New Advances in Vibration Control and Nonlinear Dynamics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 August 2024) | Viewed by 1074

Special Issue Editors


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Guest Editor
School of Physics and Astronomy, Sun Yat-Sen University, Guangzhou 519082, China
Interests: active vibration control; nonlinear dynamics; piezoelectric shunting; dynamic analysis; inertial sensors

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Guest Editor
Aerospace and Mechanical Engineering Department, University of Liège, 4000 Liège, Belgium
Interests: nonlinear dynamics; piezoelectric shunt; vibration control; digital vibration absorber; modal analysis

Special Issue Information

Dear Colleagues,

Light structures have been used increasingly more frequently for system constructions for the sake of fuel efficiency, increased flexibility, and other higher levels of performance requirements. However, this will often make these structures lightly damped, and responses could be unacceptably amplified around the resonance, causing problems such as a reduction in structural integrity, compromise of instrument functionality, and even a threat to human lives. Vibration control has been known to be a frequent companion of these structures in recent decades, yet the research community’s interest is now shifting more from linear vibration control to nonlinear vibration control, which opens a wide range of research opportunities.

This Special Issue on “New Advances in Vibration Control and Nonlinear Dynamics” will gather relevant research contributions about the most significant and emerging topics in the field of vibration control and nonlinear structural dynamics. Relevant topics include the following:

  • Numerical methods for nonlinear systems: harmonic balance, multiple time/space scales, iterative solvers, nonlinear modeling;
  • Experimental nonlinear dynamics: random and harmonic excitations, shaker–structure interaction, benchmark experiments;
  • Model validation and system identification: data-driven model updates, experimental validation of nonlinear models;
  • Nonlinear phenomena in structures and structural monitoring: bridges, cable transportation systems, overhead contact lines, turbines, vehicles, etc.;
  • Control of vibrations and noise;
  • Vibration control of nonlinear structures: nonlinear control theory, stability, linearization.

Dr. Guoying Zhao
Dr. Ghislain Raze
Guest Editors

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Keywords

  • vibration control
  • nonlinear dynamics
  • nonlinear vibration control
  • active systems
  • instrument

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Published Papers (1 paper)

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Research

18 pages, 10629 KiB  
Article
H Differential Game of Nonlinear Half-Car Active Suspension via Off-Policy Reinforcement Learning
by Gang Wang, Jiafan Deng, Tingting Zhou and Suqi Liu
Mathematics 2024, 12(17), 2665; https://doi.org/10.3390/math12172665 - 27 Aug 2024
Viewed by 551
Abstract
This paper investigates a parameter-free H differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H control problem is reformulated [...] Read more.
This paper investigates a parameter-free H differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation’s solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method’s effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H control policy enhances both ride comfort and stability. Full article
(This article belongs to the Special Issue New Advances in Vibration Control and Nonlinear Dynamics)
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