scholarly journals Optimal bilinear control problem related to a chemo-repulsion system in 2D domains

2020 ◽  
Vol 26 ◽  
pp. 29 ◽  
Author(s):  
Francisco Guillén-González ◽  
Exequiel Mallea-Zepeda ◽  
María Ángeles Rodríguez-Bellido
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Optimal Solution ◽  
Strong Solutions ◽  
Global Optimal Solution ◽  
Production Term ◽  
Bilinear Control ◽  
First Order ◽  
Global Optimal ◽  
Bilinear Control Problem

In this paper, we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term in a bidimensional domain. The existence, uniqueness and regularity of strong solutions of this model are deduced, proving the existence of a global optimal solution. Afterwards, we derive first-order optimality conditions by using a Lagrange multipliers theorem.

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.

scholarly journals An Optimal Control Problem Governed by Nonlinear First Order Dynamic Equation on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jian-Ping Sun ◽  
Qiu-Yan Ren ◽  
Ya-Hong Zhao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Scales ◽  
Dynamic Equation ◽  
Optimal Solution ◽  
Control Policy ◽  
Controlled System ◽  
First Order ◽  
Nonlinear Controlled System

In this paper, we are concerned with a class of optimal control problem governed by nonlinear first order dynamic equation on time scales. By imposing some suitable conditions on the related functions, for any given control policy, we first obtain the existence of a unique solution for the nonlinear controlled system. Then, we study the existence of an optimal solution for the optimal control problem.

scholarly journals On Locally and Globally Optimal Solutions in Scalar Variational Control Problems

Mathematics ◽  
2019 ◽  
Vol 7 (9) ◽  
pp. 829 ◽  
Author(s):  
Savin Treanţă
Keyword(s):  
Control Problem ◽  
Optimal Solution ◽  
Control Problems ◽  
Optimal Solutions ◽  
Global Optimal Solution ◽  
New Class ◽  
Minimal Criterion ◽  
Local Optimal Solution ◽  
Global Optimal ◽  
Curvilinear Integral

In this paper, optimality conditions are studied for a new class of PDE and PDI-constrained scalar variational control problems governed by path-independent curvilinear integral functionals. More precisely, we formulate and prove a minimal criterion for a local optimal solution of the considered PDE and PDI-constrained variational control problem to be its global optimal solution. The effectiveness of the main result is validated by a two-dimensional non-convex scalar variational control problem.

AO-BBO: A Novel Optimization Algorithm and Its Application in Plant Drug Extraction

2019 ◽  
Vol 19 (2) ◽  
pp. 139-145 ◽  
Author(s):  
Bote Lv ◽  
Juan Chen ◽  
Boyan Liu ◽  
Cuiying Dong
Keyword(s):  
Optimization Algorithm ◽  
Learning Strategy ◽  
Optimal Solution ◽  
Population Diversity ◽  
Global Optimal Solution ◽  
Plant Medicine ◽  
Suitability Index ◽  
Sensing Model ◽  
Local Optimal Solution ◽  
Global Optimal

<P>Introduction: It is well-known that the biogeography-based optimization (BBO) algorithm lacks searching power in some circumstances. </P><P> Material & Methods: In order to address this issue, an adaptive opposition-based biogeography-based optimization algorithm (AO-BBO) is proposed. Based on the BBO algorithm and opposite learning strategy, this algorithm chooses different opposite learning probabilities for each individual according to the habitat suitability index (HSI), so as to avoid elite individuals from returning to local optimal solution. Meanwhile, the proposed method is tested in 9 benchmark functions respectively. </P><P> Result: The results show that the improved AO-BBO algorithm can improve the population diversity better and enhance the search ability of the global optimal solution. The global exploration capability, convergence rate and convergence accuracy have been significantly improved. Eventually, the algorithm is applied to the parameter optimization of soft-sensing model in plant medicine extraction rate. Conclusion: The simulation results show that the model obtained by this method has higher prediction accuracy and generalization ability.</P>

scholarly journals Best Proximity Point Results in Complex Valued Metric Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Binayak S. Choudhury ◽  
Nikhilesh Metiya ◽  
Pranati Maity
Keyword(s):  
Minimum Distance ◽  
Metric Spaces ◽  
Optimal Solution ◽  
Global Optimal Solution ◽  
Complex Valued Metric Space ◽  
Fixed Point Equation ◽  
Point Equation ◽  
Global Optimal ◽  
Metric Function ◽  
Complex Valued

We introduce the concept of proximity points for nonself-mappings between two subsets of a complex valued metric space which is a recently introduced extension of metric spaces obtained by allowing the metric function to assume values from the field of complex numbers. We apply this concept to obtain the minimum distance between two subsets of the complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

scholarly journals Prototype Filter Design Based on Channel Estimation for FBMC/OQAM Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongjin Liu ◽  
Xihong Chen ◽  
Yu Zhao
Keyword(s):  
Genetic Algorithm ◽  
Channel Estimation ◽  
Optimization Problem ◽  
Filter Design ◽  
Stop Band ◽  
Optimal Solution ◽  
Improved Genetic Algorithm ◽  
Global Optimal Solution ◽  
Prototype Filter ◽  
Global Optimal

A prototype filter design for FBMC/OQAM systems is proposed in this study. The influence of both the channel estimation and the stop-band energy is taken into account in this method. An efficient preamble structure is proposed to improve the performance of channel estimation and save the frequency spectral efficiency. The reciprocal of the signal-to-interference plus noise ratio (RSINR) is derived to measure the influence of the prototype filter on channel estimation. After that, the process of prototype filter design is formulated as an optimization problem with constraint on the RSINR. To accelerate the convergence and obtain global optimal solution, an improved genetic algorithm is proposed. Especially, the History Network and pruning operator are adopted in this improved genetic algorithm. Simulation results demonstrate the validity and efficiency of the prototype filter designed in this study.

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