一类Sprott-O混沌系统的H_∞状态控制和自适应控制研究

研究了一类Sprott-O混沌系统的H_∞状态反馈控制和自适应反推控制问题.首先,通过绘制系统的Lyapunov指数图、混沌吸引子图及参数变化时的分岔图等验证了系统在一定参数条件下具有的复杂混沌动力学行为;然后,分别应用H_∞状态反馈控制方法和自适应反推控制方法设计不同的控制器,对混沌系统加以控制;最后,通过数值仿真验证了所设计控制器的有效性.     

新三维自治混沌系统动力学性质研究

采用动力系统理论分析和计算机数值仿真相结合的方法,研究了一类新三维自治混沌系统的非线性动力学行为,如平衡点及其稳定性、不变集、混沌吸引子、吸引域等,从而展示了该混沌系统的丰富的动力学特性并且用matlab给出了相应的计算机模拟.创新点在于同时考虑了该混沌系统的最终界和全局吸引集,并且对于这个混沌系统的任意正参数,分别得到了该混沌系统最终界的一个参数族数学表达式和全局指数吸引集的一个参数族数学表达式,最后利用交集的思想分别得到了混沌系统最终界和全局吸引集的一个较小的数学表达式.混沌系统有望在实际保密通信中得到应用.     

基于稳定性理论的一类激光混沌模型的动力学特性研究

采用动力系统理论分析和计算机数值仿真相结合的方法,研究了LorenzHaken激光混沌系统的非线性动力学行为,如平衡点及其稳定性、波形图、不变集、混沌吸引子、吸引域等,从而展示了该混沌系统的丰富的动力学特性并且用matlab给出了相应的计算机模拟.的创新点在于同时考虑了Lorenz-Haken激光混沌系统的最终界和全局吸引集,并且对于这个混沌系统的任意正参数,分别得到了该混沌系统最终界的一个参数族数学表达式和全局指数吸引集的一个参数族数学表达式,最后利用交集的思想分别得到了该混沌系统最终界和全局吸引集的一个较小的数学表达式.混沌系统有望在实际保密通信中得到应用.     

新三维非线性系统的动力学分析

通过代数方法,构造出来一个具有复杂混沌吸引子的非线性混沌自治三维系统．从理论和数值两方面对吸引子进行了分析和仿真,得到了系统在平衡点处不稳定的参数范围．通过分岔图和Lyapunov指数谱进一步揭示了系统丰富的动力学行为.     

两时滞广义Logistic模型的Hopf分支与混沌

构建了具有两个时滞的广义Logistic模型,分情况讨论了系统正平衡点发生局部Hopf分支和稳定性切换的条件,分析了分支点关于系统参数的单调性和极限性质.数值模拟佐证了理论结果,展示了周期振动,倍周期分支,混沌等复杂的动力学行为.     

一个四维超混沌系统及对应环状多翅膀系统的研究

构造一个具有三个参数和两个非线性项的新四维超混沌系统,运用数值模拟的方法分析该系统的基本动力学行为,并设计了该系统的混沌电路,得到了吻合度较高的实验结果.通过在新系统中运用Julia变换,可以得到相应的环状多翅膀系统.     

波动位移变化引起的大气环流问题的全局稳定性分析及数值仿真

探讨分析了一个低维的大气环流系统的动力学行为及其仿真问题.给出了三模系统的动力学行为及其演化历程.通过构造正定的径向无界李雅普诺夫函数,研究了该混沌系统的全局指数吸引集和正向不变集.通过李雅普诺夫指数图、分岔图和庞加莱截面图,描述了系统的动力学行为.在某些参数区间上,该系统存在混沌现象.仿真和分析的结果为今后研究天气和气候预测提供了数据和理论基础.     

