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Approximation-error-ADP-based optimal tracking control for chaotic systems with convergence proof

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Chinese Physics B 2013年第9期22卷 305-311页

作者：宋睿卓肖文栋孙长银魏庆来 School of Automation and Electrical Engineering University of Science and Technology Beijing The State Key Laboratory of Management and Control for Complex systems Institute of AutomationChinese Academy of Sciences

In this paper, an optimal tracking control scheme is proposed for a class of discrete-time chaotic systems using the approximation-error-based adaptive dynamic programming （ADP） algorithm. Via the system transformation, the optimal tracking problem is transformed into an optimal regulation problem, and then the novel optimal tracking control method is proposed. It is shown that for the iterative ADP algorithm with finite approximation error, the iterative performance index functions can converge to a finite neighborhood of the greatest lower bound of all performance index functions under some convergence conditions. Two examples are given to demonstrate the validity of the proposed optimal tracking control scheme for chaotic systems.

关键词： chaotic systems approximation error adaptive dynamic programming optimal tracking control

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

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Chinese Physics B 2009年第9期18卷 3751-3757页

作者：张化光马铁东浮洁佟绍成 Key Laboratory of Integrated Automation for the Process Industry Ministry of EducationNortheastern University School of Information Science and Engineering Northeastern University Department of Mathematics and Physics Liaoning University of Technology

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.

关键词： chaotic systems lag synchronization dual-stage impulsive control parametric uncertainty

ON THE PREDICTABILITY OF chaotic systems WITH RESPECT TO MAXIMALLY EFFECTIVE COMPUTATION TIME

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Acta Mechanica Sinica 2003年第2期19卷 134-139页

作者：高新全封国林董文杰丑纪范 Department of Meteorological Sciences Lanzhou University Lanzhou 730000 China Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China Mathematics and Physics College Yangzhou University Yangzhou 225009 China

The round-off error introduces uncertainty in the numerical solution. A computational uncertainty principle is explained and validated by using chaotic systems, such as the climatic model,the Rossler and super chaos system. Maximally effective computation time (MECT) and optimal stepsize (OS) are discussed and obtained via an optimal searching method. Under OS in solving nonlinear ordinary differential equations, the self-memorization equations of chaotic systems are set up, thus a new approach to numerical weather forecast is described.

关键词： climate prediction chaotic systems numerical calculation maximally effective computation time retrospective scheme

Improvement on generalised synchronisation of chaotic systems

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Chinese Physics B 2010年第3期19卷 193-201页

作者：朱会宾邱芳崔宝同 College of Communications and Control Engineering Jiangnan University Department of Mathematics Binzhou University

In this paper, the problem of generalised synchronisation of two different chaotic systems is investigated. Some less conservative conditions are derived using linear matrix inequality other than existing results. Furthermore, a simple adaptive control scheme is proposed to achieve the generalised synchronisation of chaotic systems. The proposed method is simple and easy to implement in practice and can be applied to secure communications. Numerical simulations are also given to demonstrate the effectiveness and feasibility of the theoretical analysis.

关键词： chaotic systems generalised synchronisation secure communication

A novel adaptive-impulsive synchronization of fractional-order chaotic systems

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Chinese Physics B 2015年第10期24卷 86-92页

作者： Leung Y.T.Andrew Li Xian-Feng Chu Yan-Dong Zhang Hui Department of Architecture and Civil Engineering City University of Hong Kong School of Mathematics and Physics Lanzhou Jiaotong University School of Mechatronic Engineering Lanzhou Jiaotong University

A novel adaptive-impulsive scheme is proposed for synchronizing fractional-order chaotic systems without the necessity of knowing the attractors＇ bounds in priori. The nonlinear functions in these systems are supposed to satisfy local Lipschitz conditions but which are estimated with adaptive laws. The novelty is that the combination of adaptive control and impulsive control offers a control strategy gathering the advantages of both. In order to guarantee the convergence is no less than an expected exponential rate, a combined feedback strength design is created such that the symmetric axis can shift freely according to the updated transient feedback strength. All of the unknown Lipschitz constants are also updated exponentially in the meantime of achieving synchronization. Two different fractional-order chaotic systems are employed to demonstrate the effectiveness of the novel adaptive-impulsive control scheme.

关键词： adaptive-impulsive synchronization fractional order chaotic systems combined feedbackstrength

Impulsive control of chaotic systems and its applications in synchronization

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Chinese Physics B 2011年第5期20卷 184-190页

作者：吴波刘洋卢剑权 College of Mathematics Physics and Information EngineeringZhejiang Normal University Department of Mathematics Southeast University Potsdam Institute for Climate Impact Research TelegraphenbergD-14415 PotsdamGermany

In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.

关键词： comparison systems impulsive control chaotic systems synchronization

Synchronisation of chaotic systems using a novel sampled-data fuzzy controller

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Chinese Physics B 2011年第1期20卷 33-41页

作者：冯毅夫张庆灵 School of Mathematics Jilin Normal University Institute of systems Science Northeastern University

This paper presents the synchronisation of chaotic systems using a sampled-data fuzzy controller and is meaningful for many physical real-life applications. Firstly, a Takagi-Sugeno （T-S） fuzzy model is employed to represent the chaotic systems that contain some nonlinear terms, then a type of fuzzy sampled-data controller is proposed and an error system formed by the response and drive chaotic system. Secondly, relaxed LMI-based synchronisation conditions are derived by using a new parameter-dependent Lyapunov-Krasovskii functional and relaxed stabilisation techniques for the underlying error system. The derived LMI-based conditions are used to aid the design of a sampled-data fuzzy controller to achieve the synchronisation of chaotic systems. Finally, a numerical example is provided to illustrate the effectiveness of the proposed results.

关键词： chaotic systems synchronisation sampled-data systems parameter-dependentLyapunov-Krasovskii functional

An improved impulsive control approach to robust lag synchronization between two different chaotic systems

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Chinese Physics B 2010年第9期19卷 226-232页

作者：马铁东浮洁孙跃 College of Automation Chongqing University

In this paper, a novel robust impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the theory of impulsive functional differential equations and a new differential inequality, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined region. Finally, some numerical simulations for the Lorenz system and Chen system are given to demonstrate the effectiveness and feasibility of the proposed method. Compared with the existing results based on so-called dual-stage impulsive control, the derived results reduce the complexity of impulsive controller, moreover, a larger stable region can be obtained under the same parameters, which can be shown in the numerical simulations finally.

关键词： chaotic systems robust lag synchronization impulsive control parametric uncertainty

Adaptive fuzzy nonlinear inversion-based control for uncertain chaotic systems

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Chinese Physics B 2012年第12期21卷 123-129页

作者：刘恒余海军向伟 School of Mathematics and Computer Science Huainan Normal University School of Physics and Electronic Information Huainan Normal University

This paper presents a robust output feedback control method for uncertain chaotic systems, which comprises a nonlinear inversion-based controller with a fuzzy robust compensator. The proposed controller eliminates the unknown nonlinear function by using a fuzzy system, whose inputs are not the state variables but feedback error signals. The underlying stability analysis as well as parameter update law design are carried out by using the Lyapunov-based technique. The proposed method indicates that the nonlinear inversion-based control approach can also be applied to uncertain chaotic systems. Theoretical results are illustrated through two simulation examples.

关键词： chaotic systems nonlinear inversion-based control adaptive fuzzy control variable struc- ture control