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arXiv · 2603.23131

Optimal Control of Switched Systems Governed by Logical Switching Dynamics

Xiao Zhang·Min Meng·Changxi Li·Ka-Fai Cedric Yiu
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Abstract

This paper investigates the optimal co-design of logical and continuous controls for switched linear systems governed by controlled logical switching dynamics. Unlike traditional switched systems with arbitrary or state-dependent switching, the switching signals here are generated by an internal logical dynamical system and explicitly integrated into the control synthesis. By leveraging the semi-tensor product (STP) of matrices, we embed the coupled logical and continuous dynamics into a unified algebraic state-space representation, transforming the co-design problem into a tractable linear-quadratic framework. We derive Riccati-type backward recursions for both deterministic and stochastic logical dynamics, which yield optimal state-feedback laws for continuous control alongside value-function-based, state-dependent decision rules for logical switching. To mitigate the combinatorial explosion inherent in logical decision-making, a hierarchical algorithm is developed to decouple offline precomputation from efficient online execution. Numerical simulations demonstrate the efficacy of the proposed framework.

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Xiao Zhang, Min Meng, Changxi Li, Ka-Fai Cedric Yiu. 2026-03-24. Optimal Control of Switched Systems Governed by Logical Switching Dynamics. https://arxiv.org/abs/2603.23131

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