Mixed $\mathcal{H}_2/\mathcal{H}_\infty$ LQ Games for Robust Policy Optimization Under Unknown Dynamics

We consider some aspects of mixed $\mathcal{H}_2/\mathcal{H}_\infty$ control in a policy optimization setting. We study the convergence and robustness properties of our proposed policy scheme for autonomous systems described by stochastic differential equations with non-trivial additive Brownian motion as a disturbance. We then propose efficiently \textit{learning} \textit{robustly stabilizing optimal control policies} for such systems when the dynamics is unknown. We evaluate our proposed schemes on two- and three-link kinematic chains. Our evaluations demonstrate robust steady-state convergence to equilibrium under worst-case disturbance and Brownian motion alike. This policy optimization scheme is well-suited to reinforcement learning, and learning-enabled control systems where modeling errors, unknown dynamics, parametric and non-parametric uncertainties typically hamper system operations.