Nonlinear impulsive and hybrid systems with time delay: theory, methods and applications

具有时滞的非线性脉冲和混合系统：理论、方法和应用

• 批准号: 106000-2006
• 负责人: Liu, Xinzhi
• 金额: $ 1.38万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=365843
• 关键词: Nonlinear; impulsive; hybrid; systems; time

There has been a growing world-wide interest in the study of impulsive and hybrid dynamical systems in recent years. Such systems arise in many applications such as communication networks, drug administration in cancer chemotherapy and diabetes, constrained impact mechanics, switching circuits in power electronics, non-smooth and hybrid control of spacecrafts, and ecosystems management. However, there are many challenging issues. Firstly, many theorems of continuous dynamical systems fail for impulsive and hybrid dynamical systems, especially  when the systems contain time delays. New ideas need to be developed that deal with impacts, jumps, switching, and chattering problems in a robust and easily applicable way. Secondly, the qualitative understanding of their dynamics requires specific methods and cannot be solved with simple adaptations of known techniques for continuous linear or nonlinear dynamical systems. The objectives of the proposed research program are (i) to develop the fundamental theory for impulsive and hybrid dynamical systems with time delay; (ii) to develop some general methods that deal with impacts, jumps, switching, and chattering problems; (iii) to develop stability and robust stability criteria and methods of computing the domain of  attraction; (iv) to develop stabilizing control design methods for impulsive and hybrid dynamical systems with delayed feedback; (v) to develop algorithms for impulsive synchronization of complex networks; (vi) to develop efficient computational algorithms for simulation and control of impulsive and hybrid dynamical systems; (vii) to apply the obtained methods to real world problems. In this program, both fundamental research (philosophy, concepts and theoretical investigation) and technical development (system design and computer simulation) will be conducted. The outcomes will enhance Canada's reputation for leading edge research and facilitate opportunities for international collaboration. It will also provide an excellent opportunity for research training of highly qualified personnel.

近年来，世界范围内对脉冲动力系统和混合动力系统的研究日益引起人们的兴趣。这样的系统出现在许多应用中，如通信网络、癌症化疗和糖尿病的药物管理、约束冲击力学、电力电子中的开关电路、航天器的非平滑和混合控制以及生态系统管理。然而，有许多具有挑战性的问题。首先，连续动力系统的许多定理不适用于脉冲和混合动力系统，特别是当系统包含时滞时。需要开发新的想法，以稳健和易于应用的方式处理冲击、跳跃、切换和抖振问题。其次，对其动力学的定性理解需要特定的方法，不能简单地适应连续线性或非线性动力系统的已知技术。提出的研究计划的目标是：(1)发展具有时滞的脉冲和混合动力系统的基本理论；（ii）发展一些处理撞击、跳跃、切换和抖动问题的一般方法；（iii）制定稳定性和稳健稳定性标准和计算引力域的方法；(4)发展具有延迟反馈的脉冲和混合动力系统的稳定控制设计方法；(v)开发复杂网络脉冲同步算法；（vi）为脉冲和混合动力系统的模拟和控制开发有效的计算算法；（vii）将获得的方法应用于现实世界的问题。在这个项目中，将进行基础研究（哲学、概念和理论研究）和技术开发（系统设计和计算机仿真）。其成果将提高加拿大在前沿研究方面的声誉，并促进国际合作的机会。它还将为高素质人才的研究培训提供极好的机会。