Mathematical Sciences: Geometry of highly nonlinear multi-input systems

数学科学：高度非线性多输入系统的几何

• 批准号: 9308289
• 负责人: Matthias Kawski
• 金额: $ 10.46万
• 依托单位: Arizona State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1997-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9308289&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; highly; nonlinear

This research program aims at developing the geometric foundations that underlie practically relevant properties of highly nonlinear control systems (that is, systems whose dynamics are inadequately, or not at all, described by linear approximations). Highly oscillatory control variations will be examined with the goal of obtaining better criteria for controllability and optimality than presently exist, and to obtain new algorithms for stabilizing feedback laws. Methods from algebraic combinatorics will be used to characterize the computational complexity of deciding controllability, stabilizability and other relevant control objectives and to develop new path planning algorithms. This project will develop the geometric foundations that underlie the dynamics of high-performance automatic control systems. It focuses primarily on systems that have very highly nonlinear dynamics and that have many interconnected components influencing each other. The engineering demands for ever higher performance, or even optimality, often require completely new control designs since classical linearization techniques for control design is often inadequate in such situations. By bringing together techniques from various areas of pure mathematics, such as differential geometry and algebraic combinatorics, new algorithms for finding optimal solutions to path planning problems (e.g., for robot arms or largely autonomously operating intelligent vehicles) will be developed.

这项研究计划旨在发展构成高度非线性控制系统(即其动态不能或根本不能用线性近似描述的系统)的实际相关性质的几何基础。我们将研究高度振荡的控制变化，目的是获得比目前存在的更好的可控性和最优性准则，并获得稳定反馈律的新算法。利用代数组合学的方法来刻画确定可控性、镇定性和其他相关控制目标的计算复杂性，并开发新的路径规划算法。该项目将发展构成高性能自动控制系统动力学基础的几何基础。它主要关注具有高度非线性动力学的系统，这些系统具有许多相互关联的组件相互影响。工程上对更高性能甚至最优性的要求往往需要全新的控制设计，因为在这种情况下，传统的线性化控制设计技术往往是不够的。通过将各种纯数学领域的技术结合在一起，例如微分几何和代数组合学，将开发出寻找路径规划问题的最优解的新算法(例如，对于机械臂或在很大程度上自主操作的智能车辆)。