Theory and applications of optimal control problems with multiple time-delays

Laurenz Göllmann; Helmut Maurer

doi:10.3934/jimo.2014.10.413

Article Contents

2014, Volume 10, Issue 2: 413-441. Doi: 10.3934/jimo.2014.10.413

This issue Previous Article A ladder method for linear semi-infinite programming Next Article Computation of bang-bang and singular controls in collision avoidance

Theory and applications of optimal control problems with multiple time-delays

Laurenz Göllmann^1, and
Helmut Maurer^2,

1.
Department of Mechanical Engineering, Münster University of Applied Sciences, Stegerwaldstrasse 39, 48565 Steinfurt
2.
Institute of Computational and Applied Mathematics, Westfälische Wilhelms-Universität Münster, Einsteinstrasse 62, 48149 Münster

Received: November 2012

Revised: July 2013

Published: April 2014

Abstract / Introduction Related Papers Cited by

Abstract

In this paper we study optimal control problems with multiple time delays in control and state and mixed type control-state constraints. We derive necessary optimality conditions in the form of a Pontryagin type Minimum Principle. A discretization method is presented by which the delayed control problem is transformed into a nonlinear programming problem. It is shown that the associated Lagrange multipliers provide a consistent numerical approximation for the adjoint variables of the delayed optimal control problem. We illustrate the theory and numerical approach on an analytical example and an optimal control model from immunology.

Keywords:

Optimal control,
multiple delays,
maximum principle,
discretization method,
optimal control of innate immune response.

Mathematics Subject Classification: Primary: 49J15; Secondary: 37N25, 37N40.

Citation:

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