Direct solution of the parametric Stochastic Distribution Control problem

The stochastic distribution control (SDC) problem is a generalised form of the minimum variance control problem where non-Gaussian noise distributions are encountered. The problem has been previously solved using two alternative approaches. When it is assumed that the output probability distribution function (PDF) is measurable, then a parameterized controller is obtained. If on the other hand this assumption is removed (which corresponds to most practical cases), then the controller found is no longer parameterisable (i.e. it is a control action sequence). Both these approaches have thus far been solved using local Newtonian methods. In this paper a third alternative is presented which combines the desirable features of the previous two methods by finding a parameterized controller, without having to assume that the output PDF is directly measurable at the same time. In addition, global direct search algorithms are used to avoid convergence to local solutions. The approach is demonstrated on a SISO nonlinear system corrupted by non-Gaussian input noise.