M-measurements Indefinite Linear Quadratic Optimal Control for Bilinear Stochastic Systems with Multiplicative Noises

The finite horizon indefinite linear quadratic (LQ) optimal output feedback control problem for discrete time stochastic systems with multiplicative noises and disturbed measurements is considered. In this problem, the weighting matrices of the quadratic cost functional are indefinite, and the optimal control does have the so-called dual effect. In order to make a compromise between the optimality and the computation complexity, a kind of M-measurements feedback control design approach is adopted. Based on the dynamic programming, the M-measurements feedback control for the bilinear stochastic systems (BLSS), which incorporates future measurements into the current control computation, can be solved in backward time, and the optimal solution is given in terms of a kind of generalized difference Riccati equation of the same dimensions as that of the plant. Simulation results show the superiority of the proposed algorithm over other widely used methods based on the certainty equivalence.