In this research, Euler-Lagrange Method approach, for solving optimal control problems of both one dimensional and generalized form was considered. In years past, calculus of variation, has been used to solve functional optimization problems. However, with some special features in Calculus of Variation technique, making it unique in solving functional unconstrained optimization problems, these features will be advantageous to solving optimal control problems if it can be amended and modified in one way or the other. This call for the Euler-Lagrange Method which is a modification of the Calculus of Variation Method for solving optimal control problems. It is desired that, with the construction of the new algorithm, it will circumvent the difficulties undergone in constructing control operators which are embedded in Conjugate Gradient Method (CGM) for solving optimal control problems. Its application on some test problems have shown improvement in the results compared with existing results of solving this class of problems.
The objective function values for problems 3, 4, 6, 7, 8, 9 and 10 which are: 1.359141, -5.000, 0.36950416, 0.51699120, 0.27576806, 1.5934159×[10]^(-2) and -3.880763×[10]^(-2) appreciate to the existing results 1.359141, -5.000, 0.4146562, 0.613969, 0.2739811, 1.5935×[10]^(-3) and -3.9992×[10]^(-2) respectively while the objective function values for problems 1, 2 and 5 do not fully appreciate to the existing results with slight differences. These results is an indication that the method has some advantages over some existing computational techniques built to take care of the said problems.
Inhaltsverzeichnis (Table of Contents)
- Chapter One: Introduction
- 1.1 Background of the Study
- 1.2 Statement of the Problem
- 1.3 Aims and Objectives of the Study
- 1.4 Scope of the Study
- 1.5 Significance of the Study
- 1.6 Research Questions
- 1.7 Methodology
- Chapter Two: Literature Review
- 2.1 Concepts of Optimal Control Problems
- 2.2 Types of Optimal Control Problems
- 2.3 History of Optimal Control Problems
- 2.4 Applications of Optimal Control Problems
- 2.5 The Euler-Lagrange Method
- Chapter Three: Methodology
- 3.1 Introduction
- 3.2 Formulation of the Problem
- 3.3 The Euler-Lagrange Equation
- 3.4 The Hamiltonian Approach
- Chapter Four: Results and Discussion
- 4.1 Introduction
- 4.2 Application of the Euler-Lagrange Method to Optimal Control Problems
- 4.3 Analysis of the Results
- 4.4 Discussion of the Findings
- Chapter Five: Conclusion and Recommendations
- 5.1 Conclusion
- 5.2 Recommendations
- 5.3 Future Research
Zielsetzung und Themenschwerpunkte (Objectives and Key Themes)
This dissertation aims to demonstrate the effectiveness of the Euler-Lagrange method in solving optimal control problems. It delves into the theoretical foundations of optimal control and the Euler-Lagrange method, exploring its historical development and various applications.
- Application of the Euler-Lagrange method to optimal control problems
- Theoretical foundations of optimal control and the Euler-Lagrange method
- History of optimal control and its applications
- Formulation and solution of optimal control problems using the Euler-Lagrange approach
- Analysis and discussion of results obtained through the application of the Euler-Lagrange method
Zusammenfassung der Kapitel (Chapter Summaries)
Chapter One provides an introduction to the study, outlining the background, problem statement, aims, scope, significance, research questions, and methodology. It establishes the context for the dissertation and introduces the key concepts and objectives.
Chapter Two offers a comprehensive literature review, covering the essential concepts of optimal control problems, their types, historical background, and diverse applications. It also delves into the theory behind the Euler-Lagrange method, a pivotal technique for solving optimal control problems.
Chapter Three elaborates on the methodology employed in the dissertation. It details the formulation of the problem, the derivation of the Euler-Lagrange equation, and the Hamiltonian approach to solving optimal control problems.
Chapter Four presents and analyzes the results obtained by applying the Euler-Lagrange method to real-world optimal control problems. The chapter includes a detailed discussion of the findings and their implications.
Schlüsselwörter (Keywords)
This dissertation explores the application of the Euler-Lagrange method to optimal control problems, focusing on key themes like theoretical foundations, historical development, diverse applications, and the formulation and solution of real-world control problems. The work emphasizes the use of the Euler-Lagrange equation and the Hamiltonian approach to solve these problems, providing a comprehensive analysis of the results and their implications.
- Citation du texte
- Olaosebikan Temitayo Emmanuel (Auteur), 2019, Application of the Euler-Lagrange-Method for solving optimal control problems, Munich, GRIN Verlag, https://www.grin.com/document/506832
