Adaptive Control of Time-Varying Systems Using Multiple Models

ecs -0601618多模型时变系统的自适应控制当动态系统参数时变大且变化迅速时，传统的自适应控制是不够的。针对上述困难，提出了多种模型。自1992年以来，PI和他的研究生一直在研究这种结合模型切换和调谐的方法。采用开关对时变进行快速响应，避免突变，并进行调谐以达到稳定性和精度。在这个建议中，提出了一种使用多个模型进行识别和控制的全新方法。随着对象参数的变化（以及输入输出特性的变化），所有识别模型都是同步调整的，但步长不同。这些步长与不同模型的估计误差呈负相关（即误差最小的模型步长最大）。如果工厂的参数向量是分段常数，并且假设随着时间的推移有N个常数值，那么目标是证明N个模型中的每一个都收敛于这些值中的一个。这是问题1。问题2和问题3涉及时变系统自适应控制的不同方面。问题2关注的是具有周期系数的线性系统，问题3处理的是非线性系统，它在未知参数下是线性的。智力优势：这项研究提出了一种全新的识别时变情况的方法。它将极大地扩展自适应控制理论的边界，并将在包括医学、神经科学、经济学和视觉在内的许多领域得到广泛应用。更广泛的影响：自1979年以来，PI每两年组织一次国际研讨会。关于赠款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。其中许多是妇女和少数民族。此外，本科生（包括男性和女性）在夏季与他一起参与国家科学基金项目。该项目将使PI能够在新的数学领域培训研究生和本科生。

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.