通过同步实现从混沌到有序的转变

本文旨在研究连续的混沌系统是否存在“混沌＋混沌=有序”的现象．证明了两个双向耦合的连续混沌系统在一些情况下可产生有序的动力学行为．作为例子，通过选取适当的耦合参数使Lorenz系统以及Chen和Lee引入的混沌系统同步，进而对同步系统的动力学行为进行了理论分析和数值模拟．结果表明，逐渐改变参数，系统实现了从混沌到有序的过渡．     

托卡马克中低模态到高模态转迁模型的混沌运动

利用Melnikov方法详细研究了在托卡马克(Tokamaks)中,等离子区边缘附近低模态到高模态转迁方程的混沌动力学.该转迁方程是一个含外激励和参数激励的系统.对含周期外激励和线性参数激励、三次参数激励的系统分别绘出了用来划分混沌区和非混沌区的临界曲线.得到的结果表明,含有线性或三次参数激励的系统存在不可控区域,在该区域中异宿轨分岔总是导致混沌发生.特别地,三次参数激励系统存在一个"可控频率",施以该频率的激励,不论激励的振幅多大,同宿轨分岔总是不会导致混沌发生.得到了这类系统的一些复杂的动力学行为.     

平面不可压缩磁流体动力学五模类Lorenz方程组的动力学行为及其数值仿真北大核心CSCD

该文研究了平面正方形区域上不可压缩的磁流体动力学方程组五模截断所得到的十维模型的动力学行为问题.首先,利用模式截断方法推导了十模系统,讨论了该方程组定常解及其稳定性,其次,发现了Hopf分叉和混沌,证明了该方程组吸引子的存在性和全局稳定性,最后,给出了系统从分叉到混沌整个过程所呈现的动力学行为演变的详细数值模拟结果,分析了磁性对系统动力学行为的影响.基于分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等数值模拟结果揭示了这个低维系统的动力学行为特征.这个新混沌系统通过周期倍分岔过渡到混沌(费根鲍姆途径).     

Switching Control of Nonlinear Systems Based on the Quasi-ARX Model and the SVR Algorithm北大核心CSCD

该文基于改进的含有外部输入项的准线性自回归(准ARX)径向基函数(RBF)网络模型和支持向量回归(SVR)算法,提出了一种非线性切换控制方法.改进的准ARX模型非线性部分采用RBF网络.控制系统设计过程分为三个部分:首先,利用聚类方法确定模型的非线性参数;然后,采用线性SVR算法来解决控制系统的鲁棒性问题;接下来,基于控制误差给出切换判定函数,确定切换律给出控制序列.最后通过数值仿真验证了该方法的有效性.     

Centers and isochronous centers of a class of quasi-analytic switching systems

In this paper, we study the integrability and linearization of a class of quadratic quasi-analytic switching systems. We improve an existing method to compute the focus values and periodic constants of quasianalytic switching systems. In particular, with our method, we demonstrate that the dynamical behaviors of quasi-analytic switching systems are more complex than those of continuous quasi-analytic systems, by showing the existence of six and seven limit cycles in the neighborhood of the origin and infinity, respectively, in a quadratic quasi-analytic switching system. Moreover, explicit conditions are obtained for classifying the centers and isochronous centers of the system.     

The improved quantum switching mechanism based on contention

Quantum switching architecture is one of the promising schemes for transmitting quantum data to its destination. In this paper, we propose an improved quantum switching mechanism for solving the output contention problem. Firstly we analyze the impropriety of Tsai and Kuo’s quantum switching scheme for multicast service. Secondly an improved quantum switching scheme is presented for completing the switching task with output contention. Lastly an illustrative example is given to evaluate our method and the result shows that the present improved mechanism can ensure the data reliable in transmitting and is scalable for quantum switching with output contention.     

Moment decay rates of infinite dimensional stochastic evolution equations with memory and Markovian jumps

The strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. Asymptotic behaviors with a general decay rate for the second moments of mild solutions of the above equations are obtained. An example is given to illustrate our theory.     

