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Efficient Direct Multiple Shooting for Nonlinear Model Predictive Control on Long Horizons

Christian Kirches (christian.kirches***at***iwr.uni-heidelberg.de)
Leonard Wirsching (leonard.wirsching***at***iwr.uni-heidelberg.de)
Hans Georg Bock (bock***at***iwr.uni-heidelberg.de)
Johannes P. Schlöder (johannes.schloeder***at***iwr.uni-heidelberg.de)

Abstract: We address direct multiple shooting based algorithms for nonlinear model predictive control, with a focus on problems with long prediction horizons. We describe different efficient multiple shooting variants with a computational effort that is only linear in the horizon length. Proposed techniques comprise structure exploiting linear algebra on the one hand, and approximation of derivative information in an adjoint Sequential Quadratic Programming method on the other. For explicit one--step methods for ordinary differential equations we address the issue of consistent and fast generation of both forward and adjoint derivatives of dynamic process models according to the principle of Internal Numerical Differentiation. We discuss the applicability of the proposed methods at the example of three benchmark problems. These have recently been addressed in literature and serve to evaluate the relative performance of each of the proposed methods for both off--line optimal control and on--line nonlinear model predictive control. Throughout, we compare against results published for a recently proposed collocation approach based on finite elements.

Keywords: nonlinear model predictive control, direct and simultaneous methods for optimal control, sensitivity generation, benchmarks

Category 1: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Applications -- Science and Engineering (Other )

Citation: Accepted for publication in Journal of Process Control.

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Entry Submitted: 05/31/2011
Entry Accepted: 05/31/2011
Entry Last Modified: 11/06/2012

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