Polytopic outer approximations of semialgebraic sets

This paper deals with the problem of finding a polytopic outer approximation P* of a compact semialgebraic set S ⊆ Rⁿ. The computed polytope turns out to be an approximation of the linear hull of the set S. The evaluation of P* is reduced to the solution of a sequence of robust optimization problems with nonconvex functional, which are efficiently solved by means of convex relaxation techniques. Properties of the presented algorithm and its possible applications in the analysis, identification and control of uncertain systems are discussed.