Multiscale Singularly Perturbed Control Systems

多尺度奇异摄动控制系统

• 批准号: DP0346099
• 负责人: Prof Vladimir Gaitsgory
• 金额: $ 11.38万
• 依托单位: University of South Australia
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Projects
• 财政年份: 2003
• 资助国家: 澳大利亚
• 起止时间: 2003-01-01 至 2005-12-31
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DP0346099
• 关键词: Multiscale; Singularly; Perturbed; Control; Systems

We propose to develop a unified averaging technique to analyse deterministic and stochastic multiscale singularly perturbed control systems. Such systems arise as mathematical models of real-world dynamical systems in which state variables can change their values with the rates of different orders of magnitude. The technique is based on the assumption that the system, which would describe the dynamics of the fast state variables if slow ones were frozen, possesses certain ergodicity properties expressed in the existence of its limit occupational measures set. Conditions for the existence of such a set will be studied and its structure will be described.

我们提出了一个统一的平均技术来分析确定性和随机多尺度奇异摄动控制系统。这样的系统是作为真实世界动态系统的数学模型出现的，其中状态变量可以以不同数量级的速率改变它们的值。该技术是基于这样的假设，即系统，这将描述的动态的快速状态变量，如果慢的被冻结，具有一定的遍历性属性表示在其存在的极限职业措施集。 将研究存在这样一个集合的条件，并描述其结构。