Adaptive Control of Time Varying Systems using Multiple Models
Conventional 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.
