Delta-Nabla Optimal Control Problems
Ewa Girejko, Agnieszka B. Malinowska, Delfim F. M. Torres
TL;DR
This paper develops a unified framework for delta-nabla optimal control problems on arbitrary time scales, deriving necessary conditions and applying them to bi-objective problems to establish Pareto optimality.
Contribution
It introduces a comprehensive approach to delta-nabla control problems on arbitrary time scales, including necessary optimality conditions and Pareto optimality criteria.
Findings
Derived necessary optimality conditions for delta-nabla isoperimetric problems.
Unified treatment encompasses previous results as special cases.
Established Pareto optimality conditions for bi-objective control problems.
Abstract
We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and previous results in the literature obtained as particular cases. As an application of the results of the paper we give necessary and sufficient Pareto optimality conditions for delta-nabla bi-objective optimal control problems.
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