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Nonlinear Hybrid Dynamical Systems: Modeling, Optimal Control, and Applications

  • Martin Buss
  • Markus Glocker
  • Michael Hardt
  • Oskar von Stryk
  • Roland Bulirsch
  • Günther Schmidt
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 279)

Abstract

Nonlinear hybrid dynamical systems are the main focus of this paper. A modeling framework is proposed, feedback control strategies and numerical solution methods for optimal control problems in this setting are introduced, and their implementation with various illustrative applications are presented. Hybrid dynamical systems are characterized by discrete event and continuous dynamics which have an interconnected structure and can thus represent an extremely wide range of systems of practical interest. Consequently, many modeling and control methods have surfaced for these problems. This work is particularly focused on systems for which the degree of discrete/continuous interconnection is comparatively strong and the continuous portion of the dynamics may be highly nonlinear and of high dimension. The hybrid optimal control problem is defined and two solution techniques for obtaining suboptimal solutions are presented (both based on numerical direct collocation for continuous dynamic optimization): one fixes interior point constraints on a grid, another uses branch-and-bound. These are applied to a robotic multi-arm transport task, an underactuated robot arm, and a benchmark motorized traveling salesman problem.

Keywords

Optimal Control Problem Discontinuity Surface Suboptimal Solution Hybrid Automaton Hybrid Dynamical System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Martin Buss
    • 1
  • Markus Glocker
    • 2
  • Michael Hardt
    • 2
  • Oskar von Stryk
    • 2
  • Roland Bulirsch
    • 3
  • Günther Schmidt
    • 4
  1. 1.Control Systems GroupTechnische Universität BerlinBerlinGermany
  2. 2.Simulation and Systems Optimization GroupTechnische Universität DarmstadtDarmstadtGermany
  3. 3.Zentrum MathematikTechnische Universität MünchenMünchenGermany
  4. 4.Institute of Automatic Control EngineeringTechnische Universität MünchenMünchenGermany

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