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Optimal control theory is a mathematical framework that finds the best control strategy for a dynamic system to optimize a certain performance criterion. This work presents a numerical analysis of optimal control problems covering the fundamental concepts, solution methods, and computational aspects. Firstly, the basic concepts in optimal control are presented to provide a foundation for understanding and formulating optimal control problems. Then, various solution methods for optimal control problems, including direct methods, indirect methods, dynamic programming, and data-driven methods, are discussed. In addition, some challenges, such as computational complexity and scalability, handling uncertainties, and robustness, are addressed.

Solution methods for optimal control problems:

• Calculus of Variations
• Pontryagin's Maximum Principle
• Dynamic Programming
• Numerical Optimization
• Model Predictive Control
• Machine Learning