Impulsive and switched systems with applications

近年来，世界范围内对脉冲和开关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，癌症化疗中的药物管理，利率调整，约束冲击力学和生态系统管理。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在脉冲和开关动力系统上失效，特别是当系统包含时滞和随机扰动时。需要开发新的想法，以鲁棒性和易于应用的方式处理冲击、跳跃、切换、滑动和抖振问题。其次，对其动力学的定性理解需要特定的方法，不能简单地适应纯连续或纯离散动力系统的已知技术。在本研究计划中，将进行基础研究（概念、标准和理论研究）和技术开发（算法设计和计算机仿真）。提出的研究计划将产生基本理论、比较方法、不变性原理、稳定性和鲁棒稳定性准则、最优控制的条件和算法，以及具有时滞和随机扰动的脉冲和切换动力系统的仿真和稳定控制的有效计算算法和软件包。还将在通信网络、安全通信、传染病建模和控制方面进行应用。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。

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.