Constrained Physics-Informed Deep Learning for Stable System Identification and Control of Unknown Linear Systems

This paper presents a novel data-driven method for learning deep constrained continuous control policies and dynamical models of linear systems. By leveraging partial knowledge of system dynamics and constraint enforcing multi-objective loss functions, the method can learn from small and static datasets, handle time-varying state and input constraints and enforce the stability properties of the controlled system. We use a continuous control design example to demonstrate the performance of the method on three distinct tasks: system identification, control policy learning, and simultaneous system identification and policy learning. We assess the system identification performance by comparing open-loop simulations of the true system and the learned models. We demonstrate the performance of the policy learning methodology in closed-loop simulations using the system model affected by varying levels of parametric and additive uncertainties. We report superior performance in terms of reference tracking, robustness, and online computational and memory footprints compared with classical control approaches, namely LQR and LQI controllers, and with three variants of model predictive control (MPC) formulations and two traditional MPC solution approaches. We then evaluate the potential of simultaneously learning the system model and control policy. Our empirical results demonstrate the effectiveness of our unifying framework for constrained optimal control of linear systems to provide stability guarantees of the learned dynamics, robustness to uncertainty, and high sampling efficiency.