scholarly journals Numerical study of polynomial feedback laws for a bilinear control problem

2018 ◽  
Vol 8 (3) ◽  
pp. 557-582 ◽  
Author(s):  
Tobias Breiten ◽  
◽  
Karl Kunisch ◽  
Laurent Pfeiffer ◽  
Keyword(s):  
Control Problem ◽  
Numerical Study ◽  
Bilinear Control ◽  
Feedback Laws ◽  
Bilinear Control Problem

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.

Numerical Approximation of Bilinear Control of the Schroedinger Equation

2005 ◽  
Author(s):  
Katherine A. Kime
Keyword(s):  
Control Problem ◽  
Numerical Approximation ◽  
Schroedinger Equation ◽  
Quantum Systems ◽  
One Dimensional ◽  
Bilinear Control ◽  
The One ◽  
Localized Initial Data ◽  
Bilinear Control Problem ◽  
Crank Nicolson

We consider the one-dimensional Schroedinger equation in which the control is a time-dependent rectangular potential barrier/well. This is a bilinear control problem, as the potential multiplies the state. Differential geometric methods have been used to treat the bilinear control of systems of finitely many ODEs, and have been applied to the Schroedinger equation (quantum systems). In this paper we will calculate, using MATLAB, explicit controls which steer localized initial data to localized terminal data. These will be obtained using the Crank-Nicolson approximation, in which both space and time are discretized. If one semi-discretizes, in space, one obtains a bilinear control problem for a system of finitely many ODEs. One may pass from the semi-discretized system to Crank-Nicolson using the trapezoid rule. Thus the controls we calculate may be used to construct approximations to controls for the system of ODEs.

Very Large Eddy Simulation of Passive Drag Control for a D-Shaped Cylinder

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Xingsi Han ◽  
Siniša Krajnović
Keyword(s):  
Large Eddy Simulation ◽  
Flow Control ◽  
Control Problem ◽  
Bluff Body ◽  
Numerical Study ◽  
Numerical Results ◽  
Complex Flow ◽  
Local Disturbance ◽  
Eddy Simulation ◽  
Large Eddy

The numerical study reported here deals with the passive flow control around a two-dimensional D-shaped bluff body at a Reynolds number of Re=3.6×104. A small circular control cylinder located in the near wake behind the main bluff body is employed as a local disturbance of the shear layer and the wake. 3D simulations are carried out using a newly developed very large eddy simulation (VLES) method, based on the standard k − ε turbulence model. The aim of this study is to validate the performance of this method for the complex flow control problem. Numerical results are compared with available experimental data, including global flow parameters and velocity profiles. Good agreements are observed. Numerical results suggest that the bubble recirculation length is increased by about 36% by the local disturbance of the small cylinder, which compares well to the experimental observations in which the length is increased by about 38%. A drag reduction of about 18% is observed in the VLES simulation, which is quite close to the experimental value of 17.5%. It is found that the VLES method is able to predict the flow control problem quite well.

scholarly journals Optimal bilinear control of eddy current equations with grad–div regularization

2015 ◽  
Vol 23 (1) ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Electric Conductivity ◽  
Eddy Current ◽  
Regularity Property ◽  
Control Approach ◽  
Bilinear Control ◽  
Time Harmonic ◽  
Eddy Current Equations ◽  
Higher Regularity

AbstractAn optimal bilinear control problem governed by time-harmonic eddy current equations is considered to estimate the electric conductivity of a 3D bounded isotropic domain. The model problem is mainly complicated by the possible presence of non-conducting materials in the domain. We introduce an optimal control approach based on grad-div regularization and divergence penalization. The estimation for the electric conductivity obtained by solving the optimal control problem is allowed to be discontinuous. Here, no higher regularity property can be derived from the corresponding optimality conditions. We analyze the approach and present various numerical results exhibiting its numerical performance

Constrained bilinear control problem: Application to a cancer chemotherapy model

2017 ◽  
Vol 10 (04) ◽  
pp. 1750054 ◽  
Author(s):  
El Hassan Zerrik ◽  
Nihale El Boukhari
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Cancer Chemotherapy ◽  
Sufficient Conditions ◽  
Treatment Protocol ◽  
Bilinear Model ◽  
Bilinear Control ◽  
Finite Dimensional ◽  
Quadratic Cost ◽  
Admissible Controls

The aim of this paper is to investigate the optimal control problem for finite-dimensional bilinear systems and its application to a chemotherapy model. We characterize an optimal control that minimizes a quadratic cost functional in two cases of constrained admissible controls, then we give sufficient conditions for the uniqueness of such a control, and we derive useful algorithms for the computation of the optimal control. The established results are applied to a cancer chemotherapy bilinear model in order to simulate the optimal treatment protocol using two different approaches: one based on a limited instant toxicity, and the other on a limited cumulative toxicity along the therapy session.

Distributed H∞ Control for Leader-Following Coordination with Switching Topology

2011 ◽  
Vol 135-136 ◽  
pp. 455-463
Author(s):  
Yan Ping Luo ◽  
Li Xin Gao
Keyword(s):  
Control Problem ◽  
External Disturbance ◽  
Switching Topology ◽  
Consensus Control ◽  
Common Lyapunov Function ◽  
Control Laws ◽  
Leader Following ◽  
Multi Agent ◽  
Feedback Laws ◽  
Parameter Dependent

In this paper, we consider multi-agent H∞consensus control problems with external disturbance under the undirected switching topologies. The agent dynamics is expressed in the form of a second-order model and the control laws are neighbor-based feedback laws. By using the model transformation, the multi-agent H∞consensus control problem is converted into H∞ control problem for a switching linear system with special structure. A sufficient condition is established under which all agents can reach consensus with the desired H∞performance in switching topology case by constructing a parameter-dependent common Lyapunov function. Moreover, we give an explicit estimation expression to estimate H∞ performance index. Finally, a numerical example is provided to illustrate the effectiveness of our results.

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