منابع مشابه
Optimality of Broken Extremals
In this paper we analyse the optimality of broken Pontryagin extremal for an n -dimensional affine control system with a control parameter, taking values in a k dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the sing...
متن کاملRoughening instability of broken extremals
We derive a new general jump condition on a broken Weierstrass-Erdmann extremal of a vectorial variational problem. Such extremals, containing surfaces of gradient discontinuity, are ubiquitous in shape optimization and in the theory of elastic phase transformations. The new condition, which does not have a one dimensional analog, reflects the stationarity of the singular surface with respect t...
متن کاملOn Second-Order Necessary Conditions for Broken Extremals
We consider optimal control problems with initial–final state equality and inequality constraints and running mixed state-control equality constraints given by smooth functions. The mixed constraints satisfy the regularity assumption of linear independence of gradients with respect to the control. We present simple proofs of second-order necessary conditions for (extended) weak minimum for extr...
متن کاملOn strong optimality of bang-bang Pontryagin extremals with multiple switches
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...
متن کاملNonregular Abnormal Extremals
We study existence and rigidity (W1-isolatedness) of nonregular abnormal extremals of completely nonholonomic 2-distribution (nonregularity means that such extremals do not satisfy the strong generalized Legendre-Clebsch condition). Introducing the notion of diagonal form of the second variation, we generalize some results of A. Agrachev and A. Sarychev about rigidity of regular abnormal extrem...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Dynamical and Control Systems
سال: 2018
ISSN: 1079-2724,1573-8698
DOI: 10.1007/s10883-018-9416-9