On Sufficient Optimality Conditions for Infinite Horizon Optimal Control Problems

We consider the Seierstad sufficiency theorem in comparison with the Mangasarian and Arrow sufficiency theorems for optimal control problems with infinite time horizon. Both finite and infinite values of the objective functional are allowed, since the concepts of overtaking and weakly overtaking optimality are implied. We extend the conditions under which the Seierstad sufficiency theorem can be applied and provide appropriate examples. The sufficient conditions are shown to be both necessary and sufficient when the Hamiltonian is linear with respect to state and control. We obtain a new form of sufficient optimality conditions in the case when the Hamiltonian is neither concave nor differentiable with respect to control.