An optimal control problem applied to the railways is discussed, where both the time and the energy are to be minimized with the prescribed weights. Utilizing minimum principle the possible values of optimal control are derived in an analytic form. To obtain the complete solution the constrained mathematical programming problem is formulated and solved. There are finally discussed some numerical calculations to show an interesting dependence of the obtained results on a choice of weight parameters. The above described reduction of the optimal control problem to a mathematical programming problem is typical for a certain class of con-trol problems. The main idea consists in the specification of all possible optimal modes (e.g. utilizing minimum principle) and then in the determination of the switching times between these modes and the ter-minal time. This determination can be done just via the corresponding constrained mathematical programming problem. The solution is mainly obtained in analytic way (besides the determination of the switching times and the terminal time). The minimum principle turns out to be a very suitable tool for the con-sidered problem (other analytic methods, such as dynamic programming, fail because of the dif-ficulty of the obtained Bellman equation). Ge-nerally, most real-world problems are too com-plex to allow analytic solution. Then computa-tional algorithms are inevitable in solving these problems (e.g., discretization in time, sequential gradient--restoration algorithms, the multipliers method, the multiple shooting method, control parameterization type of algorithm). It is necessary to emphasize that these numerical calculations de-mand much harder requirements to the computing system, because here it is dealt with a computa-tional problem with a great number of optimized parameters. Finally it should be noted that it is possible to introduce more credible mathematical models for the discussed problem. These models can involve, e.g., railway profile, velocity limits or the more general criterion of optimality. In authors' opi-nion, the above utilized method can be applicable also for generalizations of this type.


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    Titel :

    On a minimum time - energy control problem


    Weitere Titelangaben:

    Entwurf einer zeit- und energieoptimalen Regelung und deren Anwendung für die Eisenbahnen


    Beteiligte:
    Kundrat, P. (Autor:in) / Urbanek, M. (Autor:in)


    Erscheinungsdatum :

    2003


    Format / Umfang :

    5 Seiten, 1 Bild, 1 Tabelle, 9 Quellen


    Medientyp :

    Aufsatz (Konferenz)


    Format :

    Print


    Sprache :

    Englisch





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