Feasible Perturbations of Control Systems with Pure State Constraints and Applications to Second-Order Optimality Conditions

Feasible Perturbations of Control Systems with Pure State Constraints and Applications to... We propose second-order necessary optimality conditions for optimal control problems with very general state and control constraints which hold true under weak regularity assumptions on the data. In particular the pure state constraints are general closed sets, the optimal control is supposed to be merely measurable and the dynamics may be discontinuous in the time variable as well. These results are obtained by an approach based on local perturbations of the reference process by second-order tangent directions. This method allows direct and quite simple proofs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

Feasible Perturbations of Control Systems with Pure State Constraints and Applications to Second-Order Optimality Conditions

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Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-013-9204-6
Publisher site
See Article on Publisher Site

Abstract

We propose second-order necessary optimality conditions for optimal control problems with very general state and control constraints which hold true under weak regularity assumptions on the data. In particular the pure state constraints are general closed sets, the optimal control is supposed to be merely measurable and the dynamics may be discontinuous in the time variable as well. These results are obtained by an approach based on local perturbations of the reference process by second-order tangent directions. This method allows direct and quite simple proofs.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2013

References

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