Optimal Control of Switched Systems Governed by Logical Switching Dynamics
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914417479778304 |
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| author | Zhang, Xiao Meng, Min Li, Changxi Yiu, Ka-Fai Cedric |
| author_facet | Zhang, Xiao Meng, Min Li, Changxi Yiu, Ka-Fai Cedric |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23131 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Control of Switched Systems Governed by Logical Switching Dynamics Zhang, Xiao Meng, Min Li, Changxi Yiu, Ka-Fai Cedric Systems and Control Optimization and Control 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. |
| title | Optimal Control of Switched Systems Governed by Logical Switching Dynamics |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2603.23131 |