introduces a model-free, data-driven control method called DMAC that enables online stabilization of systems without requiring explicit models, using recursive least-squares for dynamics estimation and adaptive control synthesis.

Contribution

The paper develops a novel DMAC framework combining recursive dynamics approximation with adaptive control, applicable to various systems without known models.

Findings

DMAC successfully stabilizes unstable linear systems.

The method demonstrates robustness to parameter variations.

Numerical examples validate convergence and stability.

Abstract

This paper presents a model-free, data-driven control synthesis method called dynamic mode adaptive control (DMAC) for systems whose mathematical models are unavailable or unsuitable for classical control design. The proposed approach combines data-driven dynamics approximation with adaptive control synthesis to enable online controller design using measured system data. DMAC comprises two main components: a dynamics-approximation module and a controller-synthesis module. The dynamics approximation module estimates a local linear representation of the system dynamics directly from measurements using a matrix recursive least-squares algorithm with a forgetting factor. The estimated dynamics are then used to compute an online stabilizing controller with full-state feedback and integral action. Theoretical analysis establishes convergence properties of the recursive dynamics approximation and boundedness of the closed-loop system under the DMAC controller. The performance of the proposed method is demonstrated through numerical examples involving representative dynamical systems, including an unstable linear system, the Van der Pol oscillator, and the Burgers' equation. Sensitivity studies further demonstrate the robustness of DMAC with respect to both algorithm hyperparameters and variations in system parameters.