Optimal control problems with delays in state and control variables subject to mixed control-state constraints

Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed con...

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Bibliographic Details
Published in:Optimal control applications & methods Vol. 30; no. 4; pp. 341 - 365
Main Authors: Göllmann, L., Kern, D., Maurer, H.
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 01.07.2009
Subjects:
Chemical engineering
Delay
delays in state and control
Discretization
discretization methods
Mathematical analysis
Mathematical models
mixed control-state inequality constraints
Nonlinear programming
Optimal control
optimal control of a CSTR reactor
optimal fishing
Pontryagin's minimum principle
retarded optimal control problems
Terminals
ISSN:0143-2087, 1099-1514
Online Access:Get full text
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Summary:Optimal control problems with delays in state and control variables are studied. Constraints are imposed as mixed control–state inequality constraints. Necessary optimality conditions in the form of Pontryagin's minimum principle are established. The proof proceeds by augmenting the delayed control problem to a nondelayed problem with mixed terminal boundary conditions to which Pontryagin's minimum principle is applicable. Discretization methods are discussed by which the delayed optimal control problem is transformed into a large‐scale nonlinear programming problem. It is shown that the Lagrange multipliers associated with the programming problem provide a consistent discretization of the advanced adjoint equation for the delayed control problem. An analytical example and numerical examples from chemical engineering and economics illustrate the results. Copyright © 2008 John Wiley & Sons, Ltd.
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ISSN:0143-2087
1099-1514
DOI:10.1002/oca.843