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A local feedback synthesis of time-optimal stabilizing controls in dimension three

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Abstract

Under generic conditions a local feedback synthesis for the problem of time-optimally stabilizing an equilibrium point in dimension three is constructed. There exist two surfaces which are glued together along a singular are on which the optimal control is singular. Away from these surfaces the optimal controls are piecewise constant with at most two switchings. Bang-bang trajectories with two switchings but different switching orders intersect in a nontrivial cut-locus and optimality of trajectories ceases at this cut-locus. The construction is based on an earlier result by Krener and Schättler which gives the precise structure of the small-time reachable set for an associated system to which time has been added as an extra coordinate.

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Authors and Affiliations

  1. Department of Systems Science and Mathematics, Washington University, Campus Box 1040, 63130, St. Louis, Missouri, U.S.A.

    Heinz Schättler

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  1. Heinz Schättler
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This work was partially supported by NSF under Grant No. DMS 8820413.

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Schättler, H. A local feedback synthesis of time-optimal stabilizing controls in dimension three. Math. Control Signal Systems 4, 293–313 (1991). https://doi.org/10.1007/BF02551282

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  • DOI: https://doi.org/10.1007/BF02551282

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