Augmented Lagrangian Method for One Dimensional Optimal Control Problems Governed by Delay Differential Equation | Chapter 09 | Advances in Mathematics and Computer Science Vol. 2
In this research, numerical solutions
of continuous optimal control problems governed by linear damping evolution
with delay and real coefficients are presented. The necessary conditions
obtained from the knowledge of calculus of variation for optimal control
problem constrained by delay differential equation is a linear two-point
boundary value problem involving both delay and advance terms. Clearly, this
coupling that exists between the state variable and the control variable is not
amenable to analytical solution hence a direct numerical approach is adopted.
We propose an augmented discretized continuous algorithm via quadratic
programming, which is capable of handling optimal control problems constrained
by delay differential equations. The discretization of the problem using
trapezoidal rule (a one-step second order numerical scheme) and Crank-Nicholson
with quadratic formulation amenable to quadratic programming technique for
solution of the optimal control problems are considered. A control operator
(penalized matrix), through the augmented Lagrangian method, is constructed.
Important properties of the operator as regards sequential quadratic
programming techniques for determining the optimal point are shown..
Author(s) Details
O. C. Akeremale
Department of Mathematics,
Federal University Lafia, P.M.B. 146, Lafia, Nasarawa State, Nigeria.
Dr. O. Olotu
Department of Mathematical
Sciences, Federal University of Technology, P.M.B. 704, Akure, Ondo State,
Nigeria.
A. Olaiju
Department of Mathematics
and Statistics, Federal Polytechnics,
Ilaro, P.M.B. 50, Ogun State, Nigeria.
Comments
Post a Comment