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

• DOI: 10.1007/s11432-015-0401-9
• Publication Date: 2016-10-18T11:24:16Z
• Authors: Lingzhi Wang; Fucai Qian
• Keywords: State variable; Stochastic control; Control variable

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.