Control of conditional output probability density functions for general nonlinear and non-Gaussian dynamic stochastic systems

A method to control the shape of the conditional output probability density function for general nonlinear-dynamic stochastic systems represented by a nonlinear ARMAX model is presented. The system is subjected to an arbitrary and bounded random input. Under the assumption that all the variables are uniformly bounded, a mathematical relationship is formulated among the conditional output probability density function, the system nonlinear structure and the characteristics of the random input. This leads to the establishment of a recursive formula for the evolution of the conditional output probability density functions for the system. An optimal control has thus been developed by embedding the system dynamics into the recursive formula and by minimising the difference between the conditional output probability density function and a target probability density function. It has been shown that the obtained control input is of an output feedback type, where the on-line measurements of the conditional output probability density functions are not required. An illustrative example is utilised to demonstrate the use of the control algorithm, some satisfactory results have been obtained.