scholarly journals Optimal control problem for the BCF model describing crystal surface growth

2016 ◽  
Vol 21 (2) ◽  
pp. 223-240 ◽  
Author(s):  
Xiaopeng Zhao ◽  
Jinde Cao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Crystal Surface ◽  
Optimal Solution ◽  
Surface Growth ◽  
Optimality System

In this paper, for the BCF model describing crystal surface growth, the optimal control problem is considered, the existence of optimal solution is proved and the optimality system is established.

scholarly journals Containing Misinformation Spread: A Collaborative Resource Allocation Strategy for Knowledge Popularization and Expert Education

2022 ◽  
Vol 2022 ◽  
pp. 1-14
Author(s):  
Linhong Li ◽  
Kaifan Huang ◽  
Xiaofan Yang
Keyword(s):  
Optimal Control ◽  
Resource Allocation ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Optimality System ◽  
Allocation Strategy ◽  
Expected Cost ◽  
Spread Model ◽  
Resource Allocation Strategy

With the prevalence of online social networks, the potential threat of misinformation has greatly enhanced. Therefore, it is significant to study how to effectively control the spread of misinformation. Publishing the truth to the public is the most effective approach to controlling the spread of misinformation. Knowledge popularization and expert education are two complementary ways to achieve that. It has been proven that if these two ways can be combined to speed up the release of the truth, the impact caused by the spread of misinformation will be dramatically reduced. However, how to reasonably allocate resources to these two ways so as to achieve a better result at a lower cost is still an open challenge. This paper provides a theoretical guidance for designing an effective collaborative resource allocation strategy. First, a novel individual-level misinformation spread model is proposed. It well characterizes the collaborative effect of the two truth-publishing ways on the containment of misinformation spread. On this basis, the expected cost of an arbitrary collaborative strategy is evaluated. Second, an optimal control problem is formulated to find effective strategies, with the expected cost as the performance index function and with the misinformation spread model as the constraint. Third, in order to solve the optimal control problem, an optimality system that specifies the necessary conditions of an optimal solution is derived. By solving the optimality system, a candidate optimal solution can be obtained. Finally, the effectiveness of the obtained candidate optimal solution is verified by a series of numerical experiments.

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.

scholarly journals On the Dynamics of Controlled Magnetohydrodynamic Systems

2008 ◽  
Vol 13 (3) ◽  
pp. 351-377 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Existence Of A Solution ◽  
Decay Properties ◽  
Long Time

In this paper we study the long time behavior of solutions for an optimal control problem associated with the viscous incompressible electrically conducting fluid modeled by the magnetohydrodynamic (MHD) equations in a bounded two dimensional domain through the adjustment of distributed controls. We first construct a quasi-optimal solution for the MHD systems which possesses exponential decay in time. We then derive some preliminary estimates for the long-time behavior of all admissible solutions of the MHD systems. Next we prove the existence of a solution for the optimal control problem for both finite and infinite time intervals. Finally, we establish the long-time decay properties of the solutions for the optimal control problem.

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 High-order homogenization in optimal control by the Bloch wave method

2021 ◽  
Author(s):  
Agnes Lamacz-Keymling ◽  
Irwin Yousept
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Periodic Coefficient ◽  
State Equation ◽  
Bloch Wave ◽  
High Order ◽  
Effective Control ◽  
Linear Quadratic

This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\eps$. The small parameter $\eps>0$ denotes the periodicity length. We propose a high-order effective control problem with constant coefficients that provides an approximation of the original one with error $O(\eps^M)$, where $M\in\N$ is as large as one likes. Our analysis relies on a Bloch wave expansion of the optimal solution and is performed in two steps. In the first step, we expand the lowest Bloch eigenvalue in a Taylor series to obtain a high-order effective optimal control problem. In the second step, the original and the effective problem are rewritten in terms of the Bloch and the Fourier transform, respectively. This allows for a direct comparison of the optimal control problems via the corresponding variational inequalities, leading to our main theoretical result on the high-oder approximation.

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.

scholarly journals Existence, uniqueness and asymptotic analysis of optimal control problems for a model of groundwater pollution

2019 ◽  
Vol 25 ◽  
pp. 53 ◽  
Author(s):  
Emmanuelle Augeraud-Véron ◽  
Catherine Choquet ◽  
Éloïse Comte
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Asymptotic Analysis ◽  
Control Problem ◽  
Optimal Control Problems ◽  
Control Process ◽  
Optimal Solution ◽  
Control Problems ◽  
Hydrogeological Model ◽  
Effective Problem

An optimal control problem of contaminated underground water is considered. The spatio-temporal objective takes into account the economic trade off between the pollutant use –for instance fertilizer– and the cleaning costs. It is constrained by a hydrogeological model for the spread of the pollution in the aquifer. We consider a broad range of reaction kinetics. The aim of the paper is two-fold. On the one hand, we rigorously derive, by asymptotic analysis, the effective optimal control problem for contaminant species that are slightly concentrated in the aquifer. On the other hand, the mathematical analysis of the optimal control problems is performed and we prove in particular that the latter effective problem is well-posed. Furthermore, a stability property of the optimal control process is provided: any optimal solution of the properly scaled problem tends to the optimal solution of the effective problem as the characteristic pollutant concentration decreases.

scholarly journals Optimal Cooperative Guidance Laws for Two UAVs Under Sensor Information Deficiency Constraints

Sensors ◽  
2020 ◽  
Vol 20 (17) ◽  
pp. 4790
Author(s):  
Daniel Lee ◽  
Han-Lim Choi ◽  
Jong-Han Kim
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Closed Form ◽  
Optimal Solution ◽  
Terminal Velocity ◽  
Cooperative Guidance ◽  
Prediction Error Minimization ◽  
Sensor Information ◽  
Guidance Laws

This paper presents closed-form optimal cooperative guidance laws for two UAVs under information constraints that achieve the required relative approach angle. Two UAVs cooperate to optimize a common cost function under a coupled constraint on terminal velocity vectors and the information constraint which defines the sensor information availability. To handle the information constraint, a general two-player partially nested decentralized optimal control problem is considered in the continuous finite-horizon time domain. It is shown that under the state-separation principle the optimal solution of the decentralized control problem can be obtained by solving two centralized subproblems which cover the prediction problem for the information-deficient player and the prediction error minimization problem for the player with full information. Based on the solution of the decentralized optimal control problem, the explicit closed-form cooperative guidance laws that can be efficiently implemented on conventional guidance computers are derived. The performance of the proposed guidance laws is investigated on both centralized and decentralized cooperative scenarios with nonlinear engagement kinematics of networked two-UAV systems.

scholarly journals Efficient Output Solution for Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Sie Long Kek ◽  
Kok Lay Teo ◽  
Mohd Ismail Abdul Aziz
Keyword(s):  
Optimal Control ◽  
Parameter Estimation ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Optimal Solution ◽  
Iterative Solution ◽  
System Optimization ◽  
The Real ◽  
Stochastic Optimal Control Problem

A computational approach is proposed for solving the discrete time nonlinear stochastic optimal control problem. Our aim is to obtain the optimal output solution of the original optimal control problem through solving the simplified model-based optimal control problem iteratively. In our approach, the adjusted parameters are introduced into the model used such that the differences between the real system and the model used can be computed. Particularly, system optimization and parameter estimation are integrated interactively. On the other hand, the output is measured from the real plant and is fed back into the parameter estimation problem to establish a matching scheme. During the calculation procedure, the iterative solution is updated in order to approximate the true optimal solution of the original optimal control problem despite model-reality differences. For illustration, a wastewater treatment problem is studied and the results show the efficiency of the approach proposed.

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