This chapter proposes two optimal control problems that are governed by a class of non-linear dynamical systems. The first problem is constrained by a convective-diffusive model, and we study the existence of an optimal control solution for the considered problem and characterize it using the adjoint method. The second problem investigates a multiplicative distributive control for a vibrating string; we show that there exists an optimal control solution of the problem considered. The optimality system offers a standard for defining the unique optimal control. The chapter ends with some conclusions.