Model-free Dynamic Mode Adaptive Control using Matrix RLS

TL;DR

This paper introduces a model-free, data-driven control method called dynamic mode adaptive control (DMAC) that uses matrix recursive least squares for system dynamics approximation and is robust across various systems.

Contribution

The paper develops a novel DMAC approach combining dynamics approximation and control modules, utilizing matrix RLS for model-free control synthesis.

Findings

Demonstrates DMAC effectiveness on multiple engineering systems.

Shows robustness of DMAC to hyperparameter and system variations.

Provides systematic sensitivity analysis of DMAC.

Abstract

This paper presents a novel, model-free, data-driven control synthesis technique known as dynamic mode adaptive control (DMAC) for synthesizing controllers for complex systems whose mathematical models are not suitable for classical control design. DMAC consists of a dynamics approximation module and a controller module. The dynamics approximation module is motivated by data-driven reduced-order modeling techniques and directly approximates the system's dynamics in state-space form using a matrix version of the recursive least squares algorithm. The controller module includes an output tracking controller that utilizes sparse measurements from the system to generate the control signal. The DMAC controller design technique is demonstrated through various dynamic systems commonly found in engineering applications. A systematic sensitivity study demonstrates the robustness of DMAC with respect to its own hyperparameters and the system's parameters.