Remarks on finite and infinite time-horizon optimal control problems

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