G. Bartolini, F. Parodi, V. I. Utkin, T. Zolezzi, "The simplex method for nonlinear sliding mode control", Mathematical Problems in Engineering, vol. 4, Article ID 851687, 27 pages, 1999. https://doi.org/10.1155/S1024123X98000921
The simplex method for nonlinear sliding mode control
General nonlinear control systems described by ordinary differential equations with a prescribed sliding manifold are considered. A method of designing a feedback control law such that the state variable fulfills the sliding condition in finite time is based on the construction of a suitable simplex of vectors in the tangent space of the manifold. The convergence of the method is proved under an obtuse angle condition and a way to build the required simplex is indicated. An example of engineering interest is presented.
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