Stability theory for set-valued stochastic hybrid systems

智力优势：混合系统模拟动态行为，结合了持续进化和瞬时变化。一大类自然发生的系统和工程系统展示了混合动力学。例如空中交通管理系统、脉冲耦合生物振荡器以及网络化和基于逻辑的控制系统。在过去的十年中，混合动力系统在刻划最坏情况下的鲁棒渐近稳定性方面取得了重大进展。建立了一般不变性原理、逆Lyapunov定理、约化原理和基于线性化的结果。最坏情况指的是，这些结果与可能允许非唯一解的混合系统有关，这种情况在混合系统建模中很常见。当前建议的目的是将这些关于混杂系统最坏情况渐近稳定性的最新见解推广到随机设置。我们建议发展一个混杂系统的鲁棒渐近稳定性理论，该理论具有一些最坏情况性质的影响和一些随机性的影响，这些影响在许多自然发生的和工程的混杂系统中普遍存在，包括网络控制系统、空中交通管理系统、生物系统和金融系统。对随机混杂系统稳定性理论的贡献将有助于为随机混杂系统控制设计的进步铺平道路。广泛影响：拟议的努力将通过深化现有的混杂系统研究生课程，并通过培训加州大学伯克利分校S控制、动态系统和计算中心的研究生，为工程教育基础做出贡献。主要控制会议上的辅导研讨会将提供给感兴趣的研究生、教师和行业人员。所有工作都将被记录在备受赞誉的国际会议和著名的控制和动力系统杂志上。将促进与国际研究人员的合作，包括学生交换项目，特别是与墨尔本大学和罗马大学的合作。拟议工作的理论成果将应用于对广大人口具有重要意义的领域，包括有效管理空中交通以提高国家吞吐量的问题-S航空系统。最值得注意的是，我们将继续与南加州大学S分校针对本科生的暑期实习项目合作，该项目最近为我们的控制型研究生带来了成功的指导经验，他们指导过来自不同代表性学生群体的本科生。

Intellectual merit:Hybrid systems model dynamic behavior that combines continuous evolution and instantaneous change. A wide class of naturally occurring and engineered systems exhibit hybrid dynamics. Examples include air traffic management systems, impulsively coupled biological oscillators, and networked and logic-based control systems. Over the last decade, significant progress has been made on characterizing worst-case, robust asymptotic stability in hybrid dynamical systems. General invariance principles, converse Lyapunov theorems, reduction principles, and linearization-based results have been established. Worst-case refers to the fact that these results pertain to hybrid systems that may admit non-unique solutions, a situation that is common in hybrid systems modeling. The aim of the current proposal is to extend these recent insights about worst-case asymptotic stability in hybrid systems to the stochastic setting. We propose to develop a robust, asymptotic stability theory for hybrid systems that feature some effects of a worst-case nature and some effects that are stochastic, a common occurrence in many naturally occurring and engineered hybrid systems, including networked control systems, air traffic management systems, biological systems, and financial systems. The proposed contributions to stability theory for stochastic hybrid systems will help pave the way for advances in control design for stochastic hybrid systems.Broader impact:The proposed effort will contribute to the engineering education base by furthering the available graduate curriculum on hybrid systems, and by training graduate students in UCSB?s Center for Control, Dynamical Systems, and Computation. Tutorial workshops at the main control conferences will be delivered to interested graduate students, faculty, and industry personnel. All work will be documented in acclaimed international conferences and prestigious control and dynamical systems journals. Collaboration with international researchers will be fostered, including student exchange programs, most notably with the University of Melbourne, and the University of Rome, Tor Vergata. The theoretical results of the proposed work will be applied to areas that are significant to the broad population, including problems like the efficient management of air traffic to enhance throughput in the nation?s aviation system. Most notably, we will continue our work with UCSB?s summer internship program aimed at undergraduate students, which has led to recent successful mentoring experiences for our control graduate students who have supervised undergraduate students from various underrepresented student populations.