A new Lyapunov approach for global synchronization of non-autonomous chaotic systems

This paper proposes a new approach for finding the Lyapunov function to study the sufficient global synchronization criterion of master-slave non-autonomous chaotic systems via linear state error feedback control. The approach is first demonstrated in a synchronization scheme for the second-order non-autonomous chaotic systems and then generalized to the schemes for the nth-order non-autonomous chaotic systems. Some algebraic synchronization criteria for the second-order chaotic systems are obtained. The sharpness of the new criteria is compared with that of the existing criteria of the same type by numerical examples.     

An analytic approximate approach for free oscillations of self-excited systems

A new analytic approximate technique for non-linear problems, namely the homotopy analysis method, is employed to propose an approach for free oscillations of self-excited systems. Different from perturbation methods on this topic, this approach does not depend upon any small/large parameters at all and therefore is valid for free oscillations of all self-excited systems. Besides, unlike other analytic techniques, this approach provides us with a convenient way to control the convergence of approximation series and adjust convergence regions when necessary. Two examples are employed to illustrate the validity and flexibility of this approach.     

Hyperchaos synchronization of fractional-order arbitrary dimensional dynamical systems via modified sliding mode control

This paper considers the design of adaptive sliding mode control approach for synchronization of a class of fractional-order arbitrary dimensional hyperchaotic systems with unknown bounded disturbances. This approach is based on the principle of sliding mode control and adaptive compensation term for solving the problem of synchronization of the unknown parameters in fractional-order nonlinear systems. In particular, a novel fractional-order five dimensional hyperchaotic system has been introduced as a representative example. Furthermore, global stability and asymptotic synchronization between the outputs of master and slave systems can be achieved based on the modified Lyapunov functional and fractional stability condition. Simulation results are provided in detail to illustrate the performance of the proposed approach.     

On the boundedness of motions of mechanical systems described by fuzzy ordinary differential equations

A new approach is proposed for analyzing the dynamics of fuzzy systems. Within the framework of the approach, boundedness conditions for the solutions of fuzzy systems are established on the basis of the classical inequalities of convex geometry __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 12, pp. 93–99, December 2005.     

A new approach to almost-sure asymptotic stability of stochastic systems of higher dimension

The almost sure asymptotic stability of higher-dimensional linear stochastic systems and of a special class of nonlinear stochastic systems with homogeneous drift and diffusion coefficients of order one is studied. Based on the well-known Khasminskii's theorem, a new approach for obtaining the regions of almost sure asymptotic stability and instability without evaluating the stationary probability density of the diffusion process defined on unit hypersphere is proposed. Two examples of two and three degree-of-freedom linear stochastic systems are given to illustrate the application and effectiveness of the proposed approach combined with stochastic averaging.     

An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude

The currently developed analytic technique known as the homotopy analysis method is employed to propose a new approach for free oscillations of positively damped systems with algebraically decaying amplitude. In contrast to perturbation techniques, this approach is valid even for damped systems without any small/large parameters. Besides, unlike other analytic techniques, this approach itself provides us with a convenient way to adjust and control convergence of approximation series. Some typical examples are employed to illustrate its validity, effectiveness and flexibility.     

Probabilistic interval reliability of structural systems

The probabilistic reliability approach is the most widely used method for reliability analysis. The recent research shows that the reliabilities of structural systems strongly depend on the parameters of the probability model. It is possible that the little error in the estimation of the parameters may lead to the remarkable error of the resulting probability. In this study, we introduce the interval approach into the conventional reliability theory. We present a novel approach which allows us to obtain the system failure probability interval from the statistical parameter intervals of the basic variables. This approach is a combination of the two techniques, namely the classical reliability theory and the interval analysis. In the end of this paper, we show the feasibility of the proposed approach through two examples of the truss systems.     

Synchronization control of oscillator networks using symbolic regression

Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far-reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly effective and interpretable control functions for such systems.     

Equations of motion for mechanical systems: A unified approach

This paper presents a unified framework from which emerge the Lagrange equations, the Gibbs-Appell Equations and the Generalized Inverse Equations for describing the motion of constrained mechanical systems. The unified approach extends the applicability of the first two approaches to systems where the constraints are non-linear functions of the generalized velocities and are not necessarily independent. Furthermore, the approach leads to the Explicit Gibbs-Appell Equations.     

Unilateral Multibody Dynamics

Contact processes may be represented by local discretization, by a rigid body approach or by a mixed method using both ideas. For the dynamics of mechanical systems a rigid body approach is described achieving good results also for multiple contact problems. This paper considers mainly contacts in multi-body systems where the corresponding contact constraints vary with time thus generating structure-variant systems. The equations of motion for dynamical systems with such an unilateral behavior are discussed, solution methods and applications are presented.     

