Robust PDF control with guaranteed stability for non-linear stochastic systems under modelling errors

The authors consider the robust probability density function (PDF) control problem for nonlinear stochastic systems. The controlled systems are described by using non-Gaussian nonlinear difference equations with the un-modelled uncertainty and modelling error, as well as time delays. The non-linear multi-step-ahead predictive cost function is adopted and the relationship between the PDFs of the input and output via the uncertain mapping is established. With these formulations, the cost function can be bounded by a non-linear functional of the control input and the known bounds of the errors. Design algorithms are presented for the robust sub-optimal controller and further for the stabilisation controllers. Simulations are given to demonstrate the effectiveness of the proposed control algorithm.