国家自然科学基金资助项目(12272283)和中国-中东欧国家联合教育资助项目(2021122)
本文研究了在FOPID控制器控制下的广义Van Der Pol随机系统瞬态概率密度函数和可靠性函数变化情况.首先,引入广义谐和函数,将快变变量转换为慢变变量,并利用分数阶微积分的性质,获得了FOPID控制器在慢变变量形式下的新表达式.在此基础上,由于径向基神经网络具有准确性高,易于求解高维问题,求解速度快等优势,所以我们应用径向基神经网络分别对该随机系统所满足的前向和后向柯尔莫哥洛夫方程进行求解,得到随机系统的瞬态概率密度函数和可靠性函数.最后,通过分析控制器中分数阶导数和分数阶积分对Van Der Pol随机系统响应和可靠性的影响,我们得到结论,分数阶控制器一定程度上会增强系统的响应,并导致分岔.
In this paper, the transient probability density function and reliability function of generalized Van Der Pol stochastic system controlled by FOFOPID controller are studied. Firstly, the generalized harmonic function is introduced to transform the fast variable into the slow variable, and the new expression of FOFOPID controller in the form of slow variable is obtained by using the properties of fractional calculus. On this basis, because the radial basis function neural network has the advantages of high accuracy, easy to solve highdimensional problems, fast solving speed and so on, we apply the radial basis function neural network to solve the forward and backward Kolmogorov equations satisfied by the stochastic system respectively, and obtain the transient probability density function and reliability function. Finally, by analyzing the influence of fractional calculus in the controller on the response and reliability of Van Der Pol stochastic system, we come to the conclusion that fractional order controller will enhance the response of the system to a certain extent and lead to bifurcation.
管煜,李伟,杨贵东,娜塔莎.特索里维奇. FOPID控制器对广义VDP随机系统瞬态响应和可靠性的控制[J].动力学与控制学报,2023,21(10):34~42; Guan Yu, Li Wei, Yang Guidong, Natasa Trisovic. FOPID Controller for Transient Response and Reliability Control of Generalized VDP Stochastic Systems[J]. Journal of Dynamics and Control,2023,21(10):34-42.
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