Optimal Control and Hamiltonian Input-Output Systems

  • A. J. van der Schaft
Part of the Mathematics and Its Applications book series (MAIA, volume 29)


Let us consider a smooth (i.e. C or Ck) nonlinear control system
$$ \dot{x} = f(x,u)\quad x \in X, u \in U $$
where f is a smooth mapping. For simplicity of exposition we will take X to be ℝn or an open subset of ℝn. (X could be an arbitrary manifold.) Furthermore we will make the (restrictive) assumption that U equals ℝm or an open subset of ℝm (or an arbitrary manifold without boundary). Let now L : X × U → ℝ and K : X → ℝ be smooth functions.


Hamiltonian System Optimal Control Problem Poisson Bracket Integral Manifold Nonlinear Control System 
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Copyright information

© D. Reidel Publishing Company 1986

Authors and Affiliations

  • A. J. van der Schaft
    • 1
  1. 1.Department of Applied MathematicsTwente University of TechnologyEnschedeThe Netherlands

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