In this paper, we establish a mathematical framework that allows us to optimize the speed profile and select the optimal gears for heavy-duty vehicles. The key idea is to solve the analogous boundary value problem analytically for a simple scenario (linear damped system with quadratic elevation profile) and use this result to initialize a numerical continuation algorithm. Then the numerical algorithm can be used to gradually introduce nonlinearities (air resistance, engine saturation), implement data-based elevation profiles, and incorporate external perturbations (wind, traffic). This approach enables real-time optimization in dynamic traffic conditions, therefore may be implemented on board.

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