https://hal.inria.fr/hal-01030531Zanon, MarioMarioZanonESAT - Department of Electrical Engineering [Leuven] - KU Leuven - Catholic University of Leuven - Katholieke Universiteit LeuvenIMTEK - Department of Microsystems Engineering [Freiburg] - University of Freiburg [Freiburg]Gros, SebastienSebastienGrosChalmers University of Technology [GĂ¶teborg]Diehl, MoritzMoritzDiehlESAT - Department of Electrical Engineering [Leuven] - KU Leuven - Catholic University of Leuven - Katholieke Universiteit LeuvenIMTEK - Department of Microsystems Engineering [Freiburg] - University of Freiburg [Freiburg]Indefinite Linear MPC and Approximated Economic MPC for Nonlinear SystemsHAL CCSD2014[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]Zidani, HasnaaSensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID - 2014-07-22 13:13:472021-11-16 10:22:012014-07-22 14:03:23enDocuments associated with scientific eventsapplication/pdf1This talk presents some new results where it has been shown that any stabilizing indefinite LQR or MPC scheme can be reformulated as a positive definite one. First, the conditions for the existence of a stabilizing indefinite LQR are given. Then, two transformations under which the LQR is unchanged are introduced. By combining these two transformations, the problem is reformulated in a form for which it is easy to prove the existence of a positive definite equivalent formulation using Lyapunov arguments. The results are finally extended to the case of a finite horizon and a terminal cost different from the LQR cost-to-go. The talk concludes by proposing a tracking nonlinear MPC formulation that approximately solves economic nonlinear MPC. The derivation is based on the results for the linear quadratic indefinite case and therefore relies on a local stabilizability assumption. The interest of such an approximated scheme is twofold as a) it has the stability properties of tracking schemes and b) it allowes the deployment of efficient numerical methods.