Optimal bounded control of stochastically excited strongly nonlinear vibro-impact system

Xudong Gu, Zichen Deng, Rongchun Hu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

An optimal bounded control strategy for strongly nonlinear vibro-impact systems under stochastic excitations with actuator saturation is proposed. First, the impact effect is incorporated in an equivalent equation by using a nonsmooth transformation. Under the assumption of light damping and weak random perturbation, the system energy is a slowly varying process. By using the stochastic averaging of envelope for strongly nonlinear systems, the partially averaged Itô stochastic differential equation for system energy can be derived. The optimal control problem is transformed from the original optimal control problem for the state variables to an equivalent optimal control problem for the system energy, which decreases the dimensions of the optimal control problem. Then, based on stochastic maximum principle, an adjoint equation for the adjoint variable and the maximum condition of partially averaged control problem are established. For infinite time-interval ergodic control, the adjoint variable is assumed to be a stationary process and the adjoint equation can be further simplified. Finally, the probability density function of the system energy and other statistics of the optimally controlled system are derived by calculating the associated Fokker–Plank–Kolmogorov equation. For comparison, the bang–bang control is also investigated and the control results are compared to show the advantages of the developed control strategy.

Original languageEnglish
Pages (from-to)477-486
Number of pages10
JournalJVC/Journal of Vibration and Control
Volume27
Issue number3-4
DOIs
StatePublished - Feb 2021

Keywords

  • Fokker–Plank–Kolmogorov equation
  • Nonlinear vibro-impact system
  • stochastic averaging
  • stochastic maximum principle
  • stochastic optimal control

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