scholarly journals On the Regularized Solutions of Optimal Control Problem in a Hyperbolic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yeşim Saraç ◽  
Murat Subaşı
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Iterative Procedure ◽  
Control Function ◽  
Optimal Solution ◽  
Test Problems ◽  
Initial Condition ◽  
Final Time ◽  
State Variable ◽  
Suitable Norm

We use the initial condition on the state variable of a hyperbolic problem as control function and formulate a control problem whose solution implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and given targets. We prove the existence and the uniqueness of the optimal solution and establish the optimality condition. An iterative algorithm is constructed to compute the required optimal control as limit of a suitable subsequence of controls. An iterative procedure is implemented and used to numerically solve some test problems.

Symbolic and Numeric Computation of Optimal Initial Velocity in a Wave Equation

2012 ◽  
Vol 8 (1) ◽  
Author(s):  
Yeşim Saraç
Keyword(s):  
Optimal Control ◽  
Wave Equation ◽  
Iterative Algorithm ◽  
Initial Velocity ◽  
Control Function ◽  
Final Time ◽  
Numerical Examples ◽  
Function Solution ◽  
State Variable ◽  
Suitable Norm

We get symbolic and numeric solutions developing a MAPLE® program which uses the initial velocity on the state variable of a wave equation as control function. Solution of this problem implies the minimization at the final time of the distance measured in a suitable norm between the solution of the problem and a given target. An iterative algorithm is constructed to compute the required optimal control as the limit of a suitable subsequence of controls. Results are tested with some numerical examples.

scholarly journals Optimal Control of HIV Dynamic Using Embedding Method

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
H. Zarei ◽  
A. V. Kamyad ◽  
M. H. Farahi
Keyword(s):  
Optimal Control ◽  
Immune System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Treatment Protocol ◽  
Optimal Solution ◽  
Embedding Method ◽  
Piecewise Constant Control ◽  
The Cost

This present study proposes an optimal control problem, with the final goal of implementing an optimal treatment protocol which could maximize the survival time of patients and minimize the cost of drug utilizing a system of ordinary differential equations which describes the interaction of the immune system with the human immunodeficiency virus (HIV). Optimal control problem transfers into a modified problem in measure space using an embedding method in which the existence of optimal solution is guaranteed by compactness of the space. Then the metamorphosed problem is approximated by a linear programming (LP) problem, and by solving this LP problem a suboptimal piecewise constant control function, which is more practical from the clinical viewpoint, is achieved. The comparison between the immune system dynamics in treated and untreated patients is introduced. Finally, the relationships between the healthy cells and virus are shown.

Dynamics Response Control of a Mindlin-Type Beam

2017 ◽  
Vol 17 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Kenan Yildirim ◽  
Seda G. Korpeoglu ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Maximum Principle ◽  
Control Problem ◽  
Control Function ◽  
Initial Boundary ◽  
Response Control ◽  
Adjoint Variables ◽  
Dynamics Response ◽  
Optimal Control Function

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

On an optimal control problem with an integral functional of a rational control function

2009 ◽  
Vol 45 (11) ◽  
pp. 1621-1635 ◽  
Author(s):  
N. L. Grigorenko ◽  
D. V. Kamzolkin ◽  
L. N. Luk’yanova ◽  
D. G. Pivovarchuk
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Integral Functional ◽  
Rational Control

Sensitivity analysis for optimal control problems described by nonlinear fractional evolution inclusions

2018 ◽  
Vol 21 (6) ◽  
pp. 1439-1470 ◽  
Author(s):  
Xiuwen Li ◽  
Yunxiang Li ◽  
Zhenhai Liu ◽  
Jing Li
Keyword(s):  
Optimal Control ◽  
Sensitivity Analysis ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Mild Solutions ◽  
Control Problems ◽  
Initial Condition ◽  
Evolution Inclusions ◽  
Technical Details

Abstract In this paper, a sensitivity analysis of optimal control problem for a class of systems described by nonlinear fractional evolution inclusions (NFEIs, for short) on Banach spaces is investigated. Firstly, the nonemptiness as well as the compactness of the mild solutions set S(ζ) (ζ being the initial condition) for the NFEIs are obtained, and we also present an extension Filippov’s theorem and whose proof differs from previous work only in some technical details. Finally, the optimal control problems described by NFEIs depending on the initial condition ζ and the parameter η are considered and the sensitivity properties of the optimal control problem are also established.

