A Pareto–Pontryagin Maximum Principle for Optimal Control

In this paper, an attempt to unify two important lines of thought in applied optimization is proposed. We wish to integrate the well-known (dynamic) theory of Pontryagin optimal control with the Pareto optimization (of the static type), involving the maximization/minimization of a non-trivial number...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 6; p. 1169
Main Authors Lovison, Alberto, Cardin, Franco
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 06.06.2022
Subjects
Calculus
Carbon
Consumption
Control theory
Functionals
Investigations
Mathematical analysis
Maximum principle
Mechanics
Multiple objective analysis
Objectives
Optimal control
Optimization
Pareto optimization
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Summary:In this paper, an attempt to unify two important lines of thought in applied optimization is proposed. We wish to integrate the well-known (dynamic) theory of Pontryagin optimal control with the Pareto optimization (of the static type), involving the maximization/minimization of a non-trivial number of functions or functionals, Pontryagin optimal control offers the definitive theoretical device for the dynamic realization of the objectives to be optimized. The Pareto theory is undoubtedly less known in mathematical literature, even if it was studied in topological and variational details (Morse theory) by Stephen Smale. This reunification, obviously partial, presents new conceptual problems; therefore, a basic review is necessary and desirable. After this review, we define and unify the two theories. Finally, we propose a Pontryagin extension of a recent multiobjective optimization application to the evolution of trees and the related anatomy of the xylems. This work is intended as the first contribution to a series to be developed by the authors on this subject.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym14061169