Finite Horizon Optimal Control of Markov Jump Linear Systems with Multiple State Delays and Multiplicative Noises

This paper examines the optimal control for discrete-time Markov jump linear systems with multiple state delays and multiplicative noises. The necessary and sufficient condition for the problem admitting a unique solution is given. According to this theory, the optimal state feedback controller in the finite time domain is given analytically, and the optimal cost is found by solving a set of coupled differential Riccati equations. Our method is based on the maximum principle of stochastic systems. Establishing the relationship between the state and the costate is the key to solving the problem.