The shape control of probability density function (PDF) of the system state is an important topic in
stochastic systems. In this paper, we propose a control technique for PDF shape of the state variable in nonlinear
stochastic systems. Firstly, we derive and prove the form of the controller by investigating the Fokker-Planck-
Kolmogorov (FPK) equation arising from the stochastic system. Secondly, an approach for getting approximate
solution of the FPK equation is provided. A special function including some parameters is taken as the approximate
stationary solution of the FPK equation. We use nonlinear least square method to solve the parameters in the
function, and capture the approximate solution of the FPK equation. Substituting the approximate solution
into the form of the controller, we can acquire the PDF shape controller. Lastly, some example simulations are
conducted to verify the algorithm.
WANG Ling-zhi1,2* (王玲芝), QIAN Fu-cai1,3 (钱富才)
. Technique of Probability Density Function Shape Control for Nonlinear Stochastic Systems[J]. Journal of Shanghai Jiaotong University(Science), 2015
, 20(2)
: 129
-134
.
DOI: 10.1007/s12204-015-1600-4
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