Necessary Optimality Conditions in Isoperimetric Constrained Optimal Control Problems

Abstract

In this paper, we focus on a new class of optimal control problems governed by a simple integral cost functional and isoperimetric-type constraints (constant level sets of some simple integral functionals). By using the notions of a variational differential system and adjoint equation, necessary optimality conditions are established for a feasible solution in the considered optimization problem. More precisely, under simplified hypotheses and using a modified Legendrian duality, we establish a maximum principle for the considered optimization problem.

On a Class of Isoperimetric Constrained Controlled Optimization Problems

“…Recently, Benner et al [15] investigated bang-bang control strategies corresponding to periodic trajectories with isoperimetric constraints for a control problem, with application to nonlinear chemical reactions. For other different but connected ideas on this subject, the reader is directed to the following reasearch works [16][17][18][19][20].…”