A control vector simplex approach to variable structure control of nonlinear systems

An effective way to extend to the multi-input case the variable structure control philosophy is the method based on a set of m + 1 control vectors forming a simplex in R-m, and on the corresponding switching of the controlled system from one to another of m + 1 different structures. In this paper, the basic method is briefly recalled and conditions for the possible extension of its validity to the case of uncertain nonlinear systems affine in the control law are sought. The possibility of guaranteeing the convergence of the simplex method also in the case of nonlinear systems non-affine in the control law is investigated. (C) 1997 by John Wiley & Sons, Ltd.