A symbolic-numeric approach to multi-parametric programming for control design

In this paper we propose a new method which enables us to obtain exact parametric solutions for multi-parametric programming problems, that is the optimal solutions as a function of the varying parameters, using symbolic quantifier elimination technique. The existing methods for multi-parametric programming are based on the sensitivity analysis theory and, in general produce approximate optimal solutions. Therefore usually there exist significant gaps between obtained numerical approximated solutions and exact ones, in particular, for multi-parametric nonlinear programming. It is desired to resolve this issue. Our method based on symbolic computation will remedy this drawback.