A design scheme of variable structure adaptive control for uncertain dynamic systems
A model reference adaptive control (MRAC) scheme that can guarantee global asymptotic stability for systems without unstable zeros and unmodeled dynamics was proposed more than fifteen years ago. This was regarded as a landmark development of MRAC theory, but it was soon shown that this scheme cannot always guarantee global asymptotic stability if unmodeled dynamics and bounded external disturbances are present. Since then, many modified MRAC schemes have been proposed. The authors of this paper propose a design scheme of adaptive control with variable structure for linear time-invariant systems with unmodeled or uncertain dynamics. Both additive and multiplicative unmodeled dynamics are considered. The transfer function of the modeled part of the plant is allowed to have unstable zeros and unstable poles. A sign-following system and logic switchings are introduced into the control system; these improve the robustness of adaptive control and simplify the algorithm. The authors prove the global stability of the overall system. They also provide simulation results which show the effectiveness of their methods.
scientific article; zbMATH DE number 885864
scientific article