Research on vibration reduction of semi-active suspension system of quarter vehicle based on time-delayed feedback control with body acceleration

In this paper, the mechanical model of two-degree-of-freedom vehicle semi-active suspension system based on time-delayed feedback control with vertical acceleration of the vehicle body was studied. With frequency-domain analysis method, the optimization of time-delayed feedback control parameters of vehicle suspension system in effective frequency band was studied, and a set of optimization method of time-delayed feedback control parameters based on “equivalent harmonic excitation” was proposed. The time-domain simulation results of vehicle suspension system show that compared with the passive control, the time-delayed feedback control based on the vertical acceleration of the vehicle body under the optimal time-delayed feedback control effectively broadens the vibration absorption bandwidth of the vehicle suspension system. The ride comfort and stability of the vehicle under random road excitation are significantly improved, which provides a theoretical basis for the selection of time-delayed feedback control strategy and the optimal design of time-delayed feedback control parameters of vehicle suspension system.

Delayed Feedback Control of Hidden Chaos in the Unified Chaotic System between the Sprott C System and Yang System

In this paper, the influence of delayed feedback on the unified chaotic system from the Sprott C system and Yang system is studied. The Hopf bifurcation and dynamic behavior of the system are fully studied by using the central manifold theorem and bifurcation theory. The explicit formula, bifurcation direction, and stability of the periodic solution of bifurcation are given correspondingly. The Hopf bifurcation diagram and chaotic phenomenon are also analyzed by numerical simulation to prove the correctness of the theory. It shows that this delay control can only be applied to the hidden chaos with two stable equilibria.

Finite-time stabilization of discontinuous fuzzy inertial Cohen–Grossberg neural networks with mixed time-varying delays

This article aims to study a class of discontinuous fuzzy inertial Cohen–Grossberg neural networks (DFICGNNs) with discrete and distributed time-delays. First of all, in order to deal with the discontinuities by the differential inclusion theory, based on a generalized variable transformation including two tunable variables, the mixed time-varying delayed DFICGNN is transformed into a first-order differential system. Then, by constructing a modified Lyapunov–Krasovskii functional concerning with the mixed time-varying delays and designing a delayed feedback control law, delay-dependent criteria formulated by algebraic inequalities are derived for guaranteeing the finite-time stabilization (FTS) for the addressed system. Moreover, the settling time is estimated. Some related stability results on inertial neural networks is extended. Finally, two numerical examples are carried out to verify the effectiveness of the established results.

Stochastic Response of Nonlinear Viscoelastic Systems with Time-Delayed Feedback Control Force and Bounded Noise Excitation

In this paper, an approximate analytical procedure is proposed to derive the stochastic response of nonlinear viscoelastic systems with time-delayed feedback control force and bounded noise excitation. The viscoelastic force and the time-delayed control force depend on the past histories of the state variables, which will result in infinite-dimensional problem in theoretical analysis. To resolve these difficulties, the viscoelastic force and the time-delayed control force are approximated by the current state variable based on the quasi-periodic behavior of the systematic response. Then, by using the stochastic averaging method for strongly nonlinear systems subjected to bounded noise excitation, an averaged equation for the equivalent system is derived. The Fokker–Plank–Kolmogorov (FPK) equation of the associated averaged equation is solved to derive the stochastic response of the equivalent system. Finally, two typical nonlinear viscoelastic oscillators are worked out and the results demonstrated the effectiveness of the proposed procedure. By utilizing the quasi-periodic behavior and stochastic averaging method of the strongly nonlinear system, the time-delayed control force and the viscoelastic terms can be simplified with equivalent damping force and equivalent restoring force and the resonant response under bounded noise excitation can be obtained analytically. The numerical results showed the accuracy of the proposed method.

Amplitude modulation control method for bursting dynamics under time-delayed feedback

Time-delayed feedback control is one of the important active control methods for complex dynamical behaviors in nonlinear systems. Yet its relationship and effectiveness on multiple time scale dynamics need to be further explored. As a purpose to gain insight into such complexity, we investigate the effectiveness of amplitude modulation in controlling (suppressing or enhancing) bursting oscillations in a classical mechanical oscillator with time-delayed feedback. It is shown how the presence of delay can change the amplitude of the singular cycle oscillations, or suppress them altogether. The results are compared to the conventional periodic perturbation method. In many cases, the amplitudes of periodic solutions under delayed feedback are easier to satisfy the technical requirements. If the delayed feedback is added, stable periodic bursting can be easily accomplished. Therefore, we demonstrate that an effective vibration modulation for bursting dynamics is possible if appropriate time delay and feedback gains are chosen.

Leader Selection and Dynamics Analysis under Leader-Based Collective Bargaining for Buyers’ Alliance

This paper focuses on the leader selection from the leader-based collective bargaining system, where buyers form an alliance and designate one of them as the leader to bargain with the supplier for a lower wholesale price of their common component. We construct the dynamic bargaining system consisting of two heterogeneous buyers and one supplier to analyze the influence of the enterprise nature and bargaining power on the leader selection. It was proved that the buyer with stronger bargaining power should be the leader. However, we find that, when the buyers are heterogeneous, the result may be different. In order to explore which factor plays a more important role in the leader selection, we design two rounds of bargaining for comparison. The interesting results imply that whether the bargaining power will reverse the leader selection in the first round depends on its growth rate. The nonlinear dynamics theory is also introduced to analyze the complex behaviors in the dynamic bargaining system. We analyze the influence of adjustment speed on the dynamic bargaining system and obtain the conditions required to maintain system stability. Considering the significance of system stability, the delayed feedback control mechanism is adopted to drive chaos back to stability.