非线性混杂系统中的非光滑优化理论与算法

项目名称： 非线性混杂系统中的非光滑优化理论与算法

项目编号： No.11261033

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 高彩霞

作者单位： 内蒙古大学

项目金额： 45万元

中文摘要： 非线性混杂系统及其最优控制问题普遍存在于生命科学、工程技术及经济学等学科中，它是无穷维函数空间中以非线性分段光滑动力系统为约束的泛函优化问题,是控制论与混杂系统交叉发展的前沿课题。目前该领域的主要成果集中于定性理论研究；而已有的理论成果很难转化为实用有效的数值优化理论与算法。本项目将应用不可微优化、区域分解、双层规划等理论研究该类约束泛函极值问题的数值优化理论与算法，给出此类问题的最优性条件、可行下降方向、以及可在计算机上实现的全局优化算法。这些成果不仅可推广到非线性不可微动力系统为约束的数值优化中，还可推动工程科学、生命科学、经济学等交叉学科的发展，促进地区经济的可持续发展和生态环境的改善，同时将创造可观的经济效益。因此该项研究具有重要的理论意义与实用价值。

中文关键词： 非线性混杂动力系统；稳定性；优化算法；；

英文摘要： The nonlinear hybrid system and its optimal control problem exist generally in biology, engineering, economics. They are functional optimization problems constrainted as nonlinear piecewise smooth dynamical system in infinite function spaces. These problems have been an important topic of research in the hybrid system and the control theory communities in recent years. Currently, the main results in this subject concentrate on the theoretical research. And the effective numerical optimization theory and algorithm have not been obtained based on these problems. In this project, applying the nondifferentiable optimization, the region decomposes and bilevel programming, we start with establishing optimization conditions and constructing the feasible descent direction. We also give the global optimization algorithm which can be realized numerically. These achievements can not only been extended to the numerical optimization problems constrainted as nonlinear nondifferentiable dynamic systems, but also promote the development of other relevant subjects, such as engineering, the life sciences and economics. Therefore this research is a meaningful work both in theory and in practice.

英文关键词： Nonlinear hybrid dynamical system；Stability；Optimization algorithm；；