Optimal Control of Switched Systems Governed by Logical Switching Dynamics
This addresses the problem of efficiently controlling complex hybrid systems for applications like robotics or automation, representing an incremental advance by integrating logical dynamics into a unified control synthesis framework.
The paper tackles the optimal co-design of logical and continuous controls for switched linear systems with internal logical switching dynamics, transforming the problem into a tractable linear-quadratic framework using semi-tensor products and deriving Riccati-type recursions for optimal feedback laws and decision rules.
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.