Analysis of sticking regions in adaptive systems

摘要

We examine convergence properties of errors in a class of adaptive systems that correspond 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 exhibited by adaptive systems with closed-loop reference models, which have been demonstrated to exhibit improved transient performance. A simulation study is 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, its impact on outer-loop control is demonstrated for systems that implement inner-loop adaptation. A flight control example is presented to illustrate this impact of sticking in a practical application.