Remarks on finite and infinite time-horizon optimal control problems

The minimization of energy-like cost functionals is addressed in the context of optimal control prob-lems. 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.(c) 2022 Elsevier B.V. All rights reserved.