Conjugate Times and Regularity of the Minimum Time Function with Differential Inclusions View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2015

AUTHORS

Piermarco Cannarsa , Teresa Scarinci

ABSTRACT

This paper studies the regularity of the minimum time function, T(⋅ ), for a control system with a closed target, taking the state equation in the form of a differential inclusion. Our first result is a sensitivity relation which guarantees the propagation of the proximal subdifferential of T along any optimal trajectory. Then, we obtain the local C 2 regularity of the minimum time function along optimal trajectories by using such a relation to exclude the presence of conjugate times. More... »

PAGES

85-110

References to SciGraph publications

  • 1988-02. New results on the relationship between dynamic programming and the maximum principle in MATHEMATICS OF CONTROL, SIGNALS, AND SYSTEMS
  • 2004. Semiconcave Functions, Hamilton—Jacobi Equations, and Optimal Control in NONE
  • 2014. Control of Nonholonomic Systems: from Sub-Riemannian Geometry to Motion Planning in NONE
  • 2004. Optimal Control Problems in SEMICONCAVE FUNCTIONS, HAMILTON—JACOBI EQUATIONS, AND OPTIMAL CONTROL
  • 2015-01. Local Regularity of the Minimum Time Function in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2000-06. Optimality Conditions and Synthesis for the Minimum Time Problem in SET-VALUED ANALYSIS
  • 2014-03. From pointwise to local regularity for solutions of Hamilton–Jacobi equations in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • Book

    TITLE

    Analysis and Geometry in Control Theory and its Applications

    ISBN

    978-3-319-06916-6
    978-3-319-06917-3

    Author Affiliations

    From Grant

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-06917-3_4

    DOI

    http://dx.doi.org/10.1007/978-3-319-06917-3_4

    DIMENSIONS

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