Shaping the PDF of the state variable based on piecewise linear control for non-linear stochastic systems  

作　　者：Lingzhi WANG Fucai QIAN 

机构地区：[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]Key Laboratory of Spacecraft In-orbit Fault Diagnosis and Repair,Xi'an Satellite Control Center,Xi'an 710043,China

出　　处：《Science China(Information Sciences)》2016年第11期102-112,共11页中国科学（信息科学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 61273127, U1534208);Key Program of National Natural Science Foundation of China (Grant No. 61533014);Key Laboratory for Fault Diagnosis and Maintenance of Spacecraft in Orbit (Grant No. SDML OF2015004);Scientific Research Plan Projects of Shannxi Education Department (Grant Nos. 16JK1690)

摘　　要：In this paper, we propose a shape-control scheme for non-linear stochastic dynamical systems to enable us to shape the probability density function （PDF） of the state variable. First, we derive the PDF analytical expression using the Fokker-Planck-Kolmogorov （FPK） equation obtained from stochastic systems. Then, we control the PDF shape by devising a piecewise linear control law whose parameters are calculated using the conjugated gradient method. Finally, we perform contrast simulation experiments to validate the effectiveness and superiority of the proposed algorithm.In this paper, we propose a shape-control scheme for non-linear stochastic dynamical systems to enable us to shape the probability density function （PDF） of the state variable. First, we derive the PDF analytical expression using the Fokker-Planck-Kolmogorov （FPK） equation obtained from stochastic systems. Then, we control the PDF shape by devising a piecewise linear control law whose parameters are calculated using the conjugated gradient method. Finally, we perform contrast simulation experiments to validate the effectiveness and superiority of the proposed algorithm.

关 键 词：non-linear stochastic systems probability density function shape control piecewise linear control Fokker-Planck-Kolmogorov （FPK） equation 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]