Mathematical Sciences: Differential Geometric and Real Analytic Methods in NonLinear Control Theory

将开展非线性控制理论的研究，继续首席研究员在这一领域的先前工作，涉及局部和全局可控性、可观性、最小实现、在机器人学中的应用、最优控制和反馈稳定等广泛类别的问题。所使用的方法将是那些通常被称为“微分几何控制理论”的方法，即真实解析地图及其相关分层的理论，以及真实解析去单一化的理论。具体地说，将努力解决连续时间系统和采样连续时间系统的最优控制、可控性和实现理论领域的一些悬而未决的问题，同时追求必要的数学工具的发展--特别是在真实分析分层理论方面。

Research will be carried out on nonlinear control theory, continuing the Principal Investigator's previous work in this area on a broad class of problems on local and global controllability, observability, minimal realizations, applications to robotics, optimal control and feedback stabilization. The methods used will be those commonly known as "differential geometric control theory," the theory of real analytic maps and their associated stratifications, and the theory of real analytic desingularization. Specifically, efforts will be made to solve a number of open problems in the areas of optimal control, controllability, and realization theory of both continuous time and sampled continuous time systems, while pursuing the development of the necessary mathematical tools -- especially on the theory of real analytic stratifications.