Stochastic Adaptive Control Algorithms Originally Designed for the Ideal System Models are Robust with Respect to Unmodeled Dynamics and External Disturbances

Originally adaptive control theory was developed for the ideal system models, i.e., linear system models under the assumption that relative degree and upper bounds on the order of the systems are known. At the beginning of the last decade, adaptive control algorithms designed for such ideal system models were strongly attacked by many researchers due to "lack of robustness" in the presence of unmodeled dynamics and external disturbances. The purpose of the present paper is to relax existing constant pressure on the adaptive control algorithms originally designed for the ideal system models. It is shown that such adaptive control algorithms are globally stable and robust with respect to unmodeled dynamics and external disturbances without any modifications, such as ¿-modification, e1-modification, relative dead-zone, projection of the parameter estimates, etc. The essential for establishing the global stability of the unmodified algorithms is to understand and mathematically formalize self-stabilization mechanism which is naturally inherent to such algorithms.