Design of feedback control of a nonlinear stochastic system for targeting a pre-specified stationary probability distribution

• The target SPDF can be any Gaussian or non-Gaussian SPDF.
• The control laws can be obtained when the system and the target SPDF are determined.
• The online measurement of output PDFs are not needed.
• The proposed control method can be applied to various nonlinear stochastic systems.

An innovative approach to designing feedback control of a nonlinear stochastic system for targeting a pre-specified stationary probability density function (SPDF) is proposed based on the techniques for obtaining the exact stationary solutions of nonlinear stochastic system. First, the techniques for obtaining the exact stationary solutions of nonlinear stochastic systems, including the stationary potential and the generalized stationary potential, are briefly reviewed. Then, the approach to designing the feedback control of nonlinear stochastic systems for targeting a pre-specified SPDF and the Lyapunov function method for proving that the transient PDF of the controlled systems do converge to the pre-specified SPDF are presented. Finally, two examples are worked out in detail to illustrate the proposed approach and its effectiveness.