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Indefinite Linear MPC and Approximated Economic MPC for Nonlinear Systems

Abstract : This 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.
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https://hal.inria.fr/hal-01030531
Contributor : Hasnaa Zidani <>
Submitted on : Tuesday, July 22, 2014 - 1:13:47 PM
Last modification on : Thursday, June 18, 2020 - 10:18:03 AM
Long-term archiving on: : Tuesday, November 25, 2014 - 11:00:47 AM

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Mario Zanon, Sebastien Gros, Moritz Diehl. Indefinite Linear MPC and Approximated Economic MPC for Nonlinear Systems. NETCO 2014 - New Trends in Optimal Control, Jun 2014, Tours, France. ⟨hal-01030531⟩

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