A dual control for linear systems with control dependent plant and measurement noise

The problem of control of a stochastic system with control dependent noise is investigated. Both the system driving noise and system measurement noise are assumed to have control dependent terms. The approximation of neglecting higher order terms in the control is introduced in the derivation of the a posteriori conditional covariance matrices of the system state. These approximate conditional covariance matrices are used in a stochastic dynamic programming algorithm to obtain a linear feedback law. The control feedback matrices multiplying the estimates for system state are not those of the equivalent deterministic system and the separation theorem in its usual form does not apply to this class of problems. The control policy given by the algorithm reduces to the optimal control policy in two cases in which the optimal control is known. These are the case of no control dependent noise and the case of no measurement noise. A third order numerical example is investigated to illustrate the nature of the algorithm.