Mathematical Sciences: Geometric Methods in the Control of Nonlinear Systems

该项目将研究非线性系统的最优控制和对称原理。在最优控制中，主要研究人员将尝试开发一种形式程序来计算由具有不同切换结构的轨迹的端点组成的表面之间的切割轨迹。这些切割轨迹是参考点附近轨迹局部最优的主要几何特征。在对称性原理中，主要研究人员将尝试将最近关于反馈函数计算的结果推广到奇异系统。这些研究将有助于进一步理解存在对称性(例如旋转)的机械系统的优化设计。

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.