Robust chaos synchronization of noise-perturbed chaotic systems with multiple time-delays

The aim of this paper is to propose an output coupling and feedback scheme, which is not only to guarantee the asymptotic synchronization between the master and the slave chaotic systems with multiple time-delays but also to attenuate the effects of noise perturbation on the overall error system to a prescribed level in terms of the performance index H_∞-norm. The output coupling and feedback gain is derived on the basis of the Lyapunov theory and the linear matrix inequality (LMI) technique. Some numerical examples are given to demonstrate the effectiveness of the main results.     

The H_∞ synchronization of nonlinear Bloch systems via dynamic feedback control approach

We consider an H ∞ synchronization problem in nonlinear Bloch systems.Based on Lyapunov stability theory and linear matrix inequality formulation,a dynamic feedback controller is designed to guarantee asymptotic stability of the master-slave synchronization.Moreover,this controller reduces the effect of an external disturbance to the H ∞ norm constraint.A numerical example is given to validate the proposed synchronization scheme.     

Fuzzy model based adaptive synchronization of uncertain chaotic systems: Robust tracking control approach

This Letter presents fuzzy model-based robust tracking control for the adaptive synchronization of uncertain chaotic systems. Fuzzy model and adaptive algorithm are employed to present the unknown chaotic systems. H^∞ and sliding mode control are combined to construct a robust tracking controller. The incorporated H^∞ controller can attenuate the external disturbance and approximation error to any prescribed level. The proposed scheme guarantees that all the variables are bounded and the tracking error is compensated.     

Critical value computation for H∞-Riccati difference equations

In designing finite horizon discrete time H_∞ controllers, the associated H_∞-Riccati difference equations must be solved. But the Riccati equation has a non-negative solution only when γ⁻² is small enough. So it is important to get the upper bound of the parameter, i.e., the critical value that ensures the existence of the solution to the Riccati equation. The solution sequence of the Riccati difference equation can be constructed by the conjoined basis of an associated linear Hamiltonian difference system. Based on this expression and the Hamiltonian difference system eigenvalue theorems, the equivalence between the critical value and the first order eigenvalue of the linear Hamiltonian difference system is presented. Since the critical value is also shown to be the fundamental eigenvalue of a generalized Rayleigh quotient, an extended form of Wittrick-Williams algorithm is presented to search this value.     

随机扰动下一般混沌系统的H∞同步

本文对随机扰动下的一般混沌系统进行了H_∞控制同步研究,其中扰动是布朗运动随机过程.基于随机李雅普诺夫稳定性理论、线性矩阵不等式、It公式以及H_∞控制方法,通过设置控制器,从理论上提出了驱动系统和随机扰动下的响应系统的H_∞渐近同步的新标准,这些标准形式简单且易于用Matlab实现.最后的数值模拟表明提出的理论结果的正确性和有效性. 关键词： 随机扰动 H_∞同步')" href="#">H_∞同步 线性矩阵不等式 It公式     

Frequency band-wise passive control of linear time invariant structural systems with H∞ optimization

A frequency band specific passive control strategy is presented based on H_∞ optimization for multi-degree of freedom (MDOF) linear time invariant (LTI) structural systems. Effective control can be achieved if passive control devices are designed by considering frequency bands of excitation. Minimization of maximum spectral norm or worst-case gain in the excitation frequency range is taken into account for the design of passive control devices for effective performance. A multi-storey shear planer frame coupled with a tuned mass damper (TMD) system as the passive control device is considered in the numerical simulation for controlling both displacement and acceleration subjected to base excitation. The band-specific H_∞ optimization problem for design of passive control devices has been transformed into GA-friendly form for the TMD system as control devices. Such a design strategy of passive control devices based on minimizing worst-case gain associated to finite frequency band is observed to provide efficient design of a TMD system with better performance than that designed based on conventional H_∞ optimization associated to entire frequency range.     

Robust control synthesis for seat suspension systems with actuator saturation and time-varying input delay

The control synthesis problem is investigated in this paper for a class of semi-active seat suspension systems with norm-bounded parameter uncertainties, time-varying input delay and actuator saturation. A vertical vibration model of human body is introduced in order to make the modeling of seat suspension systems more precise. By employing a delay-range-dependent Lyapunov function and exploring the property of the saturation nonlinearity, the existence conditions of the desired state-feedback controller are derived in terms of linear matrix inequalities (LMIs). The controller is derived by solving the LMIs and the corresponding closed-loop system is asymptotically stable with a guaranteed H_∞ performance. A design example is presented to show the usefulness and advantages of the developed theoretical results.     

