Active sliding observer scheme based fractional chaos synchronization

In this paper, a novel observer scheme is proposed for synchronization of fractional order chaotic systems. Our approach employs a combination of a classical sliding observer and an active observer, where the active observer serves to increase the attraction strength of sliding surface. Using the theory of Lyapunov function, synchronization of the fractional order response with the fractional order drive system is achieved in both ideal and mismatched cases. By merit of fractional order differentiation and integration, i.e. differintegration formula, it is proved that state synchronization is established in a finite time. Numerical simulations are presented to verify the effectiveness of the proposed observer.     

The intermittent behavior of a second-order non-linear non-autonomous oscillator

The experimental time-series produced by a second-order non-linear, non-autonomous, closed-loop electronic circuit were recorded and subsequently evaluated. The correlation and embedding dimensions, as well as the corresponding Kolmogorov entropies of the oscillating system, have been numerically calculated and compared to the corresponding Lyapunov exponents.     

Periodic solutions of non-autonomous second-order systems with a p-Laplacian

In this paper, we investigate non-autonomous second-order systems with a p-Laplacian and obtain existence results for periodic solutions with the dual least action principle.     

GLOBAL PERIODIC ATTRACTOR OF ATHIRD-ORDER PHASE-LOCKED LOOP

1.IntroductionandPreliminariesInthispaper,weconsidertheequation-..rx 7isecZx ac(a Zitgx)isecZx 7btgx~Bsinat,(1.1)wherea>0,b>0,ac>0,0andu>0areconstats.Theequivalelltthirdordersystemis(1'1)0=ohasbeenstudiedbyL.Wang,M.Q.WangandZ.Q.Luin[1];theirresultshowsthatthezerosolutionof(1.1)0=oisuniformlyasymptoticallystable.Inthispaperwewillprovetheexistenceofaglobalperiodicattractorfor(1.l)providedIIIissmallenough.Thephysicalimplicationofthisresulti.e.,theloopcanstayinlockinspiteofitisperturbed.The…     

The existence of periodic solutions of non-autonomous second-order Hamiltonian systems

The purpose of this paper is to study the existence of periodic solutions for a class of non-autonomous second-order Hamiltonian systems. Some new existence theorems are obtained by using the least action principle and the saddle point theorem.     

Nonlinear and chaos control of a micro-electro-mechanical system by using second-order fast terminal sliding mode control

In this paper, a novel second-order fast terminal sliding mode control (SFTSMC) scheme is proposed to suppress the chaotic motion of a micro-mechanical resonator with system uncertainty and external disturbance. To obtain a better disturbance rejection property, a fuzzy logic system is introduced to estimate the upper boundary of the sum of system uncertainty and external disturbance. Moreover, we employ the finite-time technique to obtain the properties of fast response and high precision. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme.     

二阶非自治Hamilton 系统周期解的新结果

研究了二阶非自治Hamilton系统（t）-B（t）x（t）＋▽H（t,x（t））=0,在局部超二次条件下周期解的存在性问题,利用山路定理和局部环绕定理得到了新的存在性定理,改进了已有结果.     

Homoclinic solutions for a class of non-autonomous subquadratic second-order Hamiltonian systems

In this paper we consider the existence of homoclinic solutions for the following second-order non-autonomous Hamiltonian system:

(HS)     

Generalized projective synchronization of a class of hyperchaotic systems based on state observer

In this paper, the generalized projective synchronization of a class of hyperchaotic systems is studied. On the basis of the state observer, it is not necessary to calculate the Lyapunov exponents, which makes this scheme simpler. Hyperchaotic Lü system and hyperchaotic Rössler systems are used as examples to validate the effectiveness of the proposed method.     

Global periodic attractor of a class of third-order phase-locked loop

The uniform boundedness and existence of a global periodic attractor for a third-order phase-locked loop with general phase detector characteristics and frequency modulation input is proved under some parametric conditions. Project supported by the National Natural Science Foundation of China.     

Existence of homoclinic solutions for a class of second-order non-autonomous Hamiltonian systems

By using the variant version of Mountain Pass Theorem, the existence of homoclinic solutions for a class of second-order Hamiltonian systems is obtained. The result obtained generalizes and improves some known works.     

