Analysis of Slow Convergence Regions in Adaptive Systems

We examine convergence properties of errors in a class of adaptive systems that corresponds to adaptive control of linear time-invariant plants with state variables accessible. We demonstrate the existence of a sticking region in the error space where the state errors move with a finite velocity independent of their magnitude. We show that these properties are also exhibited by adaptive systems with closed-loop reference models which have been demonstrated to exhibit improved transient performance as well as those that include an integral control in the inner-loop. Simulation and numerical studies are included to illustrate the size of this sticking region and its dependence on various system parametersthe Boeing University Strategic Initiativ

Analysis of slow convergence regions in adaptive systems

Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2016.Cataloged from PDF version of thesis.Includes bibliographical references (pages 77-78).In this thesis, the convergence properties of errors are examined in a class of adaptive systems that corresponds to adaptive control of linear time-invariant plants with state variables accessible. The existence of a sticking region is demonstrated in the error space where the state errors move with a finite velocity independent of their magnitude. It is shown that these properties are also exhibited by adaptive systems with closed-loop reference models, which have been demonstrated to exhibit improved transient performance, as well as those that include an integral control in the inner-loop. Simulation and numerical studies are included to illustrate the size of this sticking region and its dependence on various system parameters. With the existence of sticking regions shown for inner-loop adaptive controllers, the impact on outer-loop control is demonstrated for systems that implement inner-loop adaptation.by Oscar Nouwens.S.M