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Learning Expected Reward for Switched Linear Control Systems A Non-Asymptotic View

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Document pages: 12 pages

Abstract: In this work, we show existence of invariant ergodic measure for switchedlinear dynamical systems (SLDSs) under a norm-stability assumption of systemdynamics in some unbounded subset of $ mathbb{R}^{n}$. Consequently, given astationary Markov control policy, we derive non-asymptotic bounds for learningexpected reward (w.r.t the invariant ergodic measure our closed-loop systemmixes to) from time-averages using Birkhoff s Ergodic Theorem. The presentedresults provide a foundation for deriving non-asymptotic analysis for averagereward-based optimal control of SLDSs. Finally, we illustrate the presentedtheoretical results in two case-studies.

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