"Nonlinear Algorithms for Verification, Control, Design and Analysis of Nonlinear Continuous and Hybrid Systems"

“用于非线性连续和混合系统验证、控制、设计和分析的非线性算法”

• 批准号: 298211-2012
• 负责人: Mitchell, Ian
• 金额: $ 1.6万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=548263
• 关键词: Nonlinear; Algorithms; Verification; Control; Design

I propose to develop numerical algorithms and implementations for the verification, control and design of systems whose dynamics are best described by nonlinear continuous or hybrid (a mixture of continuous and discrete) models. Such systems arise whenever a digital computer interacts with the external world, and they are hence becoming ever more widespread as computers are embedded into devices throughout our environment. The foundation of this research program will be the study of a variety of reachability algorithms for continuous systems, including both grid and trajectory based with both parametric and nonparametric reach set representations. Application of these techniques can reduce the likelihood of undesirable behaviours, but for nonlinear continuous and hybrid systems it has rarely been possible or it has required the intervention of reachability experts. With the long-term goal of bringing these formal analysis methods into industrial practice, two distinct application domains will inform this program of research: safe collaborative control of robots, and design of robust analog and mixed-signal integrated circuits. In order to solve real problems without the intervention of experts in formal methods, this program will also address two other key needs: construction of the mathematical model of the system and problem to be solved based on descriptions typically used by domain experts, and conversion of the verification results into a form which addresses those experts' concerns. For the domain specific toolchains and, where necessary, for the core reachability algorithms I will create and release flexible, efficient, robust and well-documented implementations that will do for these techniques what the Toolbox of Level Set Methods has done for time-dependent Hamilton-Jacobi equations: permit other researchers in industry and academia to reproduce, utilize and extend published results. Trainees will gain experience in numerical algorithms, robust software development practices, integrated circuits and/or robotics, all areas with positive job prospects. Finally, the choice of distinct application areas will guide the extension of automated formal analysis into other domains exhibiting continuous and hybrid dynamics.

我建议开发用于验证，控制和设计的数值算法和实现，其动力学最好由非线性连续或混合动力车（连续和离散的）模型来描述。 每当数字计算机与外部世界互动时，就会出现这种系统，因此随着计算机嵌入到整个环境中的设备中，它们变得越来越普遍。 该研究计划的基础将是对连续系统的各种可及性算法的研究，包括基于参数和非参数触及设置表示的网格和轨迹。 这些技术的应用可以降低不良行为的可能性，但是对于非线性连续和混合系统，它很少有可能，或者需要干预可及专家。 将这些正式分析方法带入工业实践的长期目标，两个不同的应用领域将为这项研究计划提供信息：对机器人的安全协作控制以及强大的模拟和混合信号综合电路的设计。 为了在不进行正式方法的专家干预的情况下解决实际问题，该计划还将满足其他两个关键需求：构建系统的数学模型以及根据域专家通常使用的描述来解决的问题，以及将验证结果转换为解决这些专家关注的表单。 对于域特定的工具链以及必要时，对于核心可及性算法，我将创建和释放灵活，高效，可靠和有据可查的实现，这些实现将为这些技术做什么水平设置方法工具箱对时间依赖的汉密尔顿 - 雅各布方程式所做的工作：允许其他研究人员在行业和学院的其他研究人员复制，延长并扩展出来并扩展出来的结果，并延长了出现的结果。 受训人员将获得数值算法，强大的软件开发实践，集成电路和/或机器人技术的经验，所有领域都有积极的工作前景。 最后，选择不同的应用领域的选择将指导自动化的形式分析扩展到表现连续和混合动力学的其他领域。