Singular and Analytic Perturbations, Slow and Fast Time Scales in Control Theory and Viability Theory and their Applications

控制理论和生存理论中的奇异扰动和解析扰动、慢速和快速时间尺度及其应用

• 批准号: LX0560049
• 负责人: A/Prof Vladimir Ejov
• 金额: $ 4.3万
• 依托单位: University of South Australia
• 依托单位国家: 澳大利亚
• 项目类别: Linkage - International
• 财政年份: 2005
• 资助国家: 澳大利亚
• 起止时间: 2005-01-01 至 2011-11-30
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/LX0560049
• 关键词: Singular; Analytic; Perturbations; Slow; Fast

We propose an innovative approach to several important classes of mathematical problems, whose data depend analytically on small perturbation parameters. Time scale problems, and, in particular, the interaction of two types of evolution, slow and fast, arise in many scientific domains (biotechnology, physics, engineering, etc).We expect to develop new techniques for analysis and asymptotic optimisation of singularly perturbed control systems and Markov decision processes. In particular, we plan to establish links between general nonlinear optimal control problems with time average criteria and linear programming problems in the space of limit occupational measures generated by the underlying control system.

我们提出了一种创新的方法，几个重要的数学问题，其数据分析依赖于小扰动参数。时间尺度问题，特别是两种类型的进化，慢和快的相互作用，出现在许多科学领域（生物技术，物理，工程等），我们希望开发新的技术，分析和渐近优化的奇异摄动控制系统和马尔可夫决策过程。特别是，我们计划建立一般的非线性最优控制问题的时间平均标准和线性规划问题的空间中产生的基本控制系统的限制职业措施之间的联系。