Journal of Xidian University ›› 2020, Vol. 47 ›› Issue (4): 48-54.doi: 10.19665/j.issn1001-2400.2020.04.007

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Model predictive path integral method for nonlinear random vibration control

GUO Kongming1(),JIANG Jun2,XU Yalan1   

  1. 1. School of Mechano-Electronic Engineering, Xidian University, Xi’an 710071, China
    2. State Key Laboratory for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, China
  • Received:2020-04-01 Online:2020-08-20 Published:2020-08-14


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.

Key words: nonlinear vibration, random vibration, vibration control, model predictive control, path integral

CLC Number: 

  • O313