Analysis of sticking regions in adaptive systems

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.