second order condition

Second order analysis of state-constrained control-affine problems

  • M. Soledad Aronna
  • Joseph Frédéric Bonnans
  • Bean San Goh
    • Categories Systems governed by Differential Equations Optimization Tags , , ,

    In this article we establish new second order necessary and sufficient optimality conditions for a class of control-affine problems with a scalar control and a scalar state constraint. These optimality conditions extend to the constrained state framework the Goh transform, which is the classical tool for obtaining an extension of the Legendre condition. We propose … Read more

    Quadratic order conditions for bang-singular extremals

  • M. Soledad Aronna
  • Joseph Frédéric Bonnans
  • Andrei V. Dmitruk
  • Pablo A. Lotito
    • Categories Infinite Dimensional Optimization Tags , , , ,

    This paper deals with optimal control problems for systems affine in the control variable. We consider nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we derive a second order sufficient condition for the scalar control case. CitationNUMERICAL ALGEBRA, … Read more