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Journal of Dynamical and Control Systems

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19-09-2018

A Sequential Quadratic Hamiltonian Method for Solving Parabolic Optimal Control Problems with Discontinuous Cost Functionals

Authors: Tim Breitenbach, Alfio Borzì

Published in: Journal of Dynamical and Control Systems | Issue 3/2019

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Abstract

A sequential quadratic Hamiltonian (SQH) method for solving control-constrained parabolic optimal control problems with continuous and discontinuous non-convex cost functionals is investigated. The solution to these problems is characterised by the Pontryagin’s maximum principle, which is also the starting point for the development of a sequential quadratic Hamiltonian scheme. In a general setting that includes discontinuous and non-convex cost functionals, it is proved that the SQH method is well defined; however, convergence to an optimal solution is proved only in the smooth case. Results of numerical experiments are presented that successfully validate the proposed optimisation framework and demonstrate its effectiveness and large applicability.

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Title: A Sequential Quadratic Hamiltonian Method for Solving Parabolic Optimal Control Problems with Discontinuous Cost Functionals
Authors: Tim Breitenbach
Alfio Borzì
Publication date: 19-09-2018
Publisher: Springer US
Published in: Journal of Dynamical and Control Systems / Issue 3/2019
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-018-9419-6

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