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We present an approximate method for solving nonlinear control problems over long time horizons, in which the full nonlinear model is preserved over an initial part of the horizon, while the remainder of the horizon is modeled using a linear relaxation. As this approximate problem may still be too large to solve directly, we present a Benders decomposition-based solution algorithm that iterates between solving the nonlinear and linear parts of the horizon. This extends the Dual Dynamic Programming approach commonly employed for optimization of linearized hydro power systems. We prove that the proposed algorithm converges after a finite number of iterations, even when the nonlinear initial stage problems are solved inexactly. We also bound the suboptimality of the split-horizon method with respect to the original nonlinear problem, in terms of the properties of a map between the linear and nonlinear stateinput trajectories. We then apply this method to a case study concerning a multiple reservoir hydro system, approximating the nonlinear head effects in the second stage using McCormick envelopes. We demonstrate that near-optimal solutions can be obtained in a shrinking horizon setting when the full nonlinear model is used for only a short initial section of the horizon. For this example, the approach is shown to be more practical than both conventional dynamic programming and a multi-cell McCormick envelope approximation from literature.

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<pre>We present a method that operates an electrolyzer to meet the demand of a hydrogen refueling station in a cost-effective manner by solving a model-based optimal control problem. To formulate the underlying problem, we first conduct an experimental characterization of a Siemens SILYZER 100 polymer electrolyte membrane electrolyzer with \SI{100}{\kilo \watt} of rated power. We run experiments to determine the electrolyzer's conversion efficiency and thermal dynamics as well as the overload-limiting algorithm used in the electrolyzer. The resulting detailed nonlinear models are used to design a real-time optimal controller, which is then implemented on the actual system. Each minute, the controller solves a deterministic, receding-horizon problem which seeks to minimize the cost of satisfying a given hydrogen demand, while using a storage tank to take advantage of time-varying electricity prices and photovoltaic inflow. We illustrate in simulation the significant cost reduction achieved by our method compared to others in the literature, and then validate our method by demonstrating it in real-time operation on the actual system. </pre>

<pre>We present a method that operates an electrolyzer to meet the demand of a hydrogen refueling station in a cost-effective manner by solving a model-based optimal control problem. To formulate the underlying problem, we first conduct an experimental characterization of a Siemens SILYZER 100 polymer electrolyte membrane electrolyzer with \SI{100}{\kilo \watt} of rated power. We run experiments to determine the electrolyzer's conversion efficiency and thermal dynamics as well as the overload-limiting algorithm used in the electrolyzer. The resulting detailed nonlinear models are used to design a real-time optimal controller, which is then implemented on the actual system. Each minute, the controller solves a deterministic, receding-horizon problem which seeks to minimize the cost of satisfying a given hydrogen demand, while using a storage tank to take advantage of time-varying electricity prices and photovoltaic inflow. We illustrate in simulation the significant cost reduction achieved by our method compared to others in the literature, and then validate our method by demonstrating it in real-time operation on the actual system. </pre>

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