Regret-Optimal Control under Partial Observability

Joudi Hajar; Oron Sabag; Babak Hassibi

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arXiv · 2311.06433

Regret-Optimal Control under Partial Observability

Joudi Hajar·Oron Sabag·Babak Hassibi

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Abstract

This paper studies online solutions for regret-optimal control in partially observable systems over an infinite-horizon. 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 Sabag et al., 2023, 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.

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BibTeX RIS

Joudi Hajar, Oron Sabag, Babak Hassibi. 2023-11-10. Regret-Optimal Control under Partial Observability. https://arxiv.org/abs/2311.06433

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