未知系に対する学習的最小分散制御方策

抄録

A dual control problem for linear, discrete-time, single-input single-output stochastic systems with unknown parameters is considered under the criterion of minimum variance. The dual control system is designed as a recursive learning process which collects information for control through an identifier by use of the Kalman filter, and simultaneously is controlled adaptively by the minimal variance control strategy which computes, the control signal required to minimize the variance of a linear function of state in the succeeding step.
By using the observable state vector consisting of n past outputs and n-1 past inputs, the stochastic control problem can be solved analytically. The optimal regulator can be thus separated into two parts: one is a one-step predictor which predicts the distribution of the output caused by the disturbance and the parameter uncertainty, and the other is an adaptive minimum variance regulator.
It is also shown that the control law is updated at each time when a new information received. The control error for the optimal strategy gradually approaches the part caused by the disturbance of the system as the process proceeds. This means that the part caused by the parameter uncertainty disappears gradually.