Integral equivalence between a nonlinear system and its nonlinear perturbation
Si studia l'equivalenza asintotica fra le soluzioni di un sistema lineare e quelle di una perturbazione non lineare. Vengono date condizioni sufficienti per l'esistenza di un omeomorfìsmo fra le soluzioni limitate di tali sistemi.
This paper presents the role of vector relative degree in the formulation of stationarity conditions of optimal control problems for affine control systems. After translating the dynamics into a normal form, we study the Hamiltonian structure. Stationarity conditions are rewritten with a limited number of variables. The approach is demonstrated on two and three inputs systems, then, we prove a formal result in the general case. A mechanical system example serves as illustration.