We propose a split-horizon decomposition scheme to compute approximate solutions to discrete-time nonlinear control problems over long horizons. The proposed optimization scheme combines a short horizon using an accurate, complex system model, with a longer horizon using a simplified model. A piecewise-linear terminal value function found using dual dynamic programming is introduced to couple the short and long horizons of the approximate problem. We introduce a method that iterates between solving each sub-problem, and prove this converges to the optimum of the combined problem. This approach allows solutions over longer horizons than would be tractable for the full nonlinear program, with better modeling accuracy than a convex relaxation of the entire horizon. The method is applied to profit-maximizing seasonal control strategies on the Swiss day-ahead spot electricity market for an electrolyzer/fuel cell system with hydrogen storage. The problem is formulated as a mixed integer quadratically- constrained program, with per-period fixed costs and quadratic energy conversion efficiencies. We show that our method, when applied in a receding horizon manner, achieves near-optimal solutions over horizons of multiple months, using short-term exact horizons of less than three days.
