Using Nonlinear Model Predictive Control for Dynamic Decision Problems in Economics

32 Pages Posted: 3 Apr 2013 Last revised: 28 Jan 2015

See all articles by Lars Grüne

Lars Grüne

University of Bayreuth - Mathematical Institute

Willi Semmler

The New School - Department of Economics; Universitaet Bielefeld; IIASA

Marleen Stieler

University of Bayreuth - Mathematical Institute

Date Written: January 19, 2015

Abstract

This paper presents a new approach to solve dynamic decision models in economics. The proposed procedure, called Nonlinear Model Predictive Control (NMPC), relies on the iterative solution of optimal control problems on finite time horizons and is well established in engineering applications for stabilization and tracking problems. Only quite recently, extensions to more general optimal control problems including those appearing in economic applications have been investigated. Like Dynamic Programming (DP), NMPC does not rely on linearization techniques but uses the full nonlinear model and in this sense provides a global solution to the problem. However, unlike DP, NMPC only computes one optimal trajectory at a time, thus avoids to grid the state space and for this reason the computational demand grows much more moderate than for DP. In this paper we explain the basic idea of NMPC together with some implementational details and illustrate its ability to solve dynamic decision problems in economics by means of numerical simulations for various examples, including stochastic problems, models with multiple equilibria and regime switches in the dynamics.

Keywords: Complex decision models, long and short horizon models, dynamic optimization, multiple equilibria, regime changes, NMPC

JEL Classification: C00, C61, C63, C68

Suggested Citation

Grüne, Lars and Semmler, Willi and Stieler, Marleen, Using Nonlinear Model Predictive Control for Dynamic Decision Problems in Economics (January 19, 2015). Available at SSRN: https://ssrn.com/abstract=2242339 or http://dx.doi.org/10.2139/ssrn.2242339

Lars Grüne

University of Bayreuth - Mathematical Institute ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

Willi Semmler (Contact Author)

The New School - Department of Economics ( email )

65 Fifth Avenue
New York, NY 10003
United States

HOME PAGE: http://www.newschool.edu/nssr/faculty/?id=4e54-6b79-4e41-3d3d

Universitaet Bielefeld ( email )

Universitätsstraße 25
Bielefeld, NRW
Germany

IIASA ( email )

Schlossplatz 1
Laxenburg/Austria, A-2361
Austria

Marleen Stieler

University of Bayreuth - Mathematical Institute ( email )

Universitatsstr 30
Bayreuth, D-95447
Germany

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