基于线性控制的分数阶混沌系统的对偶投影同步

分数阶混沌系统的对偶同步是一个新的同步方法.有关分数阶混沌系统对偶投影同步的研究较少.基于分数阶系统的稳定性理论,通过设计线性控制器研究了分数阶混沌系统的对偶投影同步.给出了一个实现分数阶混沌系统对偶投影同步的一般方法,推广了现有对偶同步的研究结果,通过分数阶Van der Pol系统和分数阶Willis系统的数值仿真证实了该方法的有效性.     

分数阶多涡卷混沌系统滑模同步的两种控制方案

研究了分数阶多涡卷混沌系统滑模同步的两种控制方案,根据分数阶微积分的相关理论给出了系统取得同步的充分性条件,结果表明:选取适当的控制律以及滑模面,分数阶多涡卷误差系统将取得混沌同步.     

不同维分数阶混沌系统的自适应模糊滑模有限时间同步控制

针对不同维分数阶混沌系统的有限时间同步问题,提出了一个分数阶自适应模糊滑模控制方案。为增加同步误差的收敛速度,本文提出了一种新型的积分滑模面,并利用模糊逻辑系统结合分数阶自适应律估计理想控制器的未知部分。基于分数阶Lyapunov稳定性理论,设计了分数阶模糊滑模同步控制器,可使不同维分数阶混沌系统的同步误差在有限时间内达到滑模面。最后,数值仿真的结果验证了本文方法的有效性。     

一类不确定分数阶混沌系统的参数辨识

研究了一类不确定分数阶混沌系统的参数辨识问题,基于Lyapunov稳定性理论和分数阶微积分给出了系统取得混沌同步的两个充分条件,并把该结论应用到特殊情形,研究表明选取适当的滑模面和控制律,不确定分数阶混沌系统可以取得混沌同步.     

新的分数阶混沌系统及其同步

提出一个新的分数阶混沌系统,该系统含有三个参数,三个非线性项.通过理论分析,给出了分数阶混沌系统存在混沌吸引子的必要条件,通过数值仿真给出了混沌吸引子的图像,接着设计自适应同步控制器和参数自适应律,实现分数阶混沌系统的同步,数值仿真的结果表明设计控制器很好的实现了驱动系统和响应系统的同步.     

分数阶Duffing混沌系统的动力性态及其由单一主动控制的混沌同步

随着物理与技术的深入研究,分数阶非线性系统的动力性态及其分数阶混沌系统的同步成为研究的焦点.研究了分数阶Duffing系统的动力性态包括混沌性质,并且由分数阶非线性稳定性准则得到了分数阶非自治系统的混沌同步.特别地,研究了由单一主动控制的分数阶Duffing系统的同步.相应的数值结果演示了方法的有效性.     

一类整数阶分数阶单摆系统的混沌同步

基于驱动-响应法,根据Lyapunov稳定性理论和分数阶微积分的相关理论研究了一类整数阶,分数阶单摆系统的混沌同步问题,针对无阻尼和有阻尼两种情况给出了控制律的设计,并给出了严格的数学证明和推理过程,研究表明一定条件下,选取适当的控制律单摆系统的主从系统是混沌同步的,最后数值仿真说明方法有效.     

一类不确定分数阶多混沌系统的终端滑模同步控制

根据分数阶系统理论利用终端滑模方法研究了分数阶不确定多混沌系统同步问题,获得了整数阶分数阶两种情形下多混沌系统取得滑模同步的充分性条件,最终结论说明设计合适的控制律和切换函数,分数阶多混沌系统取得滑模同步.     

基于分数阶滑模控制器的不确定分数阶混沌系统同步

针对具有建模误差和外部干扰的不确定分数阶混沌系统的同步问题,本文通过将分数阶到达律引入滑模控制,提出了一个新型的分数阶滑模控制器.基于Lyapunov稳定理论和分数阶系统稳定理论,分析了被控系统的稳定性.分别以两个分数阶L(u|¨)混沌系统间的同结构同步和分数阶L(u|¨)与分数阶Liu混沌系统间的异结构同步为例进行了数值仿真,仿真结果表明了该控制器的有效性和鲁棒性.     

整数阶分数阶Rucklidge混沌系统的自适应滑模同步

基于分数阶自适应滑模同步理论研究不确定Rucklidge混沌系统的同步,得到了不确定分数阶Rucklidge混沌系统取得自适应滑模同步的充分条件,研究表明:构造适当的控制律与滑模函数,整数阶分数阶不确定Rucklidge系统取得自适应滑模同步.     

