Lectures on the Calculus of Variations and Optimal Control Theory

addition admissible apply boundary bounded canonical Chapter choose clearly closed completes condition consider consists constant contains continuous convergence convex corresponding course covering curve defined definition denote derivative described determined differential equation direction equivalent exact exists expression extremal fact final finite fixed flow follows function further given Hamiltonian hand Hence hyperplane inequality initial integral interval joining Lagrangian latter lemma length lies limit line element linear mathematics maximum means measure method Moreover multiplier necessary neighborhood notion obtain optimal control origin pair parametric particular polygonal positive principle problem proof prove reader reduces regard relation remark require respectively restriction result satisfy secondary segment sequence simply smooth solution space subset sufficient suppose term theorem theory trajectory unit vanishes variables vector write