Adaptive Control of Time-Varying Systems Using Multiple Models

使用多个模型的时变系统的自适应控制

• 批准号: 0601618
• 负责人: Kumpati Narendra
• 金额: $ 22万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-06-01 至 2009-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0601618&HistoricalAwards=false
• 关键词: Adaptive; Control; Time; Varying; Systems

ECS-0601618Adaptive Control of Time Varying Systems using Multiple ModelsConventional adaptive control is not adequate when time-variations in the parameters of dynamical systems are both large and rapid. Multiple models have been proposed to cope with the above difficulties. The PI and his graduate students have been investigating such methods since 1992 which combining switching between models and tuning. Switching is used to respond rapidly to time-variations to avoid catastrophe, and tuning is carried out to achieve stability and accuracy.In this proposal a radically new way of using multiple models is proposed for identification and control. As the plant parameters (and consequently the input-output characteristics vary) all the identification models are adjusted simultaneously, but with different step sizes. These step sizes are inversely related to the estimation error of the different models (i.e. the model with the smallest error has the largest step size). If the parameter vector of the plant is piecewise constant and assumes N constant values over time, the objective is to prove that each of the N models will converge to one of these values. This is posed as Problem 1. Problems 2 and 3 deal with different aspects of adaptive control of time-varying systems. While Problem 2 is concerned with linear systems with periodic coefficients, Problem 3 deals with nonlinear systems, which are linear in the unknown parameters.Intellectual Merit: The research proposed is a radically new way of identifying time-varying situations. It will significantly extend the boundaries of adaptive control theory and will have wide application in many areas including medicine, neuroscience, economics, and vision. Broader Impact: The PI has organized International Workshops once every two years since 1979. The research carried out on the Grant will be disseminated widely at these workshops. The PI has had forty-two Ph.D students and over thirty-five visiting fellows during the past 44 years. Many of them were women and minorities. Further, undergraduates (both men and women) have worked with him on NSF projects during the summer. This project will enable the PI to train both graduate and undergraduates in new areas of mathematics.

ECS-0601618使用多模型时变系统的自适应控制当动态系统参数的时变既大又快时，传统的自适应控制是不够的。已经提出了多种模型来科普上述困难。PI和他的研究生们从1992年开始研究这种方法，它结合了模型之间的切换和调整。切换用于快速响应时间变化，以避免灾难，并进行调整，以实现稳定性和准确性。在这个建议中，提出了一个全新的方式使用多个模型的识别和控制。由于设备参数（因此输入输出特性变化），所有的识别模型同时调整，但具有不同的步长。这些步长与不同模型的估计误差成反比（即，具有最小误差的模型具有最大步长）。如果被控对象的参数向量是分段常数，并假设N个随时间变化的常数值，则目标是证明N个模型中的每一个都将收敛到这些值中的一个。这被称为问题1。问题2和问题3涉及时变系统自适应控制的不同方面。虽然问题2是与线性系统的周期系数，问题3涉及非线性系统，这是线性的未知parameters.Intellectual优点：提出的研究是一个全新的方式识别时变的情况。它将大大扩展自适应控制理论的边界，并将在许多领域，包括医学，神经科学，经济学和视觉有广泛的应用。更广泛的影响：自1979年以来，PI每两年举办一次国际讲习班。利用赠款进行的研究将在这些讲习班上广泛传播。在过去的44年里，PI有42名博士生和超过35名访问学者。其中许多人是妇女和少数民族。此外，本科生（男性和女性）在夏季与他一起参与NSF项目。该项目将使PI能够在新的数学领域培训研究生和本科生。