非线性随机振动控制的模型预测路径积分方法  

Model predictive path integral method for nonlinearrandom vibration control

作　　者：郭空明[1] 江俊[2] 徐亚兰[1] GUO Kongming;JIANG Jun;XU Yalan(School of Mechano-Electronic Engineering,Xidian University,Xi’an 710071,China;State Key Laboratory for Strength and Vibration,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安电子科技大学机电工程学院,陕西西安710071 [2]西安交通大学机械结构强度与振动国家重点实验室,陕西西安710049

出　　处：《西安电子科技大学学报》2020年第4期48-54,共7页Journal of Xidian University

基　　金：国家自然科学基金(11502183,11332008);陕西省自然科学研究计划(2018JQ1081,2018JQ1055)。

摘　　要：为了探索将非线性随机振动系统远离平凡平衡点的状态转移至平凡平衡点的手段,引入了一种模型预测路径积分控制方法。在特定条件下通过指数变换,非线性随机振动最优控制的哈密顿-雅可比-贝尔曼方程可以进行线性化。基于费曼-卡茨定理,可以采用路径积分方法求解最优控制力。引入模型预测控制的思想,可以根据系统实际状态实时更新控制力。针对随机扰动下范德波尔方程和三势阱达芬方程这两类典型系统的控制开展了数值仿真。仿真结果表明,系统状态可以很快地转移至平凡平衡点附近,控制力和即时成本在初始的波动后即转为单调下降。因此,该模型预测控制路径积分方法可以很好地应用于随机非线性系统远离平凡平衡点的振动。In order to find a way to transfer back the state of a nonlinear random vibration system which is far away from the trivial equilibrium point,a model predictive path integral control method is introduced.Under certain conditions,the Hamilton-Jacobi-Bellman equation for optimal control of nonlinear random vibration can be linearized by exponential transformation.Based on the Feynman-Kac theorem,the path integral method can be used to solve the optimal control force.By introducing the idea of model predictive control,the control force can be updated in real time according to the actual state of the system.Numerical simulation is carried out for the control of two typical systems,van der Pol equation and Duffing equation.The results show that the state of the system can be quickly transferred to the vicinity of the ordinary equilibrium point,while the control force and real-time cost decreases monotonically after the initial fluctuation.Therefore,the model predictive control path integration method can be well applied to the vibration of random nonlinear systems far from the trivial equilibrium point.

关 键 词：非线性振动 随机振动 振动控制 模型预测控制 路径积分 

分 类 号：O313[理学—一般力学与力学基础]