Algunos aspectos matemáticos de los sistemas de control lineales a través de un problema de optimización

Through a specific optimization problem, we develop in some detail the main ingredients of the mathematical theory of linear control systems on Euclidean spaces. We address the concepts of controllability, observability and a particular case of the Pontryagin Maximum Principle for this kind of systems. With the results established, we explain how to solve the proposed problem. The main objective of this article is to show to the scientific community certain mathematical techniques that could be replicated in different disciplines of interest for Interciencia's readers.