A guidance law for the control of a system in the neighborhood of a nominal suboptimal trajectory is developed. The guidance law is demonstrated using a lunar launch problem with constraints at orbit entry. A set of precomputed gains is used by the guidance law to operate on an extremal path in the neighborhood of the suboptimal trajectory. The guidance law and gains are designed to minimize the change in the desired performance index while still satisfying the final path constraints. In the lunar launch problem, the nominal suboptimal trajectory minimizes the final time using piecewise linear control. This trajectory is obtained to provide a nominal control history. The guidance law is found by minimizing the second variation of the suboptimal trajectory performance index subject to the final constraints being satisfied. For the lunar launch problem, the guidance law leads to a set of gains that relates deviations from the suboptimal trajectory to required changes in the nominal control history. The deviations from the suboptimal trajectory, used together with the precomputed gains, determines the change in the nominal control history required to meet the final constraints while minimizing the change in the final time.


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    Title :

    Neighboring Extremal Guidance for Systems with Piecewise Linear Control Using Time As the Reference Variable


    Contributors:
    W. A. Libby (author)

    Publication date :

    1993


    Size :

    58 pages


    Type of media :

    Report


    Type of material :

    No indication


    Language :

    English







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