Reduction of Euler Lagrange problems for constrained variational problems and relation with optimal control problems

2002 ◽  
Author(s):  
A.M. Bloch ◽  
P.E. Croach
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Variational Problems ◽  
Control Problems ◽  
Lagrange Problems ◽  
Constrained Variational Problems

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.

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 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.  

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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