Further advances in stability analysis for hybrid adversarial Markov decision processes

智能优点：这项研究的目标是结合非随机混合动力系统分析的进展和对抗性马尔可夫决策过程，为一大类混合随机系统产生新的结果。混合随机系统的显著特征是：1)模型结合了随机和最坏情况的影响来产生不唯一的随机过程；2)解结合了连续变化和瞬时变化。关于混杂随机系统的研究大多集中在具有唯一解的系统上。然而，最坏情况和随机效应的组合是自然的，并在广泛的工程系统中表现出来，包括空中交通管理系统、金融系统以及网络和基于逻辑的控制系统。近年来，在刻划非随机混合系统和对抗马尔可夫决策过程的鲁棒渐近稳定性方面取得了重要进展。给出了一般不变性原理、逆Lyapunov定理和基于松弛Lyapunov定理的稳定性充分条件。此外，强大的降阶原理和基于线性化的结果也被推广到混杂系统。本工作的目的是发展混合对抗马尔可夫决策过程的类似结果，这将为随机混合系统的鲁棒控制设计的发展铺平道路。更广泛的影响：拟议的发展将通过促进关于随机和混合系统的现有研究生课程和通过培训研究生来加强工程学教育基础。主要控制会议的辅导研讨会将提供给研究生、研究人员和行业人员。所有技术成果将被记录在备受赞誉的国际会议和著名的系统和控制杂志上。这项工作将促进与国际研究人员的合作，继续与几所国际大学的学生交换项目。拟议工作的进展将应用于对广大人口重要的领域，例如有效管理空中交通，以提高国家-S航空系统的吞吐量。此外，将通过新生研讨会寻求早期教育机会，通过优化和动态的流行应用，在课程早期吸引学生的注意力。

Intellectual Merit: The objective of this research is to combine advances in the analysis of non-stochastic hybrid dynamical systems and adversarial Markov decision processes to generate new results for a broad class of hybrid stochastic systems. The salient features of hybrid stochastic systems are that 1) the models combine stochastic and worst-case effects to generate non-unique random processes and 2) solutions combine continuous change with instantaneous change. Most work on hybrid stochastic systems has focused on systems with unique solutions. Nevertheless, the combination of worst-case and stochastic effects is natural and manifests itself in a wide class of engineered systems, including air traffic management systems, financial systems, and networked and logic-based control systems. In recent years, important progress has been made on characterizing robust asymptotic stability for non-stochastic hybrid systems as well as for adversarial Markov decision processes. General invariance principles, converse Lyapunov theorems and relaxed Lyapunov-based sufficient conditions for stability have been codified. In addition, powerful reduction principles and linearization-based results have been extended to hybrid systems. The aim of the current work is to develop analogous results for hybrid adversarial Markov decision processes, which will help pave the way for advances in robust control design for stochastic hybrid systems. Broader Impacts:The proposed developments will enhance the engineering education base by furthering the available graduate curriculum on stochastic and hybrid systems, and by training graduate students. Tutorial workshops at the main control conferences will be made available to graduate students, researchers, and industry personnel. All technical results will be documented in acclaimed international conferences and prestigious systems and control journals. The work will foster collaboration with international researchers, continuing student exchange programs with several international universities. The progress of the proposed work will be applied to areas that are important to the broad population, for example the efficient management of air traffic to enhance throughput in the nation?s aviation system. In addition, early educational opportunities, down to the freshman level via freshman seminars, will be pursued to capture the attention of students early in the curriculum through popular applications of optimization and dynamics.