Making a dynamical system chaotic: feedback control of Lyapunovexponents for discrete-time dynamical systems

Guanrong Chen; Dejian Lai

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Making a dynamical system chaotic: feedback control of Lyapunovexponents for discrete-time dynamical systems

机译：使动态系统混乱：离散动态系统的Lyapunov指数的反馈控制

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A simple, yet mathematically precise and rigorous, feedback control design procedure is suggested in this paper, which can rearrange all the Lyapunov exponents of the controlled system according to the user's desire, namely, to make them positive, zero, and/or negative in any desired order, for any given n-dimensional discrete-time smooth nonlinear dynamical system that could be originally nonchaotic or even asymptotically stable. The argument used is purely algebraic and the design procedure is completely schematic, without using any approximations throughout the derivation. A numerical example is included to visualize the anticontrol

机译：本文提出了一种简单但在数学上精确且严格的反馈控制设计程序，该程序可以根据用户的需求重新排列受控系统的所有Lyapunov指数，即在控制系统中使其为正，零和/或负。对于任何给定的n维离散时间平滑非线性动力学系统，其任何所需的阶次本来就可能是非混沌的，甚至是渐近稳定的。所使用的参数纯粹是代数的，设计过程是完全示意性的，在整个推导过程中均未使用任何近似值。包含一个数值示例以直观显示反控制

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《IEEE Transactions on Circuits and Systems. I, Regular Papers》 |1997年第3期|p.250-253|共4页
作者
Guanrong Chen; Dejian Lai;
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原文格式 PDF
正文语种 eng
中图分类 TN71;
关键词
Lyapunov methods; chaos; control system synthesis; discrete time systems; feedback; nonlinear dynamical systems; time series; Lyapunov exponents; chaotic system; design procedure; discrete-time dynamical systems; dynamical system design; feedback control; smooth nonl;

机译：Lyapunov方法;混沌;控制系统综合;离散时间系统;反馈;非线性动力系统;时间序列;Lyapunov指数;混沌系统;设计程序;离散时间动力系统;动力学系统设计;反馈控制;平滑非线性;

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专利

1. Making a dynamical system chaotic: feedback control of Lyapunov exponents for discrete-time dynamical systems [J] . Guanrong Chen, Dejian Lai IEEE Transactions on Circuits and Systems. 1 . 1997,第3期

机译：使动态系统变得混乱：离散动态系统的Lyapunov指数的反馈控制
2. Controlling chaotic behaviour for spin generator and Rossler dynamical systems with feedback control [J] . Hegazi A., El-Dessoky MM., Agiza HN. Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2001,第4期

机译：具有反馈控制的自旋发电机和Rossler动力系统的混沌行为控制
3. Global dynamics of unbalanced delta-modulated feedback-controlled discrete-time systems [J] . Gai RD, Chen GR, Xia XH Dynamics of continuous, discrete & impulsive systems, Series B. Applications & algorithms . 2006,第5期

机译：不平衡增量调制反馈控制离散时间系统的全局动力学
4. Stabilization of chaotic discrete-time systems by linear dynamical delayed feedback control [C] . Shigeru Yamamoto, Toshimitsu Ushio システム制御情報学会研究発表講演会 . 1999

机译：通过线性动力延迟反馈控制稳定混沌离散时间系统
5. Discrete-time model regulation control for systems with uncertain dynamics: Applications to electromechanical and electropneumatic systems. [D] . Hsia, Kan-Chun. 1993

机译：动力学不确定的系统的离散模型调节控制：在机电和电动气动系统中的应用。
6. Dynamical Analysis of a New Chaotic Fractional Discrete-Time System and Its Control [O] . A. Othman Almatroud, Amina-Aicha Khennaoui, Adel Ouannas, 2020

机译：新混沌分数离散时间系统的动态分析及对照
7. DIGITAL CONTROL SYSTEMS IMPLEMENTATION TECHNIQUES, VOLUME 70 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 390 pp., ISBN 0-12-0127702, $99.00 DISCRETE-TIME CONTROL SYSTEM ANALYSIS AND DESIGN, VOLUME 71 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 410 pp., ISBN 0-12-0127715, $99.00 DISCRETE-TIME CONTROL SYSTEM IMPLEMENTATION TECHNIQUES, VOLUME 72 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 388 pp., ISBN 0-12-0127725, $99.00 TECHNIQUES IN DISCRETE-TIME STOCHASTIC CONTROL SYSTEMS, VOLUME 73 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 380 pp., ISBN 0-12-0127734, $99.00 TECHNIQUES IN DISCRETE AND CONTINUOUS ROBUST SYSTEMS, VOLUME 74 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 412 pp., ISBN 0-12-0127741, $99.00 [O] . D. SUBBARAM NAIDU 1997

机译：数字控制系统的实施技术，控制和动态系统的第70卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,390 PP，ISBN 0-12-0127702，99.00美元离散时间控制系统分析和设计，控制和动态系统的第71卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,410 PP，ISBN 0-12-0127715，99.00美元离散时间控制系统实现技术，控制和动态系统的第72卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,388 pp，ISBN 0-12-0127725，99.00美元的离散 - 时间随机控制系统，控制和动态系统的VOLUME 73：前进，理论与应用，C Leondes（ED），学术出版社，圣地亚哥，1995年，380页，ISBN 0-12-0127734，在离散和$ 99.00技术。连续稳健的系统，控制和动态系统的第74卷：理论和应用的进步，C. leondes（ed），学术出版社，圣地亚哥，1995,412 pp。，ISBN 0-12-0127741，99.00美元
8. Nonlinear Dynamics and Chaotic Motions in Feedback Controlled Elastic Systems [R] . Holmes, P. J., Moon, F. C., Rand, R. H. 1985

机译：反馈控制弹性系统的非线性动力学与混沌运动

Making a dynamical system chaotic: feedback control of Lyapunovexponents for discrete-time dynamical systems

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