## Optimal Control of Discrete Systems |

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### Contents

STA TEMENT OF PROBLEM AND NA TV RE OF RESUL | 1 |

BA SIC CONCEPTS OF MUL TIDIMENSIONA L GEOMETR | 76 |

ELEMENTS OF THEOR Y OF CON VEX SETS | 162 |

Copyright | |

3 other sections not shown

### Common terms and phrases

according to Theorem affine function affine mapping affine space arbitrary point belongs to set carrier plane Consequently considered on set constraints contained convex cones convex field convex hull convex set Corollary covering of set definition different from zero dimensional direction of vector discrete controlled object dynamic programming equation Euclidean space example exist a number Figure formulated function F grad F half-space homomorphism inequalities interior point intersection let Q lies in cone linearly independent minimum of function Moreover n-dimensional nonpositive obtain open set optimal control orthogonal parallelepiped passing through point phase coordinates point of set point Q point z0 polyhedron possess separability problem of optimal Proof reaches a maximum real numbers relint satisfying conditions scalar product segment set of space set Q space of variables Subsection subspace supporting hyperplane system of cones tangent Theorem valid vector space vectors grad view of Theorem