Perturbation analysis of dual control problem for linear systems with unknown parameters

An approach to a dual control problem for nonlinear stochastic systems is presented. In general, an optimal stochastic controller has a complicated structure. This is due to the nonlinear Riccati equation involved in the optimization problem. This nature of the problem leads to probing and cautious properties of the control. For linear systems with unknown parameters, the perturbation analysis is used to obtain an optimal controller that minimizes a quadratic performance index, considering that noise intensities of the system disturbances are small. Explicit expression of the probing term and cautious term in the controller are derived