## Topics in Control Theory: A Seminar Given at the Forschungsinstitut Für Mathematik, ETH, in 1964 |

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### Contents

Preliminaries | 1 |

Controls and attainability The spaceU U I | 27 |

Boundary points of sets of attainability | 46 |

Copyright | |

1 other sections not shown

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A(xQ admissible class assume au(t Banach space class CP compact interval compact set complement cone of attainability Consider continuous linear mapping continuous mapping control space control vector field countable set CP-manifold modelled cp,h dA(x defined DEFINITION denote Df(x diffeomorphism differentiable manifolds Dold elements exist a neighborhood exists a control extremal with respect f is called finite sequence following properties Forschungsinstitut fur Mathematik h x,T Hausdorff CP-manifold hence homeomorphism i-th variable Ih^I initial condition initial condition X,T integral curve Let f lim h lw(x manuscript mapping f mean value theorem obviously open set partial mapping point x e primitive of f PROOF PROPOSITION regulated mapping restriction satisfying Seiten Seminar set of attainability steers the point subset sufficiently small tangent space topological space topological vector space U,cp unique mapping x e A(x