scholarly journals Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1472
Author(s):  
Savin Treanţă
Keyword(s):  
Control Problem ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Multiple Integral ◽  
Second Order ◽  
Final Part ◽  
Control Problems ◽  
Partial Derivatives ◽  
The One ◽  
Cost Functionals

The present paper deals with a class of second-order PDE constrained controlled optimization problems with application in Lagrange–Hamilton dynamics. Concretely, we formulate and prove necessary conditions of optimality for the considered class of control problems driven by multiple integral cost functionals involving second-order partial derivatives. Moreover, an illustrative example is provided to highlight the effectiveness of the results derived in the paper. In the final part of the paper, we present an algorithm to summarize the steps for solving a control problem such as the one investigated here.

scholarly journals On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1473
Author(s):  
Savin Treanţă
Keyword(s):  
Optimization Problems ◽  
Integral Functional ◽  
Optimal Solution ◽  
Multiple Integral ◽  
Second Order ◽  
Control Problems ◽  
Mathematical Framework ◽  
Mixed Constraints ◽  
Scalar Multiple ◽  
Cost Functionals

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution.

scholarly journals On a Class of Isoperimetric Constrained Controlled Optimization Problems

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 112
Author(s):  
Savin Treanţă
Keyword(s):  
Boundary Conditions ◽  
Control Problem ◽  
Optimality Conditions ◽  
Optimization Problems ◽  
Necessary Optimality Conditions ◽  
Control Problems ◽  
Integral Functionals ◽  
Curvilinear Integral ◽  
The One ◽  
Theoretical Results

In this paper, we investigate the Lagrange dynamics generated by a class of isoperimetric constrained controlled optimization problems involving second-order partial derivatives and boundary conditions. More precisely, we derive necessary optimality conditions for the considered class of variational control problems governed by path-independent curvilinear integral functionals. Moreover, the theoretical results presented in the paper are accompanied by an illustrative example. Furthermore, an algorithm is proposed to emphasize the steps to be followed to solve a control problem such as the one studied in this paper.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals CONSTRAINT ALGORITHM FOR EXTREMALS IN OPTIMAL CONTROL PROBLEMS

2009 ◽  
Vol 06 (07) ◽  
pp. 1221-1233 ◽  
Author(s):  
MARÍA BARBERO-LIÑÁN ◽  
MIGUEL C. MUÑOZ-LECANDA
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Theory ◽  
Control Problem ◽  
Optimal Control Theory ◽  
Optimal Control Problems ◽  
Necessary Conditions ◽  
Control Problems ◽  
Affine System

A geometric method is described to characterize the different kinds of extremals in optimal control theory. This comes from the use of a presymplectic constraint algorithm starting from the necessary conditions given by Pontryagin's Maximum Principle. The algorithm must be run twice so as to obtain suitable sets that once projected must be compared. Apart from the design of this general algorithm useful for any optimal control problem, it is shown how to classify the set of extremals and, in particular, how to characterize the strict abnormality. An example of strict abnormal extremal for a particular control-affine system is also given.

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