In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control ...In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.展开更多
基金supported in part by the National Natural Science Foundation of China(61903298,62073259,61773016)。
文摘In this work,a novel shape control approach of the probability density function(PDF)for nonlinear stochastic systems is presented.First,we provide the formula for the PDF shape controller without devising the control law of the controller.Then,based on the exact analytical solution of the Fokker-PlanckKolmogorov(FPK)equation,the product function of the polynomial and the exponential polynomial is regarded as the stationary PDF of the state response.To validate the performance of the proposed control approach,we compared it with the exponential polynomial method and the multi-Gaussian closure method by implementing comparative simulation experiments.The results show that the novel PDF shape control approach is effective and feasible.Using an equal number of parameters,our method can achieve a similar or better control effect as the exponential polynomial method.By comparison with the multiGaussian closure method,our method has clear advantages in PDF shape control performance.For all cases,the integral of squared error and the errors of first four moments of our proposed method were very small,indicating superior performance and promising good overall control effects of our method.The approach presented in this study provides an alternative for PDF shape control in nonlinear stochastic systems.
文摘间歇过程的优化控制依赖于过程精确的数学模型,数据驱动的建模方法是目前间歇过程模型研究中的热点问题。突破传统数据驱动建模方法中采用均方差(mean squared error,MSE)作为准则函数的思想,提出一种新颖的间歇过程数据驱动建模方法,引入了概率密度函数(probability density function,PDF)控制的概念,构造间歇过程模型误差控制系统,将模型的可调参数作为控制系统的输入,模型误差PDF的形状作为控制系统的输出,从而把开环模型参数辨识问题转化为模型误差PDF形状的闭环控制问题。通过可调参数控制模型误差PDF的空间分布状态,不仅能够保障模型精度,还可控制模型误差的空间分布状态,从而消除模型中的有色噪声。仿真实验表明,基于模型误差PDF形状的间歇过程数据驱动模型具有较好的建模精度、鲁棒性和泛化能力,为间歇过程的数据驱动建模提供了一条新途径。
