Singular optimal control problems are usually characterized by solutions that are difficult to formulate because direct application of Pontryagin’s minimum principle fails to yield the optimal control. When obtained, the singular control becomes a function of the state and the costate variables. Previous research generally showed partial solutions to the problem. In this study, the singular control is found in closed form, as a function of the state variables, via vanishing of a certain determinant. This is an extension of an existing method for finding singular surfaces. The method is applied to several one-dimensional and two-dimensional Goddard problems under various trajectory bending laws. Numerical results, obtained by direct optimization, validate the analytical results. The method can be applied to other problems containing singular arcs.


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    Title :

    Singular Control for Two-Dimensional Goddard Problems Under Various Trajectory Bending Laws


    Contributors:

    Published in:

    Publication date :

    2019-03-01




    Type of media :

    Conference paper , Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




    Singular Control for 2D Goddard Problems under Various Trajectory Bending Laws

    Indig, Nahshon / Ben-Asher, Joseph Z. / Sigal, Erez | British Library Conference Proceedings | 2018


    Goddard trajectory determination

    Dixon, B. | NTRS | 1979




    Mathematical Theory of the Goddard Trajectory Determination System

    J. O. Cappellari / C. E. Velez / A. J. Fuchs | NTIS | 1976