MR-ARL: Model Reference Adaptive Reinforcement Learning for Robustly Stable On-Policy Data-Driven LQR

This article introduces a novel framework for data-driven linear quadratic regulator (LQR) design. First, we introduce a reinforcement learning paradigm for on-policy data-driven LQR, where exploration and exploitation are simultaneously performed while guaranteeing robust stability of the whole closed-loop system encompassing the plant and the control/learning dynamics. Then, we propose model reference adaptive reinforcement learning (MR-ARL), a control architecture integrating tools from reinforcement learning (RL) and model reference adaptive control (MRAC). The approach is based on a variable reference model containing the currently identified value function. Then, an adaptive stabilizer is used to ensure convergence of the applied policy to the optimal one, convergence of the plant to the optimal reference model, and overall robust closed-loop stability. The proposed framework provides theoretical robustness guarantees against perturbations, such as measurement noise, plant nonlinearities, or slowly varying parameters. The effectiveness of the proposed architecture is showcased via realistic numerical simulations.