On the time-optimality of bang-bang trajectories in ${\mathbf{R}}^3$
نویسندگان
چکیده
منابع مشابه
On the Time-optimality of Bang-bang Trajectories in R
where ƒ and g are smooth vector fields. Admissible controls are arbitrary measurable functions with values in [—1,4-1] and a trajectory of the system corresponding to a control u( ) is an absolutely continuous curve such that x(t) — f{x(t)) + u(t)g(x(t)) holds almost everywhere. In every optimal control problem the question of regularity of the solutions comes up naturally. The standard existen...
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This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [5, 14] and [16]. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times ...
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In this paper we give sufficient conditions for a bang-bang regular extremal to be a strong local optimum for a control problem in the Mayer form; strong means that we consider the C0 topology in the state space. The controls appear linearly and take values in a polyhedron, and the state space and the end point constraints are finite-dimensional smooth manifolds. In the case of bang-bang extrem...
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Second order necessary and sufficient optimality conditions for bang–bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi–)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadr...
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This paper is an attempt to give sufficient conditions for a bang-bang extremal with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in [2, 3] and [4]. We require both the strict bang-bang Legendre condition, which takes a different form according to the multiplicity of the considered switching time, a non deg...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1987
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-1987-15479-6