On the equivalence of higher order variational problems and optimal control problems

2002 ◽  
Author(s):  
A.M. Bloch ◽  
P.E. Crouch
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Variational Problems ◽  
Higher Order ◽  
Control Problems

scholarly journals A Higher-Order Maximum Principle for Impulsive Optimal Control Problems

2020 ◽  
Vol 58 (2) ◽  
pp. 814-844 ◽  
Author(s):  
M. Soledad Aronna ◽  
Monica Motta ◽  
Franco Rampazzo
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problems ◽  
Higher Order ◽  
Control Problems

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.

scholarly journals Higher order fractional variational optimal control problems with delayed arguments

2012 ◽  
Vol 218 (18) ◽  
pp. 9234-9240 ◽  
Author(s):  
Fahd Jarad ◽  
Thabet Abdeljawad (Maraaba) ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Higher Order ◽  
Control Problems ◽  
Delayed Arguments

scholarly journals Direct method for solution variational problems by using Hermite polynomials

2021 ◽  
Vol 39 (6) ◽  
pp. 223-237 ◽  
Author(s):  
Ayatollah Yari ◽  
Mirkamal Mirnia
Keyword(s):  
Optimal Control ◽  
Numerical Approximation ◽  
Optimal Control Problems ◽  
Direct Method ◽  
Hermite Polynomials ◽  
Variational Problems ◽  
Computational Method ◽  
Control Problems ◽  
Operational Matrices

‎In this approach‎, ‎one‎ computational method is presented for numerical approximation of variational problems‎. ‎This method with variable ‎coeffici‎ents is based on Hermite polynomials‎. ‎The properties of Hermite polynomials with the operational matrices of derivative and integration are used to reduce optimal control problems to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate the validity and applicability of the technique‎.  

scholarly journals Upper and Lower bounds for a certain class of constrained variational problems

1963 ◽  
Vol 3 (4) ◽  
pp. 449-453
Author(s):  
M. A. Hanson
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Existence Of Solutions ◽  
Necessary Conditions ◽  
Optimization Problems ◽  
Inequality Constraints ◽  
Variational Problems ◽  
Upper And Lower Bounds ◽  
Control Problems ◽  
Constrained Variational Problems

Certain optimization problems involving inequality constraints, known as optimal control problems have been extensively studied during recent years especially in relation to the calculation of optimal rocket thrusts and trajectories. A summary of these works is given by Berkovitz [1] who also establishes necessary conditions for the existence of solutions for a wide class of such problems.

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