## An introduction to optimal control |

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3C function adjoint equations admissible control admissible rule bang-bang bang-bang control belongs best extremal control calculus of variations components Consequently Consider the system control is unique control set corresponding cost of transfer deducing extremal control defined and continuous denote Discuss extremal control discussed in Sec end manifolds euclidean space example of Sec existence theorem applies extremal path follows Furthermore given initial given terminal grad hence initial manifold initial point initial-point regions integral Leitmann Lemma limiting surface linear transformation linearly independent maximum principle minimum value optimal control optimal isocost surface optimal path optimal trajectory Ordinary Differential Equations parameter performance index point relative regular interior point renders the minimum rocket solution supremum switching curve switching function switching sequence tangent plane terminal manifold terminal transversality condition terminal value transfers the system uk(t value of transfer vector velocity wish to transfer Xn+i zero