pontryagin maximum principle

A SIMPLE TROLLEY-LIKE MODEL IN THE PRESENCE OF A NONLINEAR FRICTION AND A BOUNDED FUEL EXPENDITURE

  • Andrei V. Dmitruk
  • Ivan Samylovskiy
    • Categories Mechanical Engineering, Systems governed by Differential Equations Optimization Tags , , ,

    We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the … Read more

    Optimal synthesis in the Reeds and Shepp problem with a onesided variation of velocity

  • Andrei V. Dmitruk
  • Ivan Samylovskiy
    • Categories Control Applications, Mechanical Engineering Tags , , , ,

    We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a onesided variation of the speed and a free final direction of velocity. Using Pontryagin Maximum Principle, we obtain all possible types of extremals and, analyzing them and discarding nonoptimal ones, construct the optimal synthesis. Citationhttp://link.springer.com/article/10.1007/s10957-013-0286-8

    A well-posed shooting algorithm for optimal control problems with singular arcs

  • M. Soledad Aronna
  • Joseph Frédéric Bonnans
  • Pierre Martinon
    • Categories Infinite Dimensional Optimization Tags , , , , ,

    In this article we establish for the first time the well-posedness of the shooting algorithm applied to optimal control problems for which all control variables enter linearly in the Hamil- tonian. We start by investigating the case having only initial-final state constraints and free control variable, and afterwards we deal with control bounds. The shooting … Read more

    Partially affine control problems: second order conditions and a well-posed shooting algorithm

  • M. Soledad Aronna
    • Categories Infinite Dimensional Optimization Tags , , , ,

    This paper deals with optimal control problems for systems that are affine in one part of the control variables and nonlinear in the rest of the control variables. We have finitely many equality and inequality constraints on the initial and final states. First we obtain second order necessary and sufficient conditions for weak optimality. Afterwards, … Read more

    Optimal synthesis in the Reeds and Shepp problem with a free final direction

  • Andrei V. Dmitruk
  • Ivan Samylovskiy
    • Categories Applications - Science and Engineering, Mechanical Engineering Tags , , , ,

    We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a free final direction of velocity. Using Pontryagin Maximum Principle, we obtain all types of extremals and, analysing them and discarding nonoptimal ones, construct the optimal synthesis. ArticleDownload View PDF

    The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle

  • Andrei V. Dmitruk
  • Alexander Kaganovich
    • Categories Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    We give a simple proof of the Maximum Principle for smooth hybrid control systems by reducing the hybrid problem to an optimal control problem of Pontryagin type and then by using the classical Pontryagin Maximum Principle. CitationA.V. Dmitruk, A.M. Kaganovich. The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle, Systems & Control Letters, … Read more