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arXiv · 1810.01368

Speed-Gradient Control of the Brockett Integrator

M. V. Dolgopolik·A. L. Fradkov
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Abstract

A nonsmooth extension of the speed-gradient algorithms in finite form is proposed. The conditions ensuring control goal (convergence of the goal function to zero) are established. A new algorithm is applied to almost global stabilization of the Brockett integrator that has become a popular benchmark for nonsmooth and discontinuous algorithms. It is proved that the designed control law stabilizes the Brockett integrator for any initial point that does not lie on the x3-axis. Besides, it is shown that the speed-gradient algorithm ensures stabilization with an arbitrarily small control level. An important feature of the proposed control is the fact that it is continuous along trajectories of the closed-loop system.

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M. V. Dolgopolik, A. L. Fradkov. 2018-10-02. Speed-Gradient Control of the Brockett Integrator. https://doi.org/10.1137/15m1013456

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