Dynamical systems with random influences mixing logic and physics: a framework enabling control engineers to design for resilient autonomy

具有随机影响的混合逻辑和物理的动力系统：使控制工程师能够设计弹性自治的框架

• 批准号: 1508757
• 负责人: Andrew Teel
• 金额: $ 35万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1508757&HistoricalAwards=false
• 关键词: Dynamical; systems; random; influences; mixing

The goal of this project is to develop the mathematical tools necessary to describe and analyze dynamical systems that mix logic and physics while including random influences. These types of systems are sometimes called stochastic hybrid systems; where stochastic refers to the presence of random influences and hybrid refers to the mix of logic-based decision making and physical laws that determine the system evolution. These mathematical tools would be extremely useful, as they would provide a framework enabling control engineers to better design autonomous dynamical systems that are resilient in the face of uncertainty. The results of this proposal have the potential to impact researchers in a wide variety of application domains, where randomness interacts with worst-case effects and rigorous analysis tools are needed to certify desirable behavior in an engineered system. One possible application domain is the control of gene expression and other particular biological phenomena. Another application area is multi-agent resource allocation algorithms where agents invoke randomness in their allocation strategies to guarantee robustness to malicious agents in the network. Indeed, stochastic hybrid systems can be used to model complicated biological systems, financial systems, resource allocation systems, and traffic management systems, to name just a few. All of the results developed through this proposal will be published in the leading conference venues and journals, to provide avenues for the transition of the work to applications. Beyond contributions to the scientific literature, the proposed work will add to the existing graduate curriculum on stochastic and hybrid dynamical systems. Graduate students will be trained through direct financial support, but a broader group of students will be educated through teaching materials and a course that will be developed around the produced breakthroughs. These students include graduate students in all areas of engineering. To reach students broadly, the PI envisions a graduate textbook on stochastic hybrid systems emerging from this work, to complement the recent book on non-stochastic hybrid systems. The work will spawn collaboration with international researchers, and will enhance student exchange programs with several international universities. The research developments will be applied to areas that are important to the broad population. Moreover, the PI will use this opportunity to consider how to expose freshman engineering students to a broad range of dynamical systems principles. This effort will follow up the previous experience teaching a freshman seminar, to engineering and non-engineering students, on the application of optimization principles to real-world problems. The aim here aligns with the societal goal of keeping younger students engaged in topics related to science, technology, engineering, and mathematics.The specific technical objectives of the project start with establishing a mathematical framework and solution concept that is tractable yet general enough to be widely applicable. Tools from the field of variational analysis are crucial to this development. The objectives continue with the task of developing a wide range of analysis tools that can be used to certify appropriate behavior of an engineered stochastic hybrid system. The techniques will especially focus on a Lyapunov analysis for stability properties like asymptotic stability in probability and recurrence; other ideas that have been fruitful for non-stochastic hybrid systems also will be considered. Next, the aim is to establish strong sequential compactness results for the set of solutions to the models considered and, from these results, establish an invariance principle and converse Lyapunov theorems. These results would parallel recent, very useful results for non-stochastic hybrid systems. The final task is to begin to show explicitly how the developed framework and analysis tools can be used to engineer advanced, resilient, autonomous control systems.

该项目的目标是开发描述和分析混合逻辑和物理同时包含随机影响的动力系统所需的数学工具。 这些类型的系统有时称为随机混合系统；其中随机是指随机影响的存在，混合是指基于逻辑的决策和决定系统演化的物理定律的混合。 这些数学工具将非常有用，因为它们将提供一个框架，使控制工程师能够更好地设计面对不确定性时具有弹性的自主动力系统。 该提案的结果有可能影响各种应用领域的研究人员，其中随机性与最坏情况的影响相互作用，需要严格的分析工具来证明工程系统中的理想行为。一种可能的应用领域是基因表达和其他特定生物现象的控制。另一个应用领域是多代理资源分配算法，其中代理在其分配策略中调用随机性，以保证网络中恶意代理的稳健性。 事实上，随机混合系统可用于对复杂的生物系统、金融系统、资源分配系统和交通管理系统进行建模，仅举几例。通过该提案得出的所有结果都将在领先的会议场所和期刊上发表，为工作向应用的过渡提供途径。 除了对科学文献的贡献之外，拟议的工作还将添加到现有的随机和混合动力系统研究生课程中。研究生将通过直接的财政支持接受培训，但更广泛的学生群体将通过教材和围绕所取得的突破开发的课程接受教育。这些学生包括所有工程领域的研究生。 为了更广泛地接触学生，PI 设想从这项工作中出现一本关于随机混合系统的研究生教科书，以补充最近关于非随机混合系统的书。这项工作将催生与国际研究人员的合作，并将加强与几所国际大学的学生交换项目。研究进展将应用于对广大民众重要的领域。此外，PI 将利用这个机会考虑如何让工程专业的新生了解广泛的动力系统原理。这项工作将延续之前向工程和非工程学生举办的新生研讨会，讲述优化原理在实际问题中的应用。这里的目标与让年轻学生参与科学、技术、工程和数学相关主题的社会目标是一致的。该项目的具体技术目标首先是建立一个易于处理但足够通用、可广泛应用的数学框架和解决方案概念。 变分分析领域的工具对于这一发展至关重要。 目标继续是开发各种分析工具，这些工具可用于验证工程随机混合系统的适当行为。 这些技术将特别关注稳定性特性的李亚普诺夫分析，例如概率和递归的渐近稳定性；还将考虑对非随机混合系统卓有成效的其他想法。 接下来，目标是为所考虑的模型的解集建立强顺序紧性结果，并根据这些结果建立不变性原理并逆李雅普诺夫定理。 这些结果与非随机混合系统最近非常有用的结果相似。 最后的任务是开始明确展示如何使用开发的框架和分析工具来设计先进的、有弹性的、自主的控制系统。