Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

<正>This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional(2D) systems.Firstly,the fuzzy modeling method for the usual one-dimensional(1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi-Sugeno(TS) fuzzy model,which is convenient for implementing the stability analysis.Secondly,a new kind of fuzzy Lyapunov function,which is a homogeneous polynomially parameter dependent on fuzzy membership functions,is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system.In the process of stability analysis,the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques.Moreover,the obtained result is formulated in the form of linear matrix inequalities,which can be easily solved via standard numerical software.Finally,a numerical example is also given to demonstrate the effectiveness of the proposed approach.     

Adaptive Function Projective Synchronization of Discrete-Time Chaotic Systems

By backstepping control law and the active control method, adaptive function projective synchronization of 2D and 3D discrete-time chaotic systems with Uncertain parameters are investigated. To illustrate the effectiveness of the new scheme, some numerical examples are given.     

一类不确定离散混沌系统的自抗扰控制器与小脑神经网络并行优化控制

针对一类受扰不确定离散非线性混沌系统,提出了基于免疫动态微粒群优化策略的ADRC与CMAC神经网络并行控制方法(ADRC-CMAC).ADRC控制器抑制系统扰动,保证系统的稳定性;CMAC神经网络控制器实现前馈控制保证系统的控制精度和响应速度.利用动态免疫微粒群算法对ADRC-CMAC并行控制器参数进行全局优化.实验结果表明该控制方法具有较快系统的响应速度,较好的抗干扰能力,控制精度高. 关键词： 自抗扰控制器 小脑神经网络 并行控制 混沌系统     

离散时间切换广义系统的一致有限时间稳定性

针对一类离散时间切换广义系统, 研究其一致有限时间稳定性问题. 首先, 把广义系统的有限时间稳定性概念推广到离散切换广义系统; 然后, 利用Lyapunov-like函数方法, 给出了离散切换广义系统在任意给定的切换规则下是正则、 因果的, 且有限时间有界和有限时间稳定的充分条件, 同时给出了保证离散切换广义系统一致有限时间稳定的状态反馈控制器的具体设计方法. 仿真算例结果说明了该控制方法的有效性.     

Robust H_∞ control for uncertain Markovian jump systems with mixed delays

We scrutinize the problem of robust H∞control for a class of Markovian jump uncertain systems with interval timevarying and distributed delays. The Markovian jumping parameters are modeled as a continuous-time finite-state Markov chain. The main aim is to design a delay-dependent robust H∞control synthesis which ensures the mean-square asymptotic stability of the equilibrium point. By constructing a suitable Lyapunov–Krasovskii functional(LKF), sufficient conditions for delay-dependent robust H∞control criteria are obtained in terms of linear matrix inequalities(LMIs). The advantage of the proposed method is illustrated by numerical examples. The results are also compared with the existing results to show the less conservativeness.     

基于线性反馈控制的不确定混沌系统的参数辨识

基于线性反馈控制方法和Lyapunov稳定性理论,研究了参数不确定系统的混沌同步和参数辨识,设计了普遍适用的参数自适应控制律,理论证明设计的控制器可使得两个结构相同但参数不同的混沌系统渐近地达到同步,并且可以辨识出响应系统的未知参数. Lorenz系统和蔡氏电路的数值仿真进一步表明了该方法的有效性. 关键词： 不确定混沌系统 同步 参数辨识 Lyapunov函数     

V2控制Buck变换器等效建模与分岔分析

通过对V²控制Buck变换器电路进行降阶处理, 利用不同工作模式, 推导了两个边界电压, 建立了V²控制Buck变换器的等效一阶同步映射迭代模型, 研究了它的非线性分岔行为. 通过稳定性和工作模式分析, 推导了V²控制Buck变换器从稳定的周期1工作状态到次谐波振 荡状态转移以及从电感电流不连续导电模式 (DCM) 到连续导电模式 (CCM) 转移的条件. 研究结果表明, 当电路参数变化时, V²控制Buck 变换器发生了倍周期分岔和边界碰撞分岔, 不同的参数变化有着不同的分岔路由. 搭建了仿真和实验电路, 仿真和实验结果验证了等效迭代模型的有效性和理论分析的正确性. 关键词： 2控制')" href="#">V²控制 迭代模型 分岔 工作模式     

Successive lag cluster consensus on multi-agent systems via delay-dependent impulsive control

We introduce a new consensus pattern, named a successive lag cluster consensus(SLCC), which is a generalized pattern of successive lag consensus(SLC). By applying delay-dependent impulsive control, the SLCC of first-order and second-order multi-agent systems is discussed. Furthermore, based on graph theory and stability theory, some sufficient conditions for the stability of SLCC on multi-agent systems are obtained. Finally, several numerical examples are given to verify the correctness of our theoretical results.     

Pattern formation in superdiffusion Oregonator model

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional(2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction–diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.     

Synchronization of generalized Hénon map using polynomial controller

This Letter presents the chaos synchronization of two discrete-time generalized Hénon map, namely the drive and response systems. A polynomial controller is proposed to drive the system states of the response system to follow those of the drive system. The system stability of the error system formed by the drive and response systems and the synthesis of the polynomial controller are investigated using the sum-of-squares (SOS) technique. Based on the Lyapunov stability theory, stability conditions in terms of SOS are derived to guarantee the system stability and facilitate the controller synthesis. By satisfying the SOS-based stability conditions, chaotic synchronization is achieved. The solution of the SOS-based stability conditions can be found numerically using the third-party Matlab toolbox SOSTOOLS. A simulation example is given to illustrate the merits of the proposed polynomial control approach.     

