In this thesis, we study the construction of a diffeomorphism of the linear system ẏ1 = ay1 + by2 + u; ẏ2 = y1; |u| ≤ 1; (1) to the canonical system ẋ1 = u ẋ2 = x1 |u| ≤ 1 This diffeomorphism is defined on R2 except on a curve, called a switching curve. The mentioned transformation allows solving the optimal control problem for the original system (1). It is worth mentioning that the control is bounded, that is, the control satisfies the restriction |u| ≤ 1.
En esta tesis estudiamos la construcción de un difeomorfismo del sistema lineal ẏ1 = ay1 + by2 + u; ẏ2 = y1; |u| ≤ 1; (2) al sistema canónico ẋ1 = u ẋ2 = x1 |u| ≤ 1: Tal difeomorfismo, definido en R2 excepto en una curva llamada curva de conmutación, permite resolver el problema de control óptimo para el sistema original (2). Cabe mencionar que el control es acotado, es decir, el control satisface la restricción |u| ≤ 1.
