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Dissipative Decomposition and Feedback Stabilization of Nonlinear Control Systems.

机译：非线性控制系统的耗散分解和反馈镇定。

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摘要

This dissertation considers the problem of approximate dissipative potentials construction and their use in smooth feedback stabilization of nonlinear control systems. For mechanical systems, dissipative potentials, usually a generalized Hamiltonian function, can be derived from physical intuition. When a dissipative Hamiltonian is not available, one can rely on dissipative Hamiltonian realization techniques, as proposed recently by Cheng and coworkers. Extensive results are available in the literature for (robust) stabilization based on the obtained potential.;The present work employs the geometric stabilization approach proposed by Jurdjevic and Quinn, refined by Faubourg and Pomet, and by Malisoff and Mazenc, for the design of stabilizing feedback laws. This thesis seeks to extend and apply the Jurdjevic--Quinn stabilization method to nonlinear stabilization problems, assuming no a priori knowledge of a Lyapunov function.;A homotopy-based local decomposition method is first employed to study the dissipative;Hamiltonian realization problem, leading to the construction of locally defined dissipative potentials. If the obtained potential satisfies locally the weak Jurdjevic--Quinn conditions, it is then shown how to construct feedback controllers using that potential, and under what conditions a Lyapunov function can be constructed locally for time-independent control affine systems. The proposed technique is then used for the construction of state feedback regulators and for the stabilization of periodic orbits based on a construction proposed by Bacciotti and Mazzi. In the last chapter of the thesis, stabilization of time-dependent control affine systems is considered, and the main result is used for the stabilization of periodic solutions using asymptotic feedback tracking.;For systems of interest in chemical engineering, especially systems with mass action kinetics, energy is often ill-defined. Moreover, realization techniques are difficult to apply, due to the nonlinearities associated with the reaction terms. Approximate dissipative realization techniques have been considered by many researchers for analysis and feedback design of controllers in the context of chemical processes. The objective of this thesis is to study the construction of local dissipative potentials and their application to solve stabilization problems.;Low-dimensional examples are used throughout the thesis to illustrate the proposed techniques and results.
机译：本文考虑了近似耗散势构造问题及其在非线性控制系统的平稳反馈稳定中的应用。对于机械系统，可以从物理直觉中得出耗散势，通常是广义汉密尔顿函数。当耗散的哈密顿量不可用时，可以依赖于Cheng和他的同事最近提出的耗散的哈密顿量实现技术。在文献中可以基于获得的潜力获得（稳健）稳定化的广泛结果。;本工作采用了Jurdjevic和Quinn提出的几何稳定方法，并由Faubourg和Pomet以及Malisoff和Mazenc进行了改进，以进行稳定化设计反馈法。本文试图在没有先验Lyapunov函数知识的前提下，将Jurdjevic-Quinn镇定方法扩展并应用到非线性镇定问题中;;首先基于同伦基于局部分解的方法来研究耗散;哈密顿实现问题，从而建立当地定义的耗散势。如果获得的电势局部满足柔弱的Jurdjevic-Quinn条件，则说明如何使用该电势构造反馈控制器，以及在什么条件下可以为与时间无关的仿射系统局部构建Lyapunov函数。然后，根据Bacciotti和Mazzi提出的构造，将提出的技术用于状态反馈调节器的构造以及周期轨道的稳定化。在论文的最后一章中，考虑了时变控制仿射系统的镇定，其主要结果被用于通过渐进反馈跟踪的周期解的镇定。对于化学工程领域的系统，特别是具有质量作用的系统动力学上，能量常常是不确定的。此外，由于与反应项相关的非线性，实现技术难以应用。许多研究人员已考虑采用近似耗散的实现技术来对化学过程中的控制器进行分析和反馈设计。本文的目的是研究局部耗散势的构建及其在解决稳定问题中的应用。全文中使用了低维示例来说明所提出的技术和结果。

著录项

  • 作者

    Hudon, Nicolas.;

  • 作者单位

    Queen's University (Canada).;

  • 授予单位 Queen's University (Canada).;
  • 学科 Engineering Chemical.
  • 学位 Ph.D.
  • 年度 2010
  • 页码 166 p.
  • 总页数 166
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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