Adaptive dual control for stochastic nonlinear systems with free end-time

This short paper discusses the problem of controlling stochastic nonlinear systems where the end-time of the process has to be determined on-line. Since the optimal solution is not obtainable, a dual control method is developed for this class of problems. The algorithm has the property that the control, which is restricted to be causal, utilizes the statistical description of the future observations, i.e., it is of the closed-loop, rather than feedback type. This property allows the controller to enhance the estimation via the dual effect and thus improve the overall performance. The method is illustrated by applying it to an interception problem. Simulation studies on this particular problem provide further insight into how the dual effect of the control can be utilized in nonlinear problems. They also indicate the potential value of the algorithm presented here to practical problems.