Skip to main content

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.

Read full article: http://bp.bookpi.org/index.php/bpi/catalog/view/69/830/637-1
View Volume: https://doi.org/10.9734/bpi/amacs/v2
Labels:

Comments

Post a Comment

Popular posts from this blog

Greening Regional Airports: A Vision for Carbon Neutral Infrastructure | Chapter 12 | Contemporary Perspective on Science, Technology and Research Vol. 3

 This study provides an overview of the energy demand of a regional airport, divided into individual time horizons. The electrification of aircraft systems raises the question of whether airports will be among the largest electricity consumers in our infrastructure in the future. Sustainability and especially emission reductions are significant challenges for airports that are currently being addressed. The Clean Sky 2 project GENESIS addresses the environmental sustainability of hybrid-electric 50-passenger aircraft systems in a life cycle perspective to support the development of a technology roadmap for the transition to sustainable and competitive electric aircraft systems. This article originates from the GENESIS research and describes various options for ground power supply at a regional airport. Potential solutions for airport infrastructure with a short (2030), medium (2040), and long (2050) time horizon are proposed. In addition to the environmental and conservation benefi...
Post a Comment
Read more

There is No Standard Model of ZFC and ZFC2 | Chapter 03 | Advances in Mathematics and Computer Science Vol. 1

In this Chapter we obtain a contradictions in formal set theories under assumption that these theories have omega-models or nonstandard model with standard part. An possible generalization of Lob’s theorem is considered. Main results are: (i) ¬Con(ZF C+ ∃ M ZFC st ), (ii) ¬Con(N F+ ∃ M NF st ), (iii) ¬Con(ZF C 2 ), (iv) let k be an inaccessible cardinal then ¬Con(ZF C+ ∃ κ), (v) ¬Con(ZF C+ (V=L)), (vi) ¬Con(ZF+ (V=L)). Author   Details: Jaykov Foukzon Israel Institute of Technology, Haifa, Israel Men'kova Elena Romanovna All-Russian Research Institute for Optical and Physical Measurements, Moscow, Russia Read full article: http://bp.bookpi.org/index.php/bpi/catalog/view/46/221/408-1 View Volume: https://doi.org/10.9734/bpi/amacs/v1
Post a Comment
Read more

Study on Processing Method Influences the Effect of Cassava (Manihot esculenta) Consumption on Blood Lipid Profile in Rats | Chapter 8 | Current Research and Development in Chemistry Vol.1

Cassava is consumed in many tropical countries and is fast becoming the major raw material of many diets, especially in the bakery, brewery and pharmaceutical industries. In a study to determine the effects of various formulations of Cassava feeds on blood lipid profile in rats. Forty adult Wistar rats weighing between 120 and 150 g were divided into 4 groups of 10 rats each. The rats were acclimatized for one week; fed with different formulations of Cassava feeds adlibitum, after which the rats were allotted into groups. Group 1 was fed on Garri; group 2 on Cassava flour; group 3 on Tapioca, and the control group (group 4) on normal chow. After 4 weeks, each animal was anaesthetized by exposure to chloroform vapour and blood samples collected by cardiac puncture. Group 1 diet (Garri) significantly increased HDL-cholesterol (HDL-C) concentration and significantly decreased LDL-cholesterol (LDL-C) concentration (p<0.05) compared with the control group. In Group 2 (Cassava flour), t...
Post a Comment
Read more