Construction of a terminal control for a second-order system with state constraints

We consider a terminal control problem with state constraints and additional constraints on the qualitative behavior of the terminal trajectory for a second-order system in two-dimensional Euclidean space under geometric constraints on control parameters. A class of control functions solving this control problem is proposed. Numerical results for the control system with model parameters are presented.     

No-gap second-order optimality conditions for optimal control problems with a single state constraint and control

The paper deals with optimal control problems with only one control variable and one state constraint, of arbitrary order. We consider the case of finitely many boundary arcs and touch times. We obtain a no-gap theory of second-order conditions, allowing to characterize second-order quadratic growth.     

Representation of infinite-dimensional neutral non-autonomous control systems

This paper studies the well-posedness of a class of non-autonomous neutral control systems in Banach spaces. We prove that such systems are represented by absolutely regular non-autonomous linear systems in the sense of Schnaubelt [R. Schnaubelt, Feedback for non-autonomous regular linear systems, SIAM J. Control Optim. 41 (2002) 1141-1165]. This paper can be considered as the non-autonomous version of the work presented in [H. Bounit, S. Hadd, Regular linear systems governed by neutral FDEs, J. Math. Anal. Appl. 320 (2006) 836-858].     

Observer-based adaptive control of chaos in nonlinear discrete-time systems using time-delayed state feedback

A new approach to adaptive control of chaos in a class of nonlinear discrete-time-varying systems, using a delayed state feedback scheme, is presented. It is discussed that such systems can show chaotic behavior as their parameters change. A strategy is employed for on-line calculation of the Lyapunov exponents that will be used within an adaptive scheme that decides on the control effort to suppress the chaotic behavior once detected. The scheme is further augmented with a nonlinear observer for estimation of the states that are required by the controller but are hard to measure. Simulation results for chaotic control problem of Jin map are provided to show the effectiveness of the proposed scheme.     

Effects of time delays on bifurcation and chaos in a non-autonomous system with multiple time delays

Time delays are often sources of complex behavior in dynamic systems. Yet its complexity needs to be further explored, particularly when multiple time delays are present. As a purpose to gain insight into such complexity under multiple time delays, we investigate the mechanism for the action of multiple time delays on a particular non-autonomous system in this paper. The original mathematical model under consideration is a Duffing oscillator with harmonic excitation. A delayed system is obtained by adding delayed feedbacks to the original system. Two time delays are involved in such system, one of which in the displacement feedback and the other in the velocity feedback. The time delays are taken as adjustable parameters to study their effects on the dynamics of the system. Firstly, the stability of the trivial equilibrium of the linearized system is discussed and the condition under which the equilibrium loses its stability is obtained. This leads to a critical stability boundary where Hopf bifurcation or double Hopf bifurcation may occur. Then, the chaotic behavior of such system is investigated in detail. Particular emphasis is laid on the effect of delay difference between two time delays on the chaotic properties. A Melnikov’s analysis is employed to obtain the necessary condition for onset of chaos resulting from homoclinic bifurcation. And numerical analyses via the bifurcation diagram and the top Lyapunov exponent are carried out to show the actual time delay effect. Both the results obtained by the two analyses show that the delay difference between two time delays plays a very important role in inducing or suppressing chaos, so that it can be taken as a simple but efficient “switch” to control the motion of a system: either from order to chaos or from chaos to order.     

Global synchronization criteria for a class of third-order non-autonomous chaotic systems via linear state error feedback control

This paper investigates the global synchronization of a class of third-order non-autonomous chaotic systems via the master–slave linear state error feedback control. A sufficient global synchronization criterion of linear matrix inequality (LMI) and several algebraic synchronization criteria for single-variable coupling are proven. These LMI and algebraic synchronization criteria are then applied to two classes of well-known third-order chaotic systems, the generalized Lorenz systems and the gyrostat systems, proving that the local synchronization criteria for the chaotic generalized Lorenz systems developed in the existing literature can actually be extended to describe global synchronization and obtaining some easily implemented synchronization criteria for the gyrostat systems.