Indefinite LQ Optimal Control for Systems with Multiplicative Noises: The Incomplete Information Case

摘要

The finite horizon indefinite LQ optimal output feedback control based on anti-noise materials for discrete time stochastic systems with state and control dependent multiplicative noises is considered. In the case of no standard Separation Theorem, a separation property in suboptimal sense holds as long as a generalized difference Riccati equation (GDRE) admits a solution. Then, the optimal output feedback control can be computed iteratively via a state feedback control problem and an estimation problem optimal with respect to each other. A completion of squares technique was used to derive the linear output feedback control, and an equivalent system transformation approach and the Kalman filter design method were used to obtain the recursive linear optimal state estimation algorithm.