A New Control Approach of Output Probability Density Functions for Dynamic Stochastic Systems Using Parzen Window Estimate

A new control approach is proposed for the control of output probability density function (PDF) for dynamic stochastic systems with unknown prior probability. The Parzen window estimate of PDFs using the kernel function k_sigma(ldr) is used to represent the output PDFs of the dynamic stochastic system. This is then followed by a easy programming and a numeral control solution for the output distribution of the system using output PDFs tracking concept. A nonlinear quadratic optimization is performed using the PDFs minimum variance formula as a index performance to measure system characteristics, the Lyapunov stability analysis of this control strategy introduced in this note is performed to show the asymptotic stability of the closed loop system under some conditions.