The Probability Density Function Adjust for Uncertain Stochastic Systems

For nonlinear stochastic systems, a probability density function adjust algorithm is presented in this paper. Firstly, the state equation and the control equation are supposed to be the polynomial form, and an exponential form is used to represent probability density function. Then, the equations with respect to Tay lor series expansion coefficients and adjust gain accordingto the parameter relationships under steady-state conditions is obtained from FPK equation. Thus, the corresponding relationship between Taylor expansion coefficients and the polynomial coefficients of the control equation can be obtained through solving the equations. Then an optimization problem of track-target probability density function is constructed. After obtaining the optimization solution, the adjust gain can be gotten. Finally, examples show the effectiveness of the proposed method.