Impulsive and switched systems with applications

近年来，脉冲和切换动力系统的研究在世界范围内引起了越来越大的兴趣。这样的系统出现在许多应用中，如电力电子中的开关电路、航天器的轨道转移和控制、多媒体交换通信网络、癌症化疗中的药物给药、利率调整、约束影响机制和生态系统管理。然而，也有许多具有挑战性的问题。首先，许多连续动力系统的定理在脉冲动力系统和切换动力系统上失效，当系统含有时滞和随机扰动时尤其如此。需要开发新的想法，以一种健壮和易于应用的方式处理冲击、跳跃、切换、滑动和抖动问题。其次，对其动力学的定性理解需要特定的方法，不能通过对纯连续或纯离散动力系统的已知技术的简单适应来解决。在这个研究方案中，将进行基础研究(概念、准则和理论研究)和技术开发(算法设计和计算机模拟)。所提出的研究方案将产生具有时滞和随机扰动的脉冲和切换动态系统的基本理论、比较方法、不变性原理、稳定性和鲁棒稳定性判据、最优控制的条件和算法，以及用于仿真和镇定控制的高效计算算法和软件包。还将开展在通信网络、安全通信、传染病建模和控制方面的应用。这些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。它还将为高素质人员的研究培训提供一个极好的机会。

There has been a growing world-wide interest in the study of impulsive and switched dynamical systems in recent years. Such systems arise in many applications such as switching circuits in power electronics, orbital transfer and control of spacecrafts, multimedia switching communication networks, drug administration in cancer chemotherapy, interest rate adjustment, constrained impact mechanics, and ecosystems management. However, there are many challenging issues. Firstly, many theorems of continuous dynamical systems fail on impulsive and switched dynamical systems, which is especially so when the systems contain time delay and stochastic disturbance. New ideas need to be developed that deal with impacts, jumps, switching, sliding 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 purely continuous or purely discrete dynamical systems. In this research program, both fundamental research (concepts, criteria and theoretical investigation) and technical development (algorithm design and computer simulation) will be conducted. The proposed research program will result in fundamental theory, comparison methods, invariance principle, stability and robust stability criteria, conditions and algorithms for optimal control, and efficient computational algorithms and software packages for simulation and stabilizing control of impulsive and switched dynamical systems with time delay and stochastic disturbances. Applications to communication networks, secure communication, modeling and control of infectious disease will also be carried out. 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.