Value Iteration-Based Optimal Asynchronous Control for Markov Jump Systems With Application to Power Systems

In this paper, an optimal asynchronous control method via value iteration (VI) technique is proposed for Markov jump systems. Since the exact mode of the system is assumed to be unknown, a hidden Markov model (HMM) is constructed to describe the probability distribution of the system mode. By integrating the probability distribution into the design of cost function, the coupled algebraic Riccati equation (CARE) is established. Then, a VI algorithm is proposed to solve the CARE and obtain the optimal asynchronous control. Moreover, theoretical analysis is performed to confirm the convergence of the proposed VI scheme and the stochastic stability of the closed-loop system. By applying the proposed optimal asynchronous control to a power system with single-machine connected to a infinite bus model, the simulation results demonstrate its effectiveness regardless of mode transitions.