LMI approach of constrained optimization in generalized predictive control

The addition of equality and inequality constraints in generalized predictive control (GPC) strategies switches the classical problem of quadratic cost function minimization into a nonlinear optimization. Some approaches have already been developed, which consider the Lagrange multipliers and gradient optimization. This paper presents the reformulation of GPC under constraints into an adequate form for linear matrix inequalities (LMI) solvers. The optimization of the reformulated problem is performed by linear convex programming. Moreover, it is shown that this new presentation of constrained GPC provides an original flexibility for adding further constraints to the problem. Finally, some simulation results are given and compared to previous approaches of this structure.