Switching Dynamics and Control of Complementarity Systems: a Hybrid System Perspective

目的：本项目的目的是从混合系统的角度研究互补系统的动力学和控制问题，并将其应用于工程和生物系统。各种物理、生物和经济系统都受到相辅相成的不平等约束，即一对不平等中至少有一个是平等的。这类动态系统称为互补系统，在实际应用中构成了一类重要的混杂系统和切换系统。互补性方法以及系统和控制技术将被用来解决关键的动态分析和控制设计问题。智能化的优点在于三个方面：(1)互补系统的局部切换动力学的表征；(2)分段光滑系统的长期切换动态分析和控制；(3)在接触机械系统、系统生物学、安全性验证和动态优化方面的应用。本程序的分析结果将为广泛应用的非光滑系统的计算、分析和设计奠定严格的基础。获得的控制分析和反馈设计算法将应用于机器人、生物和电子领域的新兴实用系统，并将促进复杂系统的分析和设计。更广泛的影响：(1)由于重点研究主题的根本性质及其不同的应用，如机器人、生物医学系统和系统生物学，该计划是跨学科的，具有潜在的变革性。(2)拟议的研究将与教育和外联活动紧密结合，包括开发关于非顺畅系统的研究生课程，积极参与高中生的工程教育，本科生的研究指导，并通过SIAM当地的学生分会向研究生提供研究和职业发展方面的建议。

Objective: The objective of this program is to investigate dynamics and control issues of complementarity systems from a hybrid system perspective with applications to engineering and biological systems. Various physical, biological and economic systems are subject to inequality constraints that are complementary to each other, i.e., at least one of a pair of inequalities holds with equality. Such dynamical systems, called complementarity systems, constitute an important class of hybrid and switching systems in applications. Complementarity approaches, along with system and control techniques, will be exploited to address critical dynamic analysis and control design problems.Intellectual merit: The intellectual merit lies in three aspects:(1) characterization of local switching dynamics of complementarity systems; (2) long-time switching dynamic analysis and control of piecewise smooth systems; (3) applications to contact mechanical systems, systems biology, safety verification, and dynamical optimization. The analytic results to be developed in this program will lay down a rigorous foundation for computation, analysis and design of a broad class of applied nonsmooth systems. The obtained control analysis and feedback design algorithms will be applied to emerging practical systems in robotics, biology, and electronics, and will facilitate analysis and design of complex systems.Broader impacts: The broader impacts are: (1) This program is interdisciplinary and potentially transformative due to the fundamental nature of the focused research topics and their diverse applications, such as robotics, biomedical systems, and systems biology. (2) The proposed research will be closely integrated with educational and outreach activities, including development of graduate curriculum on nonsmooth systems, active involvement with high-school students for engineering education, undergraduates'research mentoring, and advising graduate students on research and career development through a local SIAM student chapter.