  The minimization of energy-like cost functionals is addressed in the context
of optimal control problems. For a general class of dynamical systems, with
possibly unstable and nonlinear free dynamics, it is shown that a sequence of
solutions of finite time-horizon optimal control problems approximates a
solution of the analog infinite time-horizon problem. The latter solution and
corresponding optimal cost value function are not assumed to be known a-priori.
Numerical simulations are presented validating the theoretical findings for
several examples, including systems governed by both ordinary and partial
differential equations.
