Implicit dual controller based on stochastic integration rule

A new implicit dual control method is proposed providing a suboptimal solution of the optimal control problem for discrete linear stochastic state space model with unknown and unobservable parameters. The solution is based on Bellman optimization recursion where two stages of optimization recursion will be pursued. The resulting controller ensures both dual properties of the suboptimal control, i.e. caution and probing. In order to be able to determine the control, the stochastic integration rule is employed for approximate evaluation of expectations. The dual control is then obtained using suitable iterative numerical algorithm. The proposed implicit dual controller is compared to the explicit dual controllers which are easier to derive but require proper tuning of design parameters.