离散型设置粘弹阻尼结构的复模态综合法

本文利用粘弹材料的本构方程,对粘弹阻尼结构的模态分析表达式进行了理论推导,进而将Craig的复模态综合法推广到粘弹阻尼系统.本文还发展了一种处理刚体模态的方法,从而克服了Craig法的不足,解决了含粘性阻尼、粘弹阻尼的复杂结构的隔振设计问题.     

Projective synchronization between two different time-delayed chaotic systems using active control approach

In this paper, we investigate the projective synchronization between two different time-delayed chaotic systems. A suitable controller is chosen using the active control approach. We relax some limitations of previous work, where projective synchronization of different chaotic systems can be achieved only in finite dimensional chaotic systems, so we can achieve projective synchronization of different chaotic systems in infinite dimensional chaotic systems. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective synchronization between two different time-delayed chaotic systems. The validity of the proposed method is demonstrated and verified by observing the projective synchronization between two well-known time-delayed chaotic systems; the Ikeda system and Mackey–Glass system. Numerical simulations fully support the analytical approach.     

Decentralized control of uncertain nonlinear stochastic systems based on DSC

In this paper, the decentralized stabilization control approach based on the dynamic surface control (DSC) is proposed for a class of large-scale interconnected stochastic nonlinear systems. The proposed approach combined the existing dynamic surface control (DSC) with back-stepping technique. This approach can overcome the problem of “explosion of complexity” inherent in the back-stepping method. Thus, the proposed control approach is simpler than the traditional back-stepping control method for the large-scale interconnected stochastic nonlinear systems. The stability analysis shows that all the signals in the closed-loop system are uniformly ultimately bounded (UUB). Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Two-scale command shaping for feedforward control of nonlinear systems

This paper presents a critical analysis of the two-scale command shaping (TSCS) feedforward control technique as applied to nonlinear Duffing oscillators. TSCS is an approach for tailoring a flexible system’s applied control input to reduce undesirable residual vibrations using multiple problem scales, command shaping of a linear subproblem, and cancelation of a remaining nonlinear subproblem. As shown herein, TSCS proves to be an effective method for feedforward control of nonlinear systems. The strategy outperforms conventional and nonlinearly informed command shaping strategies in traditional and non-traditional Duffing systems (e.g., Duffing systems with quadratic nonlinearity and Coulomb damping). The TSCS approach is also extended herein to nonlinear systems with uncertain parameters through the implementation of robust command shaping strategies and the extended Kalman filtering parameter estimation technique.     

Nonlinear state-observer control for projective synchronization of a fractional-order hyperchaotic system

In this paper, we consider an observer-based control approach for manipulating projective synchronization of nonlinear systems in high dimensional. Based on the stability theory of the fractional-order dynamical system, a nonlinear state observer is designed which can achieve projective synchronization in a class of high dimensional fractional-order hyperchaotic systems without restriction of partial-linearity and calculating the Lyapunov index of system. Simulation studies are included to demonstrate the effectiveness and feasibility of the proposed approach and synthesis procedures.     

Time domain passivity control of time-delayed bilateral telerobotics with prescribed performance

Nonlinear Dynamics - A novel approach applying the extended prescribed performance control (PPC) and the wave-based time domain passivity approach (wave-based TDPA) to teleoperation systems is...     

A Lagrangian-based continuum homogenization approach applicable to molecular dynamics simulations

The continuum notions of effective mechanical quantities as well as the conditions that give meaningful deformation processes for homogenization problems with large deformations are reviewed. A continuum homogenization model is presented and recast as a Lagrangian-based approach for heterogeneous media that allows for an extension to discrete systems simulated via molecular dynamics (MD). A novel constitutive relation for the effective stress is derived so that the proposed Lagrangian-based approach can be used for the determination of the “stress–deformation” behavior of particle systems. The paper is concluded with a careful comparison between the proposed method and the Parrinello–Rahman approach to the determination of the “stress–deformation” behavior for MD systems. When compared with the Parrinello–Rahman method, the proposed approach clearly delineates under what conditions the Parrinello–Rahman scheme is valid.     

Observer-based adaptive fuzzy backstepping control of MIMO stochastic nonlinear strict-feedback systems

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multiinput and multioutput (MIMO) uncertain stochastic nonlinear strict-feedback systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Utilizing the designed the fuzzy state observer and by combining the adaptive backstepping control design, an adaptive fuzzy output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded (SUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by appropriate choice of the design parameters. A simulation example is provided to show the effectiveness of the proposed approach.