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Patricio Ordaz, Alex Poznyak, ‘KL’-gain adaptation for attractive ellipsoid method, IMA Journal of Mathematical Control and Information, Volume 32, Issue 3, September 2015, Pages 447–469, https://doi.org/10.1093/imamci/dnt046
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Abstract
This paper presents the development of an adaptive state estimator and an output controller based on the attractive ellipsoid method (AEM) for a class of uncertain non-linear systems (quasi-Lipschitz with external perturbations). The proposed method guarantees that, under a specific persistent excitation condition, the controlled system trajectories converge to an ellipsoid having a smaller trace of the corresponding inverse ellipsoidal matrix comparing to classical AEM without adaptation. An underactuated vertical double pendulum is considered as an experimental illustrative example of the suggested approach.