scholarly journals On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Olha P. Kupenko ◽  
Rosanna Manzo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Direct Method ◽  
Dirichlet Boundary Conditions ◽  
Elliptic Variational Inequalities ◽  
The Matrix ◽  
Degenerate Elliptic ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Linear Degenerate

We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the “noncoercivity trouble.” Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions.

scholarly journals A New Direct Method for Solving Nonlinear Volterra-Fredholm-Hammerstein Integral Equations via Optimal Control Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
M. A. El-Ameen ◽  
M. El-Kady
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Integral Equations ◽  
Simple Form ◽  
Existence And Uniqueness ◽  
Direct Method ◽  
New Method ◽  
Fredholm Integral Equations ◽  
Hammerstein Integral Equations

A new method for solving nonlinear Volterra-Fredholm-Hammerstein (VFH) integral equations is presented. This method is based on reformulation of VFH to the simple form of Fredholm integral equations and hence converts it to optimal control problem. The existence and uniqueness of proposed method are achieved. Numerical results are given at the end of this paper.

Unmanned aerial vehicle trajectory planning by an integrated algorithm in a complex obstacle environment

2016 ◽  
Vol 231 (11) ◽  
pp. 2048-2067
Author(s):  
Siyu Zhang ◽  
Jianqiao Yu ◽  
Yuesong Mei ◽  
Huadong Sun ◽  
Yongbo Du
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Trajectory Planning ◽  
Potential Field ◽  
Direct Method ◽  
Field Method ◽  
Artificial Potential Field ◽  
Potential Field Method ◽  
Artificial Potential Field Method

Both the artificial potential field method and direct method for the optimal control problem have shortcomings in terms of effectiveness and computational complexity for the trajectory-planning problem. This paper proposes an integrated algorithm combining the artificial potential field method and direct method for planning in a complex obstacle-rich environment. More realistic unmanned aerial vehicle dynamics equations, which are rarely applied in the traditional artificial potential field method, are considered in this paper. Furthermore, an additional control force is introduced to transcribe the artificial potential field model into an optimal control problem, and the equality/inequality constraints on the description of the shape of the obstacles are substituted by the repulsive force originating from all the obstacles. The Legendre pseudospectral method and virtual motion camouflage are both utilized to solve the modified optimal control problem for comparison purposes. The algorithm presented in this paper improves the performance of solving the trajectory-planning problem in an obstacle-rich environment. In particular, the algorithm is suitable for addressing some conditions that cannot be considered by the traditional artificial potential field method or direct method individually, such as local extreme value points and a large numbers of constraints. Two simulation examples, a single cube-shaped obstacle and a different-shaped obstacle-rich environment, are solved to demonstrate the capabilities and performance of the proposed algorithm.

scholarly journals Solving an optimal control problem of hepatitis B virus dynamics: Efficacy of fuzzy logic strategy

2021 ◽  
Vol 4 (1) ◽  
pp. 1-18
Author(s):  
Marcel Gahamanyi ◽  
Wellars Banzi ◽  
Jean Marie Ntaganda
Keyword(s):  
Optimal Control ◽  
Fuzzy Logic ◽  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Direct Method ◽  
Linear Quadratic ◽  
B Virus ◽  
Good Agreement

This work aims at using fuzzy logic strategy to solve a hepatitis B virus (HBV) optimal control problem. To test the efficacy of this numerical method, we compare numerical results with those obtained using direct method. We consider a patient under treatment during 12 months where the two drugs are taken as controls. The results are rather satisfactory. In particular, the reaction of HBV to drugs can be modeled and a feedback can be approximated by the solution of a linear quadratic problem. The drugs reduce the risk of HBV. Furthermore, results of both numerical methods are in good agreement with experimental data and this justifies the efficacy of fuzzy logic strategy in solving optimal control problems.

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