Regret-Optimal Control under Partial Observability

This paper studies online solutions for regretoptimal control in partially observable systems over an infinitehorizon. Regret-optimal control aims to minimize the difference in LQR cost between causal and non-causal controllers while considering the worst-case regret across all
$\ell_{2}$
-norm-bounded disturbance and measurement sequences. Building on ideas from [1] on the the full-information setting, our work extends the framework to the scenario of partial observability (measurement-feedback). We derive an explicit state-space solution when the non-causal solution is the one that minimizes the
$\mathcal{H}_{2}$
criterion, and demonstrate its practical utility on several practical examples. These results underscore the framework's significant relevance and applicability in real-world systems.