Solving the Problem of the Optimal Control System General Synthesis Based on Approximation of a Set of Extremals using the Symbol Regression Method

2020 ◽  
pp. 59-74
Author(s):  
S.V. Konstantinov ◽  
A.I. Diveev
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Function ◽  
Symbolic Regression ◽  
Regression Method ◽  
Synthesis Problem ◽  
Optimal Control System ◽  
Initial States

A new approach is considered to solving the problem of synthesizing an optimal control system based on the extremals' set approximation. At the first stage, the optimal control problem for various initial states out of a given domain is being numerically sold. Evolutionary algorithms are used to solve the optimal control problem numerically. At the second stage, the problem of approximating the found set of extremals by the method of symbolic regression is solved. Approach considered in the work makes it possible to eliminate the main drawback of the known approach to solving the control synthesis problem using the symbolic regression method, which consists in the fact that the genetic algorithm used in solving the synthesis problem does not provide information about proximity of the found solution to the optimal one. Here, control function is built on the basis of a set of extremals; therefore, any particular solution should be close to the optimal trajectory. Computational experiment is presented for solving the applied problem of synthesizing the four-wheel robot optimal control system in the presence of phase constraints. It is experimentally demonstrated that the synthesized control function makes it possible for any initial state from a given domain to obtain trajectories close to optimal in the quality functional. Initial states were considered during the experiment, both included in the approximating set of optimal trajectories and others from the same given domain. Approximation of the extremals set was carried out by the network operator method

scholarly journals A nonlinear plate control without linearization

2017 ◽  
Vol 15 (1) ◽  
pp. 179-186
Author(s):  
Kenan Yildirim ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Nonlinear Systems ◽  
Control Problem ◽  
Performance Index ◽  
Control Function ◽  
Initial Boundary ◽  
Quadratic Functional ◽  
Penalty Term ◽  
Nonlinear Plate ◽  
Optimal Control Function

Abstract In this paper, an optimal vibration control problem for a nonlinear plate is considered. In order to obtain the optimal control function, wellposedness and controllability of the nonlinear system is investigated. The performance index functional of the system, to be minimized by minimum level of control, is chosen as the sum of the quadratic 10 functional of the displacement. The velocity of the plate and quadratic functional of the control function is added to the performance index functional as a penalty term. By using a maximum principle, the nonlinear control problem is transformed to solving a system of partial differential equations including state and adjoint variables linked by initial-boundary-terminal conditions. Hence, it is shown that optimal control of the nonlinear systems can be obtained without linearization of the nonlinear term and optimal control function can be obtained analytically for nonlinear systems without linearization.

scholarly journals Optimal controllability for scalar conservation laws with convex flux

2014 ◽  
Vol 11 (03) ◽  
pp. 477-491 ◽  
Author(s):  
Adimurthi ◽  
Shyam Sundar Ghoshal ◽  
G. D. Veerappa Gowda
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conservation Laws ◽  
Linear Problem ◽  
Optimal Solution ◽  
Scalar Conservation Laws ◽  
Existence Of A Solution ◽  
New Strategy ◽  
Scalar Conservation

The optimal control problem for Burgers equation was first considered by Castro, Palacios and Zuazua. They proved the existence of a solution and proposed a numerical scheme to capture an optimal solution via the method of "alternate decent direction". In this paper, we introduce a new strategy for the optimal control problem for scalar conservation laws with convex flux. We propose a new cost function and by the Lax–Oleinik explicit formula for entropy solutions, the nonlinear problem is converted to a linear problem. Exploiting this property, we prove the existence of an optimal solution and, by a backward construction, we give an algorithm to capture an optimal solution.

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