Time Optimal Control of Mechanical Systems

  • W. Schenker
  • H. P. Geering
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 115)


We treat the problem of time-optimal control of dynamical systems with the help of differential geometry.

If the problem of time-optimal control is to be solved, a system of first-order differential equations, the so-called adjoint system, has to be integrated. In most cases this cannot be done, neither analytically nor numerically. To reduce the complexity of the adjoint system we suggest to reduce its dimension by using First Integrals. In order to find those we formulate our problem in the language of differential geometry and apply the tools of the theory of dynamical systems.

We state a rule for obtaining First Integrals for several classes of systems. Our procedure and the results we gained with it, mean a step towards optimal control of nonlinear systems.


Vector Field Hamiltonian System Tensor Field Zero Section Adjoint 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

© Birkhäuser Verlag Basel 1994

Authors and Affiliations

  • W. Schenker
    • 1
  • H. P. Geering
    • 1
  1. 1.Measurement and Control LaboratorySwiss Federal Institute of Technology (ETH)ZurichSwitzerland

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