Necessary Conditions of Optimality for Constrained Infinite Horizon Differential Inclusions
This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems whose cost functional depends on the state variable at the final time and the dynamics are given by a differential inclusion. Moreover, the state variable satisfies constraints at both endpoints and the optimization is carried out over asymptotically convergent state trajectories.
The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This allows to overcome some of the drawbacks of existing necessary conditions of optimality for infinite horizon problems.