Semi-active bounded optimal control of uncertain nonlinear coupling vehicle system with rotatable inclined supports and MR damper under random road excitation

Z. G. Ying, G. F. Yan, Y. Q. Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review


The semi- active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, t he differential equations of motion of the coupling torsion- bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, t he minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

Original languageEnglish
Pages (from-to)707-729
Number of pages23
JournalCoupled Systems Mechanics
Issue number6
Publication statusPublished - 1 Dec 2018


  • Coupling vehicle system
  • Minimax strategy
  • MR damper
  • Random road excitation
  • Semi-active bounded optimal control
  • Stochastic dynamical programming
  • Stochastic nonlinear vibration
  • Uncertainty

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Mechanics of Materials

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