Global optimality in model predictive control via hidden invariant convexity

arXiv2007.07062MaRDI QIDQ6345075

Author name not available (Why is that?)

Publication date: 14 July 2020

Abstract: Non-convex optimal control problems occurring in, e.g., water or power systems, typically involve a large number of variables related through nonlinear equality constraints. The ideal goal is to find a globally optimal solution, and numerical experience indicates that algorithms aiming for Karush-Kuhn-Tucker points often find (near-)optimal solutions. In our paper, we provide a theoretical underpinning for this phenomenon, showing that on a broad class of problems the objective can be shown to be an invariantly convex function (invex function) of the control decision variables when state variables are eliminated using implicit function theory. In this way, near-global optimality can be demonstrated, where the exact nature of the global optimality guarantee depends on the position of the solution within the feasible set. In a numerical example, we show how high-quality solutions are obtained with local search for a river control problem where invexity holds.

Has companion code repository: https://github.com/jbaayen/homotopy-example

This page was built for publication: Global optimality in model predictive control via hidden invariant convexity

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6345075)