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Simplex sliding mode control for nonlinear uncertain systems via chaos optimization. (English) Zbl 1096.93009
A class of uncertain affine nonlinear control systems is considered. First, the basic idea of a simplex-type sliding mode control is briefly explained. Next, a procedure to realize this idea is described by working out a concrete three-dimensional example. An important feature of this procedure is that the computing of the simplex control vectors is based on a chaotic time series. This time series is generated by the logistic mapping. Moreover, the simplex control vectors depend on the Euclidean norm of the sliding vector. This reduces the chattering effect and speeds up the convergence. Some computer simulations illustrate the effectiveness of the proposed approach.

MSC:
93B12 Variable structure systems
93C10 Nonlinear systems in control theory
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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