认知不确定二维声场的响应特性数值分析

针对声学参数存在认知不确定性的问题,为实现认知不确定声场声压响应的预测。提出了解决二维认知不确定声场的有限元法(Evidence Theory-based Finite Element Method,ETFEM),引入证据理论,采用焦元和基本可信度的概念来描述认知不确定参数,基于摄动法的区间分析技术,推导了认知不确定声场声压响应的标准差、期望求解公式。为验证本文方法的可行性。以认知不确定参数下的二维管道声场模型和某轿车二维声腔模型为例进行了数值计算,对比离散随机变量得到认知不确定参数的声场分析结果和相应的随机声场所得分析结果,研究表明:该方法能够有效的处理认知不确定参数下的二维声场,为工程问题中噪声预测提供可靠的分析模型。      

A unified approach to fuzzy modelling and robust synchronization of different hyperchaotic systems

In this paper, a Takagi Sugeno （T-S） fuzzy model-based method is proposed to deal with the problem of synchronization of two identical or different hyperchaotic systems. The T S fuzzy models with a small number of fuzzy IF-THEN rules are employed to represent many typical hyperchaotic systems exactly. The benefit of employing the T-S fuzzy models lies in mathematical simplicity of analysis. Based on the T-S fuzzy hyperchaotic models, two fuzzy controllers arc designed via parallel distributed compensation （PDC） and exact linearization （EL） techniques to synchronize two identical hyperchaotic systems with uncertain parameters and two different hyperchaotic systems, respectively. The sufficient conditions for the robust synchronization of two identical hyperchaotic systems with uncertain parameters and the asymptotic synchronization of two different hyperchaotic systems are derived by applying the Lyapunov stability theory. This method is a universal one of synchronizing two identical or different hyperchaotic systems. Numerical examples are given to demonstrate the validity of the proposed fuzzy model and hyperchaotic synchronization scheme.     

数字控制单相全桥电压型逆变电路的改进离散迭代模型

针对数字控制单相全桥电压型逆变电路的非线性动力学特性分析,本文建立了一种改进离散迭代模型. 改进离散迭代模型结合了平均模型和传统离散迭代模型的优点, 能够精确分析数字控制延时以及采样保持过程对系统非线性动力学特性的影响, 可以在保证精确度的前提下显著降低离散迭代建模过程的复杂程度.本文以LC滤波器电容电压外环、电感电流内环反馈加给定电压前馈的数字控制系统为例,建立了数字控制单相全桥电压型逆变电路的改进离散迭代模型,采用新模型分析了系统的非线性动力学特性,并准确预测了系统的稳定范围以及失稳现象. 最后,利用SIMULINK仿真模型和物理实验验证了改进离散迭代模型的正确性和有效性. 关键词： 单相全桥逆变电路 离散迭代模型 数字控制 分岔     

Pinning control of weighted general complex dynamical networks with time delay

Time delays commonly exist in the real world. In the present work we consider weighted general complex dynamical networks with time delay, which are undirected and connected. Control of such networks, by applying local feedback injections to a fraction of network nodes, is investigated for both continuous-time and discrete-time cases. Both delay-independent and delay-dependent asymptotical stability criteria for network stabilization are derived. It is also shown that the whole network can be stabilized by controlling only one node. The efficiency of the derived results was illustrated by numerical examples.     

Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems.     

不确定分数阶时滞混沌系统自适应神经网络同步控制

针对带有完全未知的非线性不确定项和外界扰动的异结构分数阶时滞混沌系统的同步问题,基于Lyapunov稳定性理论,设计了自适应径向基函数(radial basis function,RBF)神经网络控制器以及整数阶的参数自适应律.该控制器结合了RBF神经网络和自适应控制技术,RBF神经网络用来逼近未知非线性函数,自适应律用于调整控制器中相应的参数.构造平方Lyapunov函数进行稳定性分析,基于Barbalat引理证明了同步误差渐近趋于零.数值仿真结果表明了该控制器的有效性.     

Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems

This paper is devoted to synchronization of uncertain fractional-order chaotic systems with fractional-order α: 0?相似文献   

Observer-based passive control for uncertain linear systems with delay in state and control input

This paper deals with the robust passivity synthesis problem for a class of uncertain linear systems with time-varying delay in state and control input. The parameter uncertainties are norm-bounded and allowed to appear in all matrices of the model. The problem aims at designing an observer-based dynamic output-feedback controller that robustly stabilizes the uncertain systems and achieves the strict passivity of closed-loop systems for all admissible uncertainties. By converting the problem at hand into a class of strictly passive control problem for a parameterized system, the explicit solution is established and expressed in terms of a linear matrix inequality. A numerical example is provided to demonstrate the validity of the proposed approach.     

Exact solution of three-dimensional acoustic field in a wedge with perfectly reflecting boundaries

An exact approach is presented to compute the three-dimensional(3D) acoustic field in a homogeneous wedge-shaped ocean with perfectly reflecting boundaries. This approach applies the Fourier synthesis technique, which reduces a 3D point-source ideal wedge problem into a sequence of two-dimensional(2D) line-source ideal wedge problems, whose analytical solution is well established. A comparison of numerical efficiency is provided between this solution and the solution proposed by Buckingham,which is obtained by a sequence of integral transforms. The details of numerical implementation of these two solutions are also given. To validate the present approach and at the same time compare numerical efficiency between this approach and Buckingham's analytical solution, two numerical examples are considered. One is the Acoustical Society of America(ASA) benchmark wedge problem and the other is a wide-angle wedge problem. Numerical results indicate that the present approach is efficient and capable of providing accurate 3D acoustic field results for arbitrary receiver locations, and hence can serve as a benchmark model for sound propagation in a homogeneous wedge-shaped ocean.