Numerical optimal control of a coupled ODE-PDE model of a truck with a fluid basin

Matthias  Gerdts; Sven-Joachim  Kimmerle

doi:10.3934/proc.2015.0515

Article Contents

2015, Volume 2015: 515-524. Doi: 10.3934/proc.2015.0515 open access

This issue Previous Article Manakov solitons and effects of external potential wells Next Article A posteriori error analysis of a stabilized mixed FEM for convection-diffusion problems

Numerical optimal control of a coupled ODE-PDE model of a truck with a fluid basin

Matthias Gerdts^1, and
Sven-Joachim Kimmerle^1,

1.
Institut für Mathematik und Rechneranwendung (LRT-1), Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577 Neubiberg/München

Received: August 31, 2014

Revised: May 31, 2015

Published: October 2015

Abstract Related Papers Cited by

Abstract

We consider a numerical study of an optimal control problem for a truck with a fluid basin, which leads to an optimal control problem with a coupled system of partial differential equations (PDEs) and ordinary differential equations (ODEs). The motion of the fluid in the basin is modeled by the nonlinear hyperbolic Saint-Venant (shallow water) equations while the vehicle dynamics are described by the equations of motion of a mechanical multi-body system. These equations are fully coupled through boundary conditions and force terms. We pursue a first-discretize-then-optimize approach using a Lax-Friedrich scheme. To this end a reduced optimization problem is obtained by a direct shooting approach and solved by a sequential quadratic programming method. For the computation of gradients we employ an efficient adjoint scheme. Numerical case studies for optimal braking maneuvers of the truck and the basin filled with a fluid are presented.

Keywords:

Mathematics Subject Classification: Primary: 35Q35, 49J15, 49J20; Secondary: 35L04, 49N90, 76B15.

Citation:

Related Papers

Cited by

References

[1]	J. M. Coron, Control and Nonlinearity, Mathematical Surveys and Monographs 136, American Mathematical Society, Providence, RI, 2007.
[2]	F. Dubois, N. Petit and P. Rochon, Motion planning and nonlinear simulations for a tank containing a fluid, in Proc. of the 5th European Control Conf. (ECC 99), Karlsruhe, 31.08.-03.09.1999.
[3]	L. C. Evans, Partial Differential Equations, $2^{nd}$ edition, Graduate Studies in Mathematics 19, American Mathematical Society, Providence, RI, 2010.
[4]	M. Gerdts, Optimal Control of ODEs and DAEs, de Gruyter Textbook, Walter de Gruyter & Co., Berlin, 2012.
[5]	M. Gerdts, OCPID-DAE1, Optimal Control and Parameter Identification with Differential-Algebraic Equations of Index 1. User Guide (Online Documentation), Universität der Bundeswehr München, Neubiberg/München, 2010.
[6]	M. Gugat and G. Leugering, Global boundary controllability of the De St. Venant equations between steady states, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), 1-11.
[7]	M. Gugat and G. Leugering, Global boundary controllability of the Saint-Venant system for sloped canals with friction, Inst. H. Poincaré Anal. Non Linéaire, 26 (2009), 257-270.
[8]	D. Kroener, Numerical Schemes for Conservation Laws, Wiley-Teubner Series Advances in Numerical Mathematics, John Wiley & Sons, Ltd., Chichester / B. G. Teubner, Stuttgart, 1997.
[9]	A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system, M2AN Math. Model. Numer. Anal., 36 (2002), 397-425.
[10]	P. D. Lax, Hyperbolic Partial Differential Equations, with an appendix by Cathleen S. Morawetz, Courant Lecture Notes in Mathematics 14, New York University, Courant Institute of Mathematical Sciences, New York / American Mathematical Society, Providence, RI, 2006.
[11]	C. B. Vreugdenhil, Numerical Methods for Shallow-Water Flow, reprinted edition, Kluwer Academic Publishers, Dordrecht , 1998.