The simplex method for nonlinear sliding mode control (Q1305762)

A nonlinear control system described by ordinary differential equations, with a fixed sliding manifold, is considered. It is assumed that the dynamics is completely known and every state is available to the controller. A method of designing a feedback control law such that the state variable fulfills the sliding condition is proposed. The convergence of the method in finite time is based on a construction of a suitable simplex of vectors (the edges of the simplex form uniformly obtuse angles) in the tangent space of the manifold. A real control system of engineering interest is also studied.