Robust fault-sensitive synchronization of a class of nonlinear systems

Aiming at enhancing the quality as well as the reliability of synchronization,this paper is concerned with the fault detection issue within the synchronization process for a class of nonlinear systems in the existence of external disturbances.To handle such problems,the concept of robust fault-sensitive (RFS) synchronization is proposed,and a method of determining such a kind of synchronization is developed.Under the framework of RFS synchronization,the master and the slave systems are robustly synchronized,and at the same time,sensitive to possible faults based on a mixed H /H ∞ performance.The design of desired output feedback controller is realized by solving a linear matrix inequality,and the fault sensitivity H index can be optimized via a convex optimization algorithm.A master-slave configuration composed of identical Chua’s circuits is adopted as a numerical example to demonstrate the effectiveness and applicability of the analytical results.     

Energy-to-peak control for seismic-excited buildings with actuator faults and parameter uncertainties

This paper deals with the problem of robust reliable energy-to-peak controller design for seismic-excited buildings with actuator faults and parameter uncertainties. It is assumed that uncertainties mainly exist in damping and stiffness of the buildings because they are difficult to be measured precisely. The objective of designing controllers is to guarantee the asymptotic stability of closed-loop systems and attenuate disturbance from earthquake excitation. Energy-to-peak performance is believed to be of great significance when conditions and requirements of active building vibration control are carefully considered. Based on energy-to-peak control theory and linear matrix inequality techniques, a new approach for reliable building vibration control with satisfactory energy-to-peak performance is presented. An n-degree-of-freedom linear building structure under earthquake excitation is analyzed and simulations are employed to validate the effectiveness of the proposed approach in reducing seismic-excited building vibration. Some comparisons are also made between energy-to-peak control systems and H_∞ control systems to further prove the importance of the method raised in this paper.     

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control

Adaptive H∞ synchronization of chaotic systems via linear and nonlinear feedback control is investigated.The chaotic systems are redesigned by using the generalized Hamiltonian systems and observer approach.Based on Lyapunov’s stability theory,linear and nonlinear feedback control of adaptive H∞ synchronization is established in order to not only guarantee stable synchronization of both master and slave systems but also reduce the effect of external disturbance on an H∞-norm constraint.Adaptive H∞ synchronization of chaotic systems via three kinds of control is investigated with applications to Lorenz and Chen systems.Numerical simulations are also given to identify theeffectiveness of the theoretical analysis.     

Discrete-time norms of flexible structures

The paper presents and analyses the H₂, H_∞, and Hankel norms of flexible structures. The analysis is conducted for the discrete-time models of structures and compared with the continuous-time results. The structural state-space models are presented in modal co-ordinates. Closed-form expressions for norms of structural modes are obtained, and norms of a structure are determined from the modal norms. The relationships between the Hankel, H_∞, and H₂ modal norms are derived. In addition, the paper shows that the discrete-time Hankel and H_∞ norms converge to the continuous-time counterparts when the sampling time approaches zero; however, the H₂ norm does not.     

Analyzing and controlling the network synchronization regions

In this paper, the commonly concerned issue of synchronization regions of complex dynamical networks is investigated, for the case when the synchronous state is an equilibrium point. Some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form (-∞,α₁) are established, where α₁ is a constant. In addition, a sufficient condition for the existence of a bounded synchronization region of the form (α₂,α₃) is derived, where α₂ and α₃ are constants, by using the parameter-dependent Lyapunov function method. Furthermore, some effective controller design methods are presented that can change the synchronization regions, thereby managing the synchronizability of the network. Finally, some numerical examples are given to show that a dynamical network may have disconnected synchronization regions, particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of (-∞,α₁)∪(α₂,α₃).     

Robust chaos synchronization based on adaptive fuzzy delayed feedback ${\bf{\mathcal{H}}}_{\bf{\infty}}$ control

In this paper, we propose a new adaptive H_￥\mathcal H_\infty synchronization strategy, called an adaptive fuzzy delayed feedback H_￥\mathcal H_\infty synchronization (AFDFHS) strategy, for chaotic systems with uncertain parameters and external disturbances. Based on Lyapunov–Krasovskii theory, Takagi–Sugeno (T–S) fuzzy model and adaptive delayed feedback H_￥\mathcal H_\infty control scheme, the AFDFHS controller is presented such that the synchronization error system is asymptotically stable with a guaranteed H_￥\mathcal{H}_{\infty } performance. It is shown that the design of the AFDFHS controller with adaptive law can be achieved by solving a linear matrix inequality (LMI), which can be easily facilitated by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed AFDFHS approach.     

Spectroscopy of XY3Z (C3v) molecules: A tensorial formalism adapted to the O (3) ⊃ C∞v ⊃ C3v group chain

A tensorial formalism adapted to the case of XY₃Z symmetric tops has been developed. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. All the coupling coefficients and formulas for the computation of the matrix elements are given for this chain. Such relations are also deduced in C_3v group itself.     

