Analysis and Control of Complementary Systems

互补系统的分析与控制

• 批准号: 0754374
• 负责人: Jong-Shi Pang
• 金额: $ 11.43万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-09-01 至 2009-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0754374&HistoricalAwards=false
• 关键词: Analysis; Control; Complementary; Systems

A complementarity system is a dynamical system defined by an ordinary differential equation (ODE) involving the solutions of a finite-dimensional complementarity problem parameterized by the state of the differential equation. Complementarity systems constitute a new mathematical paradigm that finds a wide range of applications in nonsmooth mechanics, robotics, multi-body dynamics, switched circuit systems, economic and traffic systems, and even biological systems. As such, the rigorous study of these systems is warranted. Due to their intrinsically nonsmooth characteristics, such a study defies classical dynamical systems theory and requires novel mathematical analysis, computational and design tools. This proposed project is devoted to the investigation of challenging issues in the analysis and control of complementarity systems. We propose to apply state-of-art techniques from mathematical programming, convex analysis, systems theory, and control theory to tackle these problems. On the analytical side, we will address several fundamental and critical issues of system behavior, e.g., existence and uniqueness of solutions and Zeno property, which are directly related to numerical computation and system analysis. Moreover, we aim at studying controllability and observability and developing control algorithms that will be applied to robot motion planning, multi-body systems subject to unilateral constraints, and constrained dynamic optimization problems.Dynamical systems modeled by ODEs provide a powerful mathematical and computational framework for the study and understanding of a wide range of time-dependent physical phenomena that naturally occur in many engineering applications. As the application areas expand, researchers and designers are encountering increasingly complex systems subject to various constraints, which arise as a result of the global behavior of the systems and the interactions between them and their complex environment and/or other systems at different levels. A trivial example of such constraints is a falling object before and after hitting the ground. At the instant where the object touches the ground, an impact occurs followed by a rebounce of the object that results in a change of direction of the object's motion. This is a mode transition. The proposed research aims at treating dynamical systems where mode transition is an unknown but important component of the overall system configuration. If successful, the results of the research will let us gain a better understanding of many complex engineering systems with mode changes and will provide a solid foundation for the improved design of such systems that in turn will have a significant impact on many practical fields. The proposed work will also contribute to the advancement of basic sciences and to the education and training of the human workforce.

互补系统是由常微分方程 (ODE) 定义的动态系统，涉及由微分方程状态参数化的有限维互补问题的解。 互补系统构成了一种新的数学范式，在非光滑力学、机器人学、多体动力学、交换电路系统、经济和交通系统，甚至生物系统中都有广泛的应用。 因此，有必要对这些系统进行严格的研究。 由于其本质上的非光滑特性，此类研究违背了经典动力系统理论，需要新颖的数学分析、计算和设计工具。 该拟议项目致力于研究互补系统分析和控制中的挑战性问题。 我们建议应用数学规划、凸分析、系统理论和控制理论等最先进的技术来解决这些问题。 在分析方面，我们将解决系统行为的几个基本和关键问题，例如解的存在性和唯一性以及芝诺性质，这些问题与数值计算和系统分析直接相关。 此外，我们的目标是研究可控性和可观测性，并开发控制算法，应用于机器人运动规划、受单边约束的多体系统以及约束动态优化问题。通过常微分方程建模的动态系统为研究和理解许多工程应用中自然发生的各种与时间相关的物理现象提供了强大的数学和计算框架。 随着应用领域的扩大，研究人员和设计人员面临着日益复杂的系统，这些系统受到各种约束，这些约束是由于系统的全局行为以及系统与其复杂环境和/或不同级别的其他系统之间的相互作用而产生的。 这种约束的一个简单例子是物体在撞击地面之前和之后的下落。 在物体接触地面的瞬间，会发生冲击，随后物体会反弹，从而导致物体运动方向的改变。 这是一种模式转换。 拟议的研究旨在处理动力系统，其中模式转换是整个系统配置的未知但重要的组成部分。 如果成功，研究结果将使我们更好地理解许多具有模式变化的复杂工程系统，并为改进此类系统的设计提供坚实的基础，进而对许多实际领域产生重大影响。 拟议的工作还将有助于基础科学的进步以及劳动力的教育和培训。