Optimal Control of Constrained Self-Adjoint Nonlinear Operator Equations in Hilbert Spaces

This paper deals with the study of a new class of optimal control problems governed by nonlinear self-adjoint operator equations in Hilbert spaces under general constraints of the equality and inequality types on state variables. While the unconstrained version of such problems has been considered i...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2016-06, Vol.169 (3), p.735-758
Main Authors: El-Gebeily, M. A., Mordukhovich, B. S., Alshahrani, M. M.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Constraints
Control theory
Engineering
Hilbert space
Mathematical analysis
Mathematical functions
Mathematics
Mathematics and Statistics
Maximum principle
Nonlinearity
Operations Research/Decision Theory
Operators
Optimal control
Optimization
Ordinary differential equations
Studies
Theory of Computation
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Summary:This paper deals with the study of a new class of optimal control problems governed by nonlinear self-adjoint operator equations in Hilbert spaces under general constraints of the equality and inequality types on state variables. While the unconstrained version of such problems has been considered in our preceding publication, the presence of constraints significantly complicates the derivation of necessary optimality conditions. Developing a geometric approach based on multineedle control variations and finite-dimensional subspace extensions of unbounded self-adjoint operators, we establish necessary optimality conditions for the constrained control problems under considerations in an appropriate form of the Pontryagin Maximum Principle.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-015-0799-4