Andrei V. Dmitruk

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. Citation … 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. Article Download View Optimal synthesis in the Reeds and … 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. Citation NUMERICAL … Read more

    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. Citation A.V. Dmitruk, A.M. Kaganovich. The Hybrid Maximum Principle is a consequence of Pontryagin Maximum Principle, Systems & Control … Read more

    Metric regularity and systems of generalized equations

  • Andrei V. Dmitruk
  • Alexander Y. Kruger
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization Tags , , , ,

    The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version … Read more