On multiparametric/explicit NMPC for Quadratically Constrained Problems

Abstract We present the expansion of the Basic Sensitivity Theorem to a second order Taylor approach and the implications to explicit model predictive control of quadratically constrained systems. The expansion enables the derivation of an algorithm for the analytical solution of convex multiparametric quadratically constraint programming (mpQCQP) problems and explicit quadratically constrained NMPC problems. We derive the analytical parametric expressions of the control actions for a quadratically constrained MPC problem and its corresponding critical regions. We show the piecewise non-linear form of the solution and closed-loop validation of the results.