@misc{Myśliński_Andrzej_Energy_2017,
 author={Myśliński, Andrzej and Nahorski, Zbigniew (1945– ) and Radziszewska, Weronika and Szulc, Katarzyna},
 copyright={Creative Commons Attribution BY 4.0 license},
 address={Warszawa},
 journal={Raport Badawczy = Research Report},
 howpublished={online},
 year={2017},
 publisher={Instytut Badań Systemowych. Polska Akademia Nauk},
 publisher={Systems Research Institute. Polish Academy of Sciences},
 language={eng},
 abstract={The paper is devoted to the solution of the energy minimization problem for a moving train. The train movement is governed by the system of the first order ordinary differential equations where the train speed and the distance along the track are the state variables. The provided locomotive power depends on the control function. The generated traction force is assumed to depend on the velocity of the train and on the control function. Using the maximum principle and Lagrangian multipliers the system of equations constituting the necessary optimality conditions is formulated. Based on the analysis of the train movement the optimal trajectories in terms of train speed and associated optimal control functions are calculated. A new simplified method is used to calculate the set of the switching times implementing the optimal control functions. Numerical examples are provided and discussed.},
 title={Energy Consumption Optimal Control of the Train Movement},
 type={Text},
 URL={http://www.rcin.org.pl/Content/144791/PDF/RB-2017-10.pdf},
 keywords={Zasada maksimum, Odes train model, Model pociągu odes, Semi analytical solutions, Energy minimization, Minimalizacja energii, Rozwiązania pół analityczne, Maximum principle, Optimal switching, Optymalne przełączanie, Numerical algorithm, Algorytm numeryczny},
}