一类随机系统完全统计特征控制
The complete statistical characterization control for a class of stochastic systems

非线性随机系统完全统计特征控制优于低阶矩控制, 但往往因为算法的复杂性难以实际应用. 本文针对受 高斯白噪声激励的标量非线性随机系统, 针对状态响应提出了一种完全统计特征控制方法. 首先将刻画完全统计 特征的概率密度函数表示成指数函数, 利用FPK(Fokker-Planck-Kolmogorov)方程求出概率密度函数的各阶导数, 进 而建立指数函数Taylor展开的系数与待求反馈控制增益间的关系. 然后, 依据控制目标给出了求解反馈增益的优化 问题. 针对目标概率密度函数的不同情况, 分别给出了跟踪控制策略: 对于指数函数Taylor展开为有限项形式的情 况, 能够直接得到控制增益并完全跟踪目标概率密度函数; 其他情况下, 也能够达到较好的控制效果. 仿真验证了本 文方法的有效性.
For nonlinear stochastic systems, although the complete statistical characterization control method is superior to the traditional low moment control methods, it is difficult to apply the control law into the real system due to its complexity. A complete statistical characteristics control algorithm is presented for nonlinear stochastic systems excited by Gaussian white noise in this paper. Firstly, an exponential function is used to represent the probability density function which characterizes the statistical characteristics completely. Subsequently, the relationship between the Taylor series expansion coefficients of the exponential function and the feedback control gain is derived by the derivation of FPK (Fokker-Planck-Kolmogorov) equation constantly. Then, on the basis of the control objective, an optimization problem is given to obtain the feedback gain. And different tracking control strategies are given for different target probability density function: for the condition that the exponential expansion is finite terms, the control gains can be obtained directly, and completely track-target probability density function; under other conditions, a nearly track-target probability density could be got. The examples show the effectiveness of the proposed method.