A Contraction Theory Approach to Singularly Perturbed Systems

Del Vecchio D.; Slotine J.-J. E.

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A Contraction Theory Approach to Singularly Perturbed Systems

机译：奇摄动系统的一种压缩理论方法

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摘要

In this technical note, we revisit standard results on singular perturbations and multiple time-scales using convergence analysis tools based on nonlinear contraction theory. Specifically, assuming that the fast and slow subsystems are each partially contracting, we obtain explicit bounds on the convergence rate of the trajectories to the slow manifold and on the asymptotic error between the trajectories of the singularly perturbed system and those of the reduced system. As an application example, we illustrate the design of a biomolecular insulation device.

机译：在本技术说明中，我们使用基于非线性收缩理论的收敛分析工具，重新审视关于奇异摄动和多个时间尺度的标准结果。具体来说，假设快子系统和慢子系统各自部分收缩，我们获得了到慢流形的轨迹收敛速度以及奇异摄动系统和精简系统的轨迹之间的渐近误差的显式边界。作为一个应用实例，我们说明了生物分子绝缘装置的设计。

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来源
《Automatic Control, IEEE Transactions on》 |2013年第3期|p.752-757|共6页
作者
Del Vecchio D.; Slotine J.-J. E.;
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作者单位

Department of Mechanical Engineering and the Laboratory of Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, United States of America;

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正文语种 eng
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关键词
Convergence; Manifolds; Measurement; Standards; Trajectory; Upper bound; Vectors; Biomolecular systems; disturbance attenuation; nonlinear systems; singular perturbation;

机译：收敛;歧管;测量;标准;弹道;上限;向量;生物分子系统;干扰衰减非线性系统奇异摄动;

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专利

1. Singularly Perturbed Linear and Semilinear Hyperbolic Systems: Kinetic Theory Approach to Some Folk's Theorems [J] . J. Banasiak Acta Applicandae Mathematicae: An International Journal on Applying Mathematics and Mathematical Applications . 1997,第2期

机译：奇摄动线性和半线性双曲系统：某些定理的动力学理论方法
2. Contraction-based stabilisation of nonlinear singularly perturbed systems and application to high gain feedback [J] . Rayguru M. M., Kar I. N. International Journal of Control . 2017,第7a9期

机译：基于收缩的非线性奇异扰动系统的稳定化和高增益反馈的应用
3. An adaptive tracking controller design for non-linear singularly perturbed systems using fuzzy singularly perturbed model [J] . Li L, Sun FC IMA Journal of Mathematical Control and Information . 2009,第4期

机译：基于模糊奇异摄动模型的非线性奇异摄动系统的自适应跟踪控制器设计
4. A contraction theory approach to singularly perturbed systems with application to retroactivity attenuation [C] . Del Vecchio, Domitilla, Slotine, Jean-Jacques Decision and Control and European Control Conference (CDC-ECC), 2011 50th IEEE Conference on . 2011

机译：奇异摄动系统的一种压缩理论方法及其在追溯衰减中的应用
5. Unified approach for singularly perturbed control systems. [D] . Singh, Hardev. 2001

机译：奇异摄动控制系统的统一方法。
6. A matrix-based approach to solving the inverse Frobenius–Perron problem using sequences of density functions of stochastically perturbed dynamical systems [O] . Xiaokai Nie, Daniel Coca -1

机译：一种基于矩阵的方法使用随机扰动动力系统的密度函数序列来解决Frobenius-Perron逆问题
7. A Contraction Theory Approach to Singularly Perturbed Systems with Application to Retroactivity Attenuation [O] . Del Vecchio Domitilla, Slotine Jean-Jacques E. 2011

机译：奇异摄动系统的收缩理论方法及其在回归衰减中的应用

A Contraction Theory Approach to Singularly Perturbed Systems

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