Optimal Asynchronous Guaranteed Cost Control of Uncertain Markov Jump Systems With Actuator Saturation and Nonideal Transition Probabilities

This paper investigates the problem of dynamic event-triggered asynchronous guaranteed cost control for uncertain Markov jump systems with actuator saturation and nonideal transition probabilities. First, a hidden Markov model is employed to estimate system modes that cannot be accurately detected in practical scenarios. Second, a dynamic event-triggered mechanism is established based on the hidden Markov model to conserve limited network resources and an asynchronous event-triggered state feedback control law is designed. Third, a convex hull representation is adopted to deal with saturated inputs and parameter uncertainties are incorporated in the system model. Moreover, since it is complex to obtain accurate transition probabilities for the Markov chain of the original system and the hidden Markov model in the observation process, unknown and uncertain transition probabilities are simultaneously considered in both mode transitions and mode observation processes, and a separation strategy is implemented to handle the nonideal probabilities in each process independently. Through the application of Lyapunov equations and linear matrix inequality techniques, sufficient conditions are derived that ensure the resulting system is stochastically stable with/without nonideal transition probabilities and satisfies specific cost bounds under three different initial boundary conditions. Finally, a convex optimization algorithm is proposed to design the optimal asynchronous event-triggered guaranteed cost control law, and a DC motor model is provided to validate its effectiveness.