## Foundations of optimal control theory |

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### Contents

Methods Theory and Practices | 1 |

Geometric theory of ordinary differential | 51 |

Algebraic theory of linear differential | 59 |

Copyright | |

10 other sections not shown

### Common terms and phrases

absolutely continuous adjoint response admissible controller Appl Assume autonomous linear process Avtomatika i Telemekhanika Banach space boundary Chapter class C1 compact set compute Consider the autonomous Consider the control constant control problem Control Systems Control Theory controller steering controller u(t convex set coordinates corollary corresponding response cost C(u cost functional curve defined differential equation differential system duration eigenvalues everywhere exterior normal extremal controller feedback controller functions u(t hence initial state x0 integral interior lemma linear control process Linear Systems Math maximal principle nonempty nonlinear process normal observed process optimal controller u*(t optimal response Optimum origin Proc process in Rn Proof prove response x(t rj(t scalar set of attainability set Q space stability matrix steepest descent steering x0 subset supporting hyperplane switching locus synthesis tangent Trans transversality conditions uk(t variation vector zero