scholarly journals A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory

2006 ◽  
Vol 13 (1) ◽  
pp. 173-182 ◽  
Author(s):  
Delfim F. M. Torres
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Control Engineering ◽  
Mathematical Question ◽  
Isoperimetric Constraints ◽  
Cost Functionals ◽  
Vector Valued ◽  
Invariance Theorem

Abstract We obtain a version of Noether's invariance theorem for optimal control problems with a finite number of cost functionals. The result is obtained by formulating E. Noether's result for optimal control problems subject to isoperimetric constraints, and then using the unimprovable (Pareto) notion of optimality. It was A. Gugushvili who drew the author's attention to a result of this kind that was posed as an open mathematical question of a great interest in applications of control engineering.

Shifted Chebyshev schemes for solving fractional optimal control problems

2019 ◽  
Vol 25 (15) ◽  
pp. 2143-2150 ◽  
Author(s):  
M Abdelhakem ◽  
H Moussa ◽  
D Baleanu ◽  
M El-Kady
Keyword(s):  
Optimal Control ◽  
Fractional Order ◽  
Chebyshev Polynomials ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Numerical Examples ◽  
Fractional Optimal Control ◽  
Functional Approximation ◽  
Fractional Optimal Control Problems

Two schemes to find approximated solutions of optimal control problems of fractional order (FOCPs) are investigated. Integration and differentiation matrices were used in these schemes. These schemes used Chebyshev polynomials in the shifted case as a functional approximation. The target of the presented schemes is to convert such problems to optimization problems (OPs). Numerical examples are included, showing the strength of the schemes.

scholarly journals Solution to Singular Optimal Control by Backward Differential Flow

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Jinghao Zhu ◽  
Shangrui Zhao ◽  
Guohua Liu
Keyword(s):  
Optimal Control ◽  
Global Optimization ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Variational Problems ◽  
Equivalent Transformation ◽  
Control Problems ◽  
Singular Optimal Control ◽  
Differential Flow ◽  
The Cost

This paper presents a backward differential flow for solving singular optimal control problems. By using Krotov equivalent transformation, the cost functional is converted to a class of global optimization problems. Some properties of the flow are given to reveal the significant relationship between the dynamic of the flow and the geometry of the feasible set. The proposed method is also used in solving a class of variational problems. Some examples are illustrated.

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