上海交通大学学报（英文版） ›› 2015, Vol. 20 ›› Issue (2): 129-134.doi: 10.1007/s12204-015-1600-4
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Technique of Probability Density Function Shape Control for Nonlinear Stochastic Systems
WANG Ling-zhi1,2* (王玲芝), QIAN Fu-cai1,3 (钱富才)
- (1. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China; 2. School of Automation, Xi’an University of Posts and Telecommunications, Xi’an 710121, China; 3. The National-Local Joint Engineering Laboratory for New Network and Detection Control, Xi’an Technological University, Xi’an 710032, China)
Technique of Probability Density Function Shape Control for Nonlinear Stochastic Systems
WANG Ling-zhi1,2* (王玲芝), QIAN Fu-cai1,3 (钱富才)
- (1. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an 710048, China; 2. School of Automation, Xi’an University of Posts and Telecommunications, Xi’an 710121, China; 3. The National-Local Joint Engineering Laboratory for New Network and Detection Control, Xi’an Technological University, Xi’an 710032, China)
摘要： 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.
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