Further advances in stability analysis for hybrid adversarial Markov decision processes

混合对抗马尔可夫决策过程稳定性分析的进一步进展

• 批准号: 1232035
• 负责人: Andrew Teel
• 金额: $ 37.6万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-10-01 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1232035&HistoricalAwards=false
• 关键词: Further; advances; stability; analysis; hybrid

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.

智力优势：本研究的目的是结合联合收割机在非随机混合动力系统和对抗马尔可夫决策过程的分析进展，产生新的结果，广泛的一类混合随机系统。混合随机系统的显著特点是：1）模型联合收割机随机和最坏情况的影响，产生非唯一的随机过程和2）解决方案联合收割机连续变化和瞬时变化。大多数关于混合随机系统的工作都集中在具有唯一解的系统上。然而，最坏情况和随机效应的结合是自然的，并表现在广泛的工程系统，包括空中交通管理系统，金融系统，网络和基于逻辑的控制系统。近年来，在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。一般不变性原则，匡威李雅普诺夫定理和放松的李雅普诺夫为基础的稳定性充分条件已编纂。此外，强大的减少原则和基于线性化的结果已扩展到混合动力系统。目前的工作的目的是开发类似的混合对抗马尔可夫决策过程的结果，这将有助于铺平道路的随机混合系统的鲁棒控制设计的进步。更广泛的影响：拟议的发展将加强工程教育基础，进一步提供随机和混合系统的研究生课程，并通过培训研究生。 在主要控制会议上的研讨会将提供给研究生，研究人员和行业人员。所有的技术成果将被记录在著名的国际会议和著名的系统和控制期刊。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流计划。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全国的吞吐量？的航空系统。 此外，早期教育的机会，通过新生研讨会下降到新生的水平，将追求捕捉学生的注意力，通过流行的应用程序的优化和动态早期的课程。