Exponential stability and applications of switched positive linear impulsive systems with time-varying delays and all unstable subsystems

The global uniform exponential stability of switched positive linear impulsive systems with time-varying delays and all unstable subsystems is studied in this paper, which includes two types of distributed time-varying delays and discrete time-varying delays. Switching behaviors dominating the switched systems can be either stabilizing and destabilizing in the new designed switching sequence. We design new linear programming algorithm process to find the feasible ratio of stabilizing switching behaviors, which can be compensated by unstable subsystems, destabilizing switching behaviors, and impulses. Specically, we add a kind of nonnegative impulses which is consistent with the switching behaviors for the systems. Employing a multiple co-positive Lyapunov-Krasovskii functional, we present several new sufficient stability criteria and design new switching sequence. Then, we apply the obtained stability criteria to the exponential consensus of linear delayed multi-agent systems, and obtain the new exponential consensus criteria. Three simulations are provided to demonstrate the proposed stability criteria.     

Adaptive event-triggered dynamic distributed control of switched positive systems with switching faults

This paper designs the dynamic output-feedback controller of switched positive systems subject to switching faults using an improved adaptive event-triggering mechanism. An adaptive event-triggering condition is addressed in the form of 1-norm by virtue of the measurable outputs of distributed sensors and the corresponding error. An error-based closed-loop control system whose dynamic variable relies on a state observer is obtained. A multiple copositive Lyapunov function is constructed to deal with the positivity and stability of the systems. The matrix decomposition and linear programming approaches are used to design and compute the controller and observer gains. An improved average dwell time scheme is proposed to handle the switching faults. The contributions of this paper lie in that: (i) An adaptive event-triggering mechanism is established for switched positive systems, (ii) A framework on the fault of switching signal is constructed, and (iii) A dynamic distributed controller is proposed for the considered systems. Finally, two illustrative examples are given to verify the effectiveness of the obtained results.     

Modelling and properties of a nonlinear autonomous switching system in fed-batch culture of glycerol

A nonlinear autonomous switching system is proposed to describe the coupled fed-batch fermentation with the pH as the feedback parameter. We prove the non-Zeno behaviors of the switching system and some basic properties of its solution, including the existence, uniqueness, boundedness and regularity. Numerical simulation is also carried out, which reveals that the proposed system can describe the factual fermentation process properly.     

Improved results on fixed-time stability of switched nonlinear time-varying systems

This paper considers the problem of fixed-time stability (FTS) for switched nonlinear time-varying (NTV) systems. Firstly, three sufficient conditions are proposed to verify the FTS of NTV systems by using the improved Lyapunov function, which has a tighter upper bound of time derivative. Then, two FTS conditions are given for the switched NTV system by extending the obtained results, moreover, a switching strategy is also provided by using the minimum dwell time method. Finally, the obtained results are extended to study the FTS of impulsive NTV systems. Comparing with the existing results, the obtained conditions have two improvements: (1) provides a more accurate estimate for the upper bound of settling time of NTV systems, and (2) allows the Lyapunov function to increase at the switching instant of switched NTV (or impulsive NTV) systems. Two numerical examples are given to illustrate the theoretical results.     

Noise suppresses exponential growth under regime switching

Consider a given system under regime switching whose solution grows exponentially, and suppose that the system is subject to environmental noise in some regimes. Can the regime switching and the environmental noise work together to make the system change significantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows exponentially become a new system whose solutions will grow at most polynomially. In other words, we reveal that the regime switching and the environmental noise will suppress the exponential growth.     

Optimal mode-switching for hybrid systems with varying initial states

This paper concerns a particular aspect of the optimal control problem for switched systems that change modes whenever the state intersects certain switching surfaces. These surfaces are assumed to be parameterized by a finite dimensional switching parameter, and the optimization problem we consider is that of minimizing a given cost-functional with respect to the switching parameter under the assumption that the initial state of the system is not a priori known. We approach this problem from two different vantage points by first minimizing the worst possible cost over the given set of initial states using results from min–max optimization. The second approach is based on a sensitivity analysis in which variational arguments give the derivative of the switching parameters with respect to the initial conditions.