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

A new paper from researchers Parham Oveissi and Ankit Goel introduces Dynamic Mode Adaptive Control (DMAC), a model-free, data-driven control synthesis method designed for systems where mathematical models are unavailable or unsuitable for classical control design. DMAC combines data-driven dynamics approximation with adaptive control to enable online controller design using measured system data. The method consists of two main modules: a dynamics-approximation module that estimates a local linear representation of system dynamics using a matrix recursive least-squares algorithm with a forgetting factor, and a controller-synthesis module that computes an online stabilizing controller with full-state feedback and integral action.

DMAC's performance was demonstrated through numerical examples on representative dynamical systems, including an unstable linear system, the Van der Pol oscillator, and the Burgers' equation. Sensitivity studies confirmed the method's robustness to algorithm hyperparameters and variations in system parameters. Theoretical analysis established convergence properties of the recursive dynamics approximation and boundedness of the closed-loop system under the DMAC controller. This approach could significantly impact fields like robotics, autonomous systems, and industrial process control, where accurate models are often hard to obtain.