Analysis and improvement of the algorithm for constrained nonlinear control via ellipsoidal techniques

The algorithm of constrained nonlinear control via ellipsoidal techniques cannot ensure the exiting of the solutions for all initial points. The improved algorithm is proposed on the basis of mathematic analysis of ellipsoidal techniques. Computing any point of intersection of the polytope and the ellipsoid is used in the improved algorithm, instead of that of the intersection of two ellipsoids in ellipsoidal techniques, for calculating the solutions of some initial points where ellipsoidal techniques cannot ensure the existence of the solutions. Analysis and the results of simulation show that the improved algorithm ensures the existence of the solution for all the initial points.