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PDE Apps for Acoustic Ducts: A Parametrized Component-to-System Model-Order-Reduction Approach Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Coupling MPC and HJB for the Computation of POD-Based Feedback Laws

Authors : Giulia Fabrini, Maurizio Falcone, Stefan Volkwein

Published in: Numerical Mathematics and Advanced Applications ENUMATH 2017

Publisher: Springer International Publishing

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Abstract

In this paper we use a reference trajectory computed by a model predictive method to shrink the computational domain where we set the Hamilton-Jacobi Bellman (HJB) equation. Via a reduced-order approach based on proper orthogonal decomposition(POD), this procedure allows for an efficient computation of feedback laws for systems driven by parabolic equations. Some numerical examples illustrate the successful realization of the proposed strategy.

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previous chapter Optimal Coarse Spaces for FETI and Their Approximation
next chapter Adaptive Multiple Shooting for Nonlinear Boundary Value Problems
Literature
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A. Alla, G. Fabrini, M. Falcone, Coupling MPC and DP methods for an efficient solution of optimal control problems, in Conference Proceedings of IFIP (2015)
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M. Gubisch, S. Volkwein, Proper orthogonal decomposition for linear-quadratic optimal control, in Model Reduction and Approximation: Theory and Algorithms, ed. by P. Benner, A. Cohen, M. Ohlberger, K. Willcox (SIAM, Philadelphia, 2017), pp. 5–66
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P. Holmes, J.L. Lumley, G. Berkooz, C.W. Rowley, Turbulence, Coherent Structures, Dynamical Systems and Symmetry. Cambridge Monographs on Mechanics, 2nd edn. (Cambridge University Press, Cambridge, 2012)
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J.B. Rawlings, D.Q. Mayne, Model Predictive Control: Theory and Design (Nob Hill Publishing, Madison, 2009)
9.
F. Tröltzsch, S. Volkwein, POD a-posteriori error estimates for linear-quadratic optimal control problems. Comput. Optim. Appl. 44, 83–115 (2009)MathSciNetCrossRef
Metadata
Title
Coupling MPC and HJB for the Computation of POD-Based Feedback Laws
Authors
Giulia Fabrini
Maurizio Falcone
Stefan Volkwein
Copyright Year
2019
Book
Numerical Mathematics and Advanced Applications ENUMATH 2017

Print ISBN: 978-3-319-96414-0

Electronic ISBN: 978-3-319-96415-7

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-319-96415-7_89

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