Geometric Theory of Time-Optimal Control

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1971 English Publisher:Society for Industrial & Applied Mathematics (SIAM)Journal:SIAM Journal on Control, volume 9, pages 339-350 (issn: 0036-1402,

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Authors: Hájek, O.;

doi: 10.1137/0309024

Geometric Theory of Time-Optimal Control

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Abstract

Properties of the minimal-time function are considered for the problem of reaching the origin within (linear autonomous finite-dimensional) control systems. The function’s continuity is first established, leading to the construction of optimal feedback controls for normal systems. For systems where the control matrix has maximal rank (= dimension of state space), the minimal-time function is locally Lipschitzian, and hence differentiable almost everywhere.

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