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.
Highlights
The optimal control theory is under continuous development
This theory is based on the optimization of some functionals with ordinary differential equations/partial differential equations constraints, all depending on the control functions
By using the concepts of a variational differential system, adjoint equation and a modified Legendrian duality, under simplified hypotheses, we establish a maximum principle for the considered optimal control problem
Summary
The optimal control theory is under continuous development This theory is based on the optimization of some functionals with ordinary differential equations/partial differential equations (in short, ODE/PDE) constraints, all depending on the control functions (for variational control problems with first-order PDE constraints, the reader is directed to Mititelu and Treanţă [1], Treanţă [2,3], and Treanţă and Arana-Jiménez [4,5]). Caputo (see [16,17]) has developed fundamental identities linking the optimal solution functions and optimal value functions for reciprocal pairs of isoperimetric control problems. By using the concepts of a variational differential system , adjoint equation and a modified Legendrian duality, under simplified hypotheses, we establish a maximum principle for the considered optimal control problem. For other ideas that are connected to this subject, the reader is directed to Evans [19], Kalaba and Spingarn [20,21], Lee and Markus [22], Barbu et al [23], van Brunt [24], and Treanţă [25,26]
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