Multi-input sliding mode control of uncertain nonlinear systems through simplex methods.

A multi-input sliding mode control technique, called the simplex method, is presented. Multi-input sliding mode control for nonlinear uncertain system is a generalization of standard single input variable stucture control (VSC). An effective mode to extend the variable structure control technique to the multi-input case is based on a set of m+1 control vectors forning a simplex in R^m, and on the corresponding switching of the controlled system from one to another of m+1 different structures. The advantage of the siplex approach relies on the fact that the number of structures among which the system switches is reduced respect to the component strategy, m+1 instead 2^m.