Global Optimal Control of Perturbed Systems

  title={Global Optimal Control of Perturbed Systems},
  author={Lars Gr{\"u}ne and Oliver Junge},
  journal={Journal of Optimization Theory and Applications},
  • L. Grüne, O. Junge
  • Published 29 March 2007
  • Mathematics, Computer Science
  • Journal of Optimization Theory and Applications
Abstract We propose a new numerical method for the computation of the optimal value function of perturbed control systems and associated globally stabilizing optimal feedback controllers. The method is based on a set-oriented discretization of the state space in combination with a new algorithm for the computation of shortest paths in weighted directed hypergraphs. Using the concept of multivalued game, we prove the convergence of the scheme as the discretization parameter goes to zero.  
Optimal stabilization of hybrid systems using a set oriented approach
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Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property
  • L. Grüne, O. Junge
  • Mathematics, Computer Science
    2007 46th IEEE Conference on Decision and Control
  • 2007
By including the discretization errors into the optimal control formulation the authors are able to compute approximate optimal value functions which preserve the Lyapunov function property and corresponding optimally stabilizing feedback laws which are constant on each partition element.
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