Optimal LQG Control for Discrete-Time System with Multiplicative Noise and Multiple State Delays

This paper focuses on the optimal linear quadratic Gaussian (LQG) control problem for stochastic discrete-time systems with multiplicative noise and multiple delays in the state. The relationship between the state and the costate is obtained by using the Pontryagin's maximum principle. The necessary and sufficient condition for the problem existing a unique optimal controller is given. Moreover, an explicit expression of the optimal LQG controller and the associated minimum cost function are presented in terms of coupled Riccati equations. It should be stressed that these results are based on the key technical tool, which established relations between the state and the costate of the LQG systems.