Adaptive dual control of discrete-time distributed-parameter stochastic systems

The problem of adaptive dual control of discrete-time distributed-parameter stochastic systems is examined. It is shown that there exists an important difference between feedback and closed-loop policies of control for this type of system as for the lumped parameter case. This difference is based on the adaptivity feature of the control. Namely, when the control policy affects both the state and its uncertainty (dual effect) it possesses the so-called feature of active adaptivity and can only be a characteristic of a closed-loop policy, whereas a feedback policy can only be passively adaptive. These results can be used to develop a control algorithm for non-linear problems for which the realization of optimal control laws involves control strategies with both learning and control features.