一类非线性时滞混沌系统的自适应脉冲同步

针对一类非线性时滞混沌系统,提出了一种新的自适应脉冲同步方案.首先基于Lyapunov稳定性理论、自适应控制理论及脉冲控制理论设计了自适应控制器、脉冲控制器及参数自适应律,然后利用推广的Barbalat引理,理论证明响应系统与驱动系统全局渐近同步,并给出了相应的充分条件.方案利用参数逼近Lipschitz常数,从而取消了Lipschitz常数已知的假设.两个数值仿真例子表明本方法的有效性.     

Financial systems: a few theoretical and algebraic considerations for their modeling

In this paper I suggest that observable entities, usually named ‘financial systems’, may be related to the general conceptual framework of systems theory. Starting from the requisite properties of a (general) system, I derive a strong and operational concept for specific financial systems (Section 1). Then a general modeling procedure is proposed, mainly based upon graph theory (with an additional and complementary use of linear systems analysis), through which it is possible to establish the general static and almost dynamic properties of these specific systems and their implications for financial analysis itself (Section 2). A numerical example (Section 3) illustrates most of the concepts and ideas introduced throughout the paper.     

Research on mean square exponential stability of networked control systems with multi-step delay

A new control mode is proposed for networked control systems whose network-induced delay is longer than a sampling period. The proposed control mode can make full use of control information and improve the performance of the system. Under the control mode, the mathematical model of networked control systems is obtained. Markov characteristic of the transfer delay is discussed. Based on Markov chain theory, the infinite horizon controller is designed, which is shown to render corresponding networked control systems mean square exponentially stable. Simulation results show the validity of the proposed theory.     

Decentralized Stabilizing State Feedback Controllers for a Class of Large-Scale Systems Including State Delays in the Interconnections

The problem of the decentralized stabilization of a class of large-scale nonlinear and linear systems including time-varying delays in the interconnections is considered. By combining the Razumikhin-type theorem with the Lyapunov stability theory, we propose a class of decentralized state feedback controllers which can guarantee always some type of stability of large-scale time-delay systems. In this paper, we assume that the time-varying delays are continuous and bounded nonnegative functions. Furthermore, since the proposed decentralized state feedback controllers are independent of the delays, the results obtained in this paper are applicable to systems without exact knowledge of the delays, i.e., systems with perturbed delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016     

一类非线性上三角系统的实用输出跟踪控制

利用齐次系统控制理论,研究了一类非线性上三角系统的实用输出跟踪控制问题,提出了一种解决上三角系统跟踪问题的齐次控制方法.所研究的系统是高阶的,允许不可测状态具有高阶增长形式.设计的控制器具有不依赖参考信号,可使跟踪误差任意小和对干扰的鲁棒性的优点.最后的仿真例子说明了结论的正确性.     

Applications of mathematical systems theory in population biology

This paper is a review of recent developments of a research line proposed on the turn of the decades, 1980s to 1990s. The main results concern basic qualitative properties of nonlinear models of population biology, such as controllability and observability. The methods applied are different for the density-dependent models of population ecology and for the frequency-dependent models of population genetics and evolutionary theory. While in the first case the classical theorems of nonlinear systems theory can be used, in the second one an extension of classical results to systems with invariant manifold is necessary. Supported by the Hungarian NFSR (OTKA K 62000, K 68187).     

网络化马尔可夫跳变系统的鲁棒无源控制

针对基于网络的凸多面体不确定离散时间马尔可夫跳变系统,研究其鲁棒无源控制问题.在网络诱导时滞是时变且有界的情况下,基于李雅普诺夫稳定性理论,通过构造参数依赖的随机李雅普诺夫泛函和运用广义系统变换,提出了不依赖模态的无源控制器存在的时滞依赖充分条件.所设计的鲁棒无源控制器保证了相应的闭环系统是鲁棒随机稳定且具有指定耗散率.将鲁棒无源控制器设计问题转化为一组线性矩阵不等式的可解性问题.仿真算例证明了本文方法的有效性.     

无限维多体复合量子系统态的约化判据

在量子信息理论中,量子纠缠态是一种非常重要的资源.探测给定量子态的纠缠性是一个极其重要的研究课题.2001年,Nielsen M A提出了一个判断两体量子态纠缠性的约化判据.之后,2005年William Hall又提出了一个有限维多体复合系统量子态的约化判据.将上述两类判据推广到了无限维多体量子系统情形,给出了无限维多体量子态全可分的两类约化判据.     

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.