Finding interpolating curves minimizing L∞ acceleration in the euclidean space via optimal control theory

C.Y. Kaya, Lyle Noakes

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    We study the problem of finding an interpolating curve passing through prescribed points in the Euclidean space. The interpolating curve minimizes the pointwise maximum length, i.e., L∞-norm, of its acceleration. We reformulate the problem as an optimal control problem and employ simple but effective tools of optimal control theory. We characterize solutions associated with singular and nonsingular controls. Some of the results we obtain are new even for the scalar interpolating function case. We reduce the infinite-dimensional interpolation problem to an ensuing finite-dimensional one and derive closed form expressions for interpolating curves. Consequently we devise efficient numerical techniques and illustrate them with examples. © 2013 Society for Industrial and Applied Mathematics.
    Original languageEnglish
    Pages (from-to)442-464
    JournalSIAM Journal on Control and Optimization
    Volume51
    Issue number1
    DOIs
    Publication statusPublished - 2013

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