基于粒子群-蒙特卡罗的PDF形状控制策略

PDF shape control strategy based on particle swarm optimization-Monte Carlo

针对传统随机控制方法不能控制随机变量的高阶矩问题,提出一种基于粒子群-蒙特卡罗的概率密度函数(Probability Density Function,PDF)形状控制策略。通过设计多项式控制器和积分形式的目标函数,将PDF形状控制问题转化为控制器增益的优化问题。采用粒子群算法优化PDF形状控制器的增益,同时引入蒙特卡罗方法求解定积分形式的目标函数,使得非线性随机系统状态变量的PDF形状与期望的PDF形状一致。实验结果表明,该控制策略能够解决PDF的形状控制问题,而且缩短了粒子群算法的计算时间,提升了粒子群算法在PDF形状控制器增益中的优化性能。

To address the problem that the traditional random control methods cannot control high-order moments of random variables,a probability density function(PDF)shape control strategy based on particle swarm optimization-Monte Carlo is proposed.By designing a polynomial controller and an objective function with integral form,the PDF shape control problem is transformed into an optimization problem for the controller gain.The particle swarm optimization algorithm is adopted to optimize the gains of PDF shape controller,and the Monte Carlo method is introduced to solve the objective function with definite integral form,to make the PDF shape of the state variable being consistent with the desired PDF shape for nonlinear stochastic systems.Experiment results show that this control strategy can solve the shape control problem of PDF,shorten the calculation time of particle swarm algorithm,and improve the optimization performance of the particle swarm algorithm in PDF shape controller gain.