scholarly journals Pareto optimal control problem and its Galerkin approximation for a nonlinear one-dimensional extensible beam equation

2016 ◽  
Vol 36 (2) ◽  
pp. 239 ◽  
Author(s):  
Andrzej Just ◽  
Zdzislaw Stempień
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Galerkin Approximation ◽  
Beam Equation ◽  
Pareto Optimal ◽  
One Dimensional

Some Sufficiency Conditions for Pareto-Optimal Control

1973 ◽  
Vol 95 (4) ◽  
pp. 356-361 ◽  
Author(s):  
G. Leitmann ◽  
W. Schmitendorf
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Pareto Optimality ◽  
Optimal Control Theory ◽  
Cooperative Games ◽  
Sufficient Conditions ◽  
Pareto Optimal ◽  
Vector Valued ◽  
Sufficiency Conditions

We consider the optimal control problem with vector-valued criterion (including cooperative games) and seek Pareto-optimal (noninferior) solutions. Scalarization results, together with modified sufficiency theorems from optimal control theory, are used to deduce sufficient conditions for Pareto-optimality. The utilization of these conditions is illustrated by various examples.

Optimal Control of a Chaotic Map: Fixed Point Stabilization and Attractor Confinement

1997 ◽  
Vol 07 (02) ◽  
pp. 437-446 ◽  
Author(s):  
C. Piccardi ◽  
L. L. Ghezzi
Keyword(s):  
Optimal Control ◽  
Fixed Point ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Chaotic Attractor ◽  
Chaotic Map ◽  
Optimal Controller ◽  
Control Of Chaos ◽  
One Dimensional ◽  
Suppression Of Chaos

Optimal control is applied to a chaotic system. Reference is made to a well-known one-dimensional map. Firstly, attention is devoted to the stabilization of a fixed point. An optimal controller is obtained and compared with other controllers which are popular in the control of chaos. Secondly, allowance is made for uncertainty and emphasis is placed on the reduction rather than the suppression of chaos. The aim becomes that of confining a chaotic attractor within a prescribed region of the state space. A controller fulfilling this task is obtained as the solution of a min-max optimal control problem.

scholarly journals Spectral Galerkin Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

2021 ◽  
Vol 5 (3) ◽  
pp. 102
Author(s):  
Fangyuan Wang ◽  
Xiaodi Li ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Jacobi Polynomials ◽  
A Priori ◽  
Galerkin Approximation ◽  
State Constraint ◽  
Diffusion Reaction ◽  
Lagrangian Multiplier ◽  
Adjoint State

In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for control, state, adjoint state and Lagrangian multiplier are derived. Numerical experiment is carried out to illustrate the theoretical findings.

scholarly journals THE OPTIMAL CONTROL PROBLEM FOR ONE-DIMENSIONAL NONLINEAR SHRODINGER EQUATIONS WITH A SPECIAL GRADIENT TERM

2019 ◽  
pp. 49-66
Author(s):  
G. Yagub ◽  
N. S. Ibrahimov ◽  
M. Zengin
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Quality Criterion ◽  
Necessary Condition ◽  
Gradient Term ◽  
Complex Coefficient ◽  
Existence And Uniqueness Theorem ◽  
One Dimensional ◽  
Nonlinear Part

In this paper we consider the optimal control problem for a one-dimensional nonlinear Schrodinger equation with a special gradient term and with a complex coefficient in the nonlinear part, when the quality criterion is a final functional and the controls are quadratically summable functions. In this case, the questions of the correctness of the formulation and the necessary condition for solving the optimal control problem under consideration are investigated. The existence and uniqueness theorem for the solution is proved and a necessary condition is established in the form of a variational inequality. Along with these, a formula is found for the gradient of the considered quality criterion.

Sign in / Sign up

Export Citation Format

Share Document