A mathematical formulation of the problem of determining energy optimal train control with regenerative breaking and its solution based on the maximum principle are presented. The results of analysis of the train model and train model errors influence on the optimal trajectory are presented. Examples of energy optimal trajectories on the lines of the Moscow and Hanoi Metro are shown.

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Introduction. The authors pay attention to the fact that there exist such technical objects, the reliability evaluation of which — if performed with the use of measures of the “classical” reliability theory (in particular, reliability function and/ or mean operating time to failure) — is ambiguous and poorly interpreted physically. A city sewer network can serve as an example of such an object. The authors consider a situation when the result of the formal sewer network reliability analysis comes into conflict with the physical interpretation of object operation. This generates a need for searching for a more informative reliability indicator peculiar to a city sewer network. Methods. The research is based on the sewer network decomposition-equivalenting method (DEM) developed previously. This method, in turn, is based on the probability theory, reliability theory and mathematical statistics. A database containing the information about all network elements’ failures and restorations over a preceding period, is used as reference material. Results. Operational risk is taken as the reliability measure of a city sewer network. It is defined as the relative volume of sewage, not delivered to treatment facilities of the network due to failures of its elements, in a certain time. A procedure for the quantitative calculation of this measure is developed. Its comprehensiveness and informative richness are demonstrated. The article shapes possible ways of using the “operational risk” indicator when developing a city sewer network renovation strategy. Conclusion. Operational risk as the reliability measure can be used in practice to improve the performance of a city sewer network.