Dual Control of Linearly Parameterised Models via Prediction of Posterior Densities

A suboptimal dual control policy is presented for linearly parameterised systems with unknown parameters, additive Gaussian noise and quadratic cost. The dual effect of the control action is taken into account through the prediction of the future posterior densities of the model parameters θ. If θ has a normal prior density, the model response is linear in θ and contains no autoregressive part, then the posterior densities of θ are normal and their covariance matrices are known functions of the control actions. Replacing the unknown future posterior means by the current parameter estimates, one can easily approximate the costto- go. Two examples of FIR models illustrate the superiority ofthis dual control policy over two classical passive policies, namely heuristic certainty equivalence control and open-loop-feedback-optimal control.