Development of the Hamiltonian and transition moment operators of symmetric top molecules using the O (3) ⊃ C∞v ⊃ C3v group chain

We present a development of the Hamiltonian, dipole moment, and polarizability operators for XY₃Z molecules. These rovibrational operators are written with the aid of a tensorial formalism derived from the one already used in Dijon and adapted to the XY₃Z symmetric tops in a recent paper [A. El Hilali, V. Boudon, M. Loëte, J. Mol. Spectrosc. 234 (2005) 166-174]. We use the O (3) ⊃ C_∞v ⊃ C_3v group chain. Expressions for the matrix elements are derived for these operators.     

Structural, sorption and thermodynamic correlations from a layered barium phenylarsonate/n-alkyldiamine system

The barium phenylarsonate compound, Ba(HO₃AsC₆H₅)₂·2H₂O, has the ability to intercalate n-alkyldiamine molecules, H₂N(CH₂)_nNH₂ (n=2-5). The amount intercalated (n_f) from a batchwise procedure and the variation of the original basal distance (d) of 1245 ppm determined through X-ray diffractions, gave linear correlations as a function of the number of carbon atoms in the aliphatic chain (n_c): n_f=(2.66±0.06)−(0.13±0.02)n_c and d=(2168±65)+(114±14)n_c. The intercalation process was calorimetrically followed to give exothermic enthalpy and negative Gibbs energy, reflecting spontaneous intercalation reactions at the solid/liquid interface. The displacement of solvent molecules bonded to amine and of those on the matrix during the intercalation increases the disorder to result in positive entropy, giving a favorable set of thermodynamic data for this system.     

时变不确定时滞连续系统的鲁棒H∞保成本控制

针对一类同时具有状态时滞和输入时滞的时变不确定连续系统,研究了H_∞保成本状态反馈控制器的设计,假定其中的时变不确定性项是范数有界的,但不需要满足匹配条件.通过构造广义Lyapunov函数和线性矩阵不等式(LMI)方法,给出了系统可H_∞鲁棒镇定同时满足保性能指标的一个充分条件,仅通过求解一个相应的线性矩阵不等式,就可得到鲁棒H_∞保性能控制器使得闭环系统的一个保成本函数对所有允许的不确定参数有上界,并经过迭代,通过求解凸优化问题得到最优鲁棒H_∞保性能控制器.最后用示例说明了该方法的有效性. 关键词： 连续系统 时滞 H_∞鲁棒控制')" href="#">H_∞鲁棒控制 保成本控制     

The tuning of quantum magnetization for organic/inorganic hybrid materials composed of Mn12-acetate and azobenzene casted into PMMA films on PVA films

In order to examine the effects of polymer matrix substituting crystalline solvents and photoisomerization of azobenzene in photo-modulation of AC susceptibility discovered recently, we have compared various quantum magnetic properties of new organic/inorganic hybrid materials composed of Mn₁₂-acetate (a typical single-molecule magnet, [Mn₁₂(CH₃COO)₁₆(H₂O)₄O₁₂]·2CH₃COOH·4H₂O) containing or not containing azobenzene casted into polymethylmethacrylate (PMMA) films on Polyvinylalchol (PVA) films. The M-H hysteresis loops below blocking temperature for both materials exhibited distinct differences of the dM/dH vs. H plots, which suggested azobenzene as well as crystalline solvents resulted in tuning of magnetic properties. Moreover, the AC susceptibility at 0.1-1000 Hz frequencies provided activation energy U_eff=87 K from Arrhenius law for both materials, albeit Cole-Cole plots indicated perturbation of quantum magnetization for both hybrid materials in polymer matrix.     

Chaos synchronization of unified chaotic systems via LMI

This Letter focuses on the master-slave synchronization problem of the unified chaotic systems. Based on Lyapunov stability theory and linear matrix inequality (LMI) formulation, a simple linear feedback control law is obtained to make the state of two identical unified chaotic systems asymptotically synchronized. Simulation results have illustrated the effectiveness of the proposed chaos synchronization solution.     

Boundedness and synchronization of y-coupled Lorenz systems with or without controllers

The purpose of this paper is to investigate the boundedness and synchronization of y-coupled Lorenz systems. When the coupling term is only added to the second variable, we call them y-coupled Lorenz systems. In this paper, we first prove the boundedness of y-coupled Lorenz systems, which ensures the existence and uniqueness of the solution when t→∞. Based on the boundedness, we prove that for y-coupled Lorenz systems, QUAD condition is satisfied. It should be pointed out that QUAD condition plays an essential role in the discussion of synchronization. Based on the boundedness and QUAD condition, we prove that if the coupling is strong enough, the y-coupled Lorenz systems can achieve the complete synchronization globally and exponentially.