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Title: Performance Improvement in Adaptive Control:An Initial Excitation based Framework
Speaker: Dr. Sayan Basu Roy, IIIT-Delhi
Date: February 28, 2019 (Thursday)
Abstract: This talk would focus on performance issues in adaptive control, which is a class of nonlinear control technique used to tackle structured uncertain dynamical systems. Adaptive control can be visualized as a real-time uncertainty handling mechanism, which uses an online parameter estimator in conjunction with the controller to control a plant with parametric uncertainty.
It is well known that classical adaptive controllers typically guarantee Lyapunov stability in the extended state space (tracking error and parameter estimation error space), and asymptotic convergence of tracking error to zero, however, parameter convergence is only guaranteed if a restrictive condition of persistence of excitation (PE) is satisfied by the regressor signal. The PE condition is stringent since it demands sufficient energy/richness of information content for the entire time duration and, in general, conflicts with the tracking requirement.
The talk would emphasize on transient improvement of adaptive controllers through ensuring parameter convergence without requiring the stringent PE condition. We have developed new class of composite adaptive controllers, which build on two-layers of low-pass filters, and ensure parameter convergence using a milder condition of initial excitation (IE) on the regressor signal. The IE condition, which is shown to be online verifiable, is significantly less stringent
than PE, since it demands sufficient energy/richness of the regressor only in the initial time window. The IE-based adaptive control guarantees exponential stability of the tracking and parameter estimation error once the online-verifiable IE condition is satisfied. Unlike conventional adaptive controllers, which only ensure asymptotic tracking, the proposed design is practically more significant due to its capability of exponentially fast tracking performance, which is especially crucial in safety-critical applications.