scholarly journals Optimal control problem for systems governed by nonlinear parabolic equations without initial conditions

2016 ◽  
Vol 8 (1) ◽  
pp. 21-37
Author(s):  
M.M. Bokalo ◽  
A.M. Tsebenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Parabolic Equations ◽  
Initial Conditions ◽  
Nonlinear Parabolic Equations ◽  
State Equations ◽  
Control Functions ◽  
Nonlinear Parabolic ◽  
Final Observation

An optimal control problem for systems described by Fourier problem for nonlinear parabolic equations is studied. Control functions occur in the coefficients of the state equations. The existence of the optimal control in the case of final observation is proved. 

scholarly journals Prevention of Leptospirosis Infected Vector and Human Population by Multiple Control Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Ilyas Khan ◽  
Sharidan Shafie ◽  
...  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Human Population ◽  
Cost Effective ◽  
Farm Animals ◽  
Effective Control ◽  
Multiple Control ◽  
Control Variables ◽  
Control Functions

Leptospirosis is an infectious disease that damages the liver and kidneys, found mainly in dogs and farm animals and caused by bacteria. In this paper, we present the optimal control problem applied to a dynamical leptospirosis infected vector and human population by using multiple control variables. First, we show the existence of the control problem and then use analytical and numerical techniques to investigate the existence cost effective control efforts for prevention of indirect and direct transmission of this disease. In order to do this, we consider three control functions two for human and one for vector population. We completely characterize the optimal control problem and compute the numerical solution of the optimality system using an iterative method.

Local generalization of transversality conditions for optimal control problem

2019 ◽  
Vol 14 (3) ◽  
pp. 310
Author(s):  
Beyza Billur İskender Eroglu ◽  
Dіlara Yapişkan
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Hamiltonian Formalism ◽  
Variational Calculus ◽  
Control Problems ◽  
Conformable Derivative ◽  
Transversality Conditions ◽  
Control Functions

In this paper, we introduce the transversality conditions of optimal control problems formulated with the conformable derivative. Since the optimal control theory is based on variational calculus, the transversality conditions for variational calculus problems are first investigated and then supported by some illustrative examples. Utilizing from these formulations, the transversality conditions for optimal control problems are attained by using the Hamiltonian formalism and Lagrange multiplier technique. To illustrate the obtained results, the dynamical system on which optimal control problem constructed is taken as a diffusion process modeled in terms of the conformable derivative. The optimal control law is achieved by analytically solving the time dependent conformable differential equations occurring from the eigenfunction expansions of the state and the control functions. All figures are plotted using MATLAB.

scholarly journals An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model

2021 ◽  
Author(s):  
Juan López-Ríos ◽  
Élder J. Villamizar-Roa
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Strong Solutions ◽  
External Source ◽  
Navier Stokes ◽  
State Equations ◽  
Velocity Equation ◽  
Concentration Equation

In this paper, we study an optimal control problem associated to a 3D-chemotaxis-Navier-Stokes model. First we prove the existence of global weak solutions of the state equations with a linear reaction term on the chemical concentration equation, and an external source on the velocity equation, both acting as controls on the system. Second, we establish aregularity criterion to get global-in-time strong solutions. Finally, we prove the existence of an optimal solution, and we establish a first-order optimality condition.

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