随机系统稳态概率密度函数控制算法

Dual Control Algorithm for Stochastic System with Parameters Drifting

对于非线性随机系统,以均值、方差为控制目标的传统控制方法难以达到满意的控制效果,而概率密度函数控制能够反映非线性随机系统的各阶统计特征,可实现较为理想的控制效果。为此,针对非线性随机系统,提出了一种对系统状态稳态响应的概率密度函数进行控制的算法。该算法将概率密度函数展开为多项式形式,以FPK方程为工具,分析并得出多项式系数和控制多项式增益的关系方程组,以该方程组的解为控制增益的函数,通过进一步构造一个优化问题来解决该方程组存在的超定问题。根据目标概率密度函数的要求,确定出控制多项式的各项增益,给出并实现该算法的计算机实施步骤。仿真结果表明,所提出的算法有效可行,可离线计算且计算效率较高,能够实现概率密度函数的良好控制。

For nonlinear stochastic systems, the traditional control methods with the mean or variance as control target are difficult to a- chieve good control effect. The probability density function could express the complete characterization of the system, therefore it can reach an ideal performance. A novel algorithm of probability density function control is proposed for the nonlinear stochastic systems in the stationary case. The relationship between steady-state probability density function and stochastic system is successfully deduced with the method of expanding the probability density function into polynomial according to the FPK equations. An optimization problem is fur- ther constructed to solve the over-determined problem of the equations. Thus the gain control of polynomials is calculated according to the requirements of the target probability density function. Its computer implementation steps are given eventually. Simulation illustrates it is effective and feasible, which can be offline computation wwith high efficiency and good control effect.