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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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This report intended to show whether it is possible to replace all gasoline-based vehicles with pure electric vehicles, whose battery characteristics and driving range are based on Nissan Leaf, in the next 25 years. The power generation in the United States from various energy sources was projected up to 2035. Also, the carbon dioxide emission from the whole life cycle of gasoline-based vehicles and pure electric vehicles were compared, in order to evaluate the "green" aspect of driving only pure electric vehicles. In summary, since United States Energy Information Administration projected that coal-fired power plants will remain the main energy source up to 2035, pure electric vehicles eventually would emit almost three times more CO2 than gasoline-based vehicles based on the assumptions the team made about energy improvements. In other words, putting only pure electric vehicles on the road did not save energy or the environment, unless a significantly better battery technology and cleaner energy resources were used in America.