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Adaptive Finite-time Disturbance Rejection for Nonlinear Systems using an Experience-Replay based Disturbance Observer

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Document pages: 10 pages

Abstract: Control systems are inevitably affected by external disturbances, and a majorobjective of the control design is to attenuate or eliminate their adverseeffects on the system performance. This paper presents a disturbance rejectionapproach with two main improvements over existing results: 1) it relaxes therequirement of calculating or measuring the state derivatives, which are notavailable for measurement, and their calculation is corrupted by noise, and 2)it achieves finite-time disturbance rejection and control. To this end, thedisturbance is first modeled by an unknown dynamics, and an adaptivedisturbance observer is proposed to estimate it. A filtered regressor form isleveraged to model the nonlinear system and the unknown disturbance. It isshown that using this filtered regressor form, the disturbance is estimatedusing only measured state of the regressor. That is, contrary to the existingresults on disturbance rejection, the presented approach does not require thestate derivative measurements. To improve the convergence speed of thedisturbance estimation, an adaptive law, equipped with experience replay, ispresented. The disturbance observer is then augmented with an adaptive integralterminal sliding mode control to assure the finite-time convergence of trackingerror to zero. A verifiable rank condition on the history of the pastexperience used by the experience-replay technique provides a sufficientcondition for convergence. Compared to the existing results, neither theknowledge of the disturbance dynamics nor the state derivatives are required,and finite-time stability is guaranteed. A simulation example illustrates theeffectiveness of the proposed approach.

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