Research on PDF Shape Control for Nonlinear Stochastic System Using an Approximate Solution of FPK Equation

In this paper, we developed a probability density function (PDF) shape control method for non-linear stochastic systems using hybrid logistic (HLF) as an approximate PDF of the state variable. First, functional relationship between and controller was established based on Fokker–Planck–Kolmogorov (FPK) equation. Then, optimal derivation completed optimization inner product definition Hilbert space. This approach is suitable any system. To evaluate effectiveness performance proposed method, conducted comparison experiment with multi-Gaussian closure (MGC) exponential polynomial (EP) method. The experimental results show that, different types targeted PDFs (symmetric unimodal, asymmetric bimodal, trimodal shapes), obtained HLF can make variable track effectively. particular, when has or complex shape, technique comparatively better effects. Compared EP our requires much smaller number parameters, greatly reducing computational complexity while achieving same study provides another controlling variables in systems, which important research significance.