GGP approach to solve non convex min-max robust model predictive controller for a class of constrained MIMO systems

This paper proposes a new mathematical method to solve min-max predictive controller for a class of constrained linear Multi Input Multi Output (MIMO) systems. A parametric uncertainty state space model is adopted to describe the dynamic behavior of the real process. Since the resulting optimization problem is non convex, a deterministic global optimization technique is adopted to solve it which is the Generalized Geometric Programming (GGP). The key idea of this method is to transform the initial non convex optimization problem to a convex one by means of variable transformations. The main achievement is that the optimal control value found with the GGP shows successful set point tracking and constraints satisfaction. Moreover, an efficient implementation of this approach will lead to an algorithm with a low computational burden. The main features of the new algorithm are illustrated through a MIMO system.