Mathematical Sciences: Geometric Methods in the Control of Nonlinear Systems

这个项目将研究最优控制和对称性 非线性系统原理 在最优控制中， 首席研究员将尝试制定一个正式的程序 计算曲面之间的切割轨迹， 具有不同切换结构的轨迹的端点。 这些切割轨迹是当地的主要几何特征， 参考点附近的最优轨迹。 对称 主要研究者将尝试扩展到 奇异系统反馈计算的最新结果 功能协调发展的 这些研究将有助于进一步了解 机械系统的优化设计，其中对称性（例如， 旋转）。

This project will study optimal control and symmetry principles of nonlinear systems. In optimal control the principal investigator will attempt to develop a formal procedure to calculate the cut-loci between surfaces consisting of endpoints of trajectories with different switching structures. These cut-loci are the dominant geometric feature for local optimality of trajectories near a reference point. In symmetry principles the principal investigator will try to extend to singular systems recent results on the calculation of feedback functions. These studies will lead to further understanding of the optimal design of mechanical systems where symmetries (e.g. rotational) are present.