Asymptotic Analysis of a Deterministic Control System via Euler's Equation Approach

Abstract

This paper provides necessary conditions in order to guarantee the existence of an unique equilibrium point in a deterministic control system. Furthermore, under additional conditions, it is proved the convergence of the optimal control sequence to this equilibrium point. The methodology to obtain these statements is based on the Euler's equation approach. A consumption-investment problem is presented with the objective to illustrate the results exposed.