Bounded stochastic distributions control for pseudo-ARMAX stochastic systems

Following the recently developed algorithms for the control of the shape of the output probability density functions for general dynamic stochastic systems, this note presents the modeling and control algorithms for pseudo-ARMAX systems, where, different from all the existing ARMAX systems, the considered system is subjected to any arbitrary bounded random input and the purpose of the control input design is to make the output probability density function of the system output as close as possible to a given distribution function. At first, the relationship between the input noise distribution and the output distribution is established. This is then followed by the description on the control algorithm design. A simulated example is used to demonstrate the use of the algorithm and encouraging results have been obtained