非线性随机系统的概率密度追踪控制

Target Control Design for Stationary Probability Density Function of Nonlinear Stochastic System

针对目前非线性随机系统控制方法的设计复杂、计算成本高以及缺乏稳定性或收敛性证明等缺点,提出了一种全新的基于等效非线性系统法求近似稳态解的思想设计的非线性随机系统的反馈控制,使受控系统输出的稳态概率密度函数逼近事先给定的目标概率密度函数.利用Lyapunov函数法证明了受控系统的收敛性.数学仿真结果证明了这种方法的可行性和正确性.

Current control methods for nonlinear stochastic system have shortcomings such as complex design procedures high costs, and lack of stability and convergence proof. Considering these problems, based on the equivalent nonlinea system method for obtaining the approximate stationary solutions of the nonlinear stochastic systems, this paper propose an innovative design procedure for the feedback control of stochastic nonlinear system. The control aims at making the statistical information of the output steady-state probability density function （SPDF） follow those of a target SPDF Lyapunov function method is presented to prove that the controlled systems do approach to the pre-specified SPDF Simulation results are given to illustrate the procedure and demonstrate the efficiency.