Approximate Dynamic Programming with Feasibility Guarantees

The safe and economical operation of large-scale networked systems is challenging. Optimization-based schemes are frequently employed, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. Hence, these schemes require solving large-scale optimization problems. Iterative techniques from distributed optimization have been proposed for complexity reduction. Yet, they achieve feasibility asymptotically, which induces a substantial computational burden. This work presents a approximate dynamic programming scheme, which is guaranteed to deliver a feasible solution in ``one shot'', i.e., in one backward-forward iteration over all subproblems. The proposed scheme generalizes and unifies successful methods from seemingly disconnected domains such as power systems and optimal control. We demonstrate its applicability to problems with non-convex constraints via numerical examples from power systems and control.