Finite-time optimal control for Markov jump systems with singular perturbation and hard constraints

This study addresses the finite-time optimal control problem for Markov jump systems subject to singular perturbations and hard constraints. The transition probabilities are considered to vary randomly within a finite set, which can be governed by a higher-level nonhomogeneous Markov process. The input signal is quantized dynamically before being passed to the controller, and a generalized framework is formulated based on the quantized control input and actuator faults. The goal is to ensure the finite-time boundedness of Markov jump singularly perturbed systems by designing a controller that satisfies the hard constraints. Then, by adopting a novel Lyapunov functional, the singularly perturbed parameter-independent sufficient conditions are obtained. For the preset finite-time interval, the optimization problem of minimizing the upper bound of the state trajectory is skillfully solved. Finally, a simulation example is presented to verify the effectiveness of the proposed design method.