Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems
Complementarity Methods in the Analysis of Piecewise Linear Dynamical Systems
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发表时间：
2001
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通讯作者：
M. Camlibel
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作者：
M. Camlibel
本论文的主要研究对象是一类与系统理论和数学规划有关的分段线性动力系统。这类动力系统被称为互补系统。针对这类非线性非光滑动力系统，本文的研究主要集中在两个方面：适定性和逼近。从模型验证的角度来看，在解的存在性和唯一性的意义上，适定性问题是相当重要的。本文给出了互补系统适定性的充分条件。此外，调查是由这些系统的近似的收敛性，着眼于模拟。
The main object of this thesis is a class of piecewise linear dynamical systems that are related both to system theory and to mathematical programming. The dynamical systems in this class are known as complementarity systems. With regard to these nonlinear and nonsmooth dynamical systems, the research in the thesis concentrates on two themes: well-posedness and approximations. The well-posedness issue, in the sense of existence and uniqueness of solutions, is of considerable importance from a model validation point of view. In the thesis, sufficient conditions are established for the well-posedness of complementarity systems. Furthermore, an investigation is made of the convergence of approximations of these systems with an eye towards simulation.