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We study the problem of minimizing over the functions that assume given boundary values on . The lagrangian and the domain are assumed convex. A new type of hypothesis on the boundary function is introduced: the (or upper) . This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary data (instead of ). We...
We continue our programme of extending the Roman-Rota umbral calculus to the setting of
delta operators over a graded ring with a view to applications in algebraic
topology and the theory of formal group laws. We concentrate on the situation where
is free of additive torsion, in which context the central issues are number-
theoretic questions of divisibility. We study polynomial algebras which admit the action
of two delta operators linked by an invertible power series, and make related
constructions...
An optimal control problem is studied, in which the state is required to remain in a compact set . A control feedback law is constructed which, for given , produces -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of and a related trajectory tracking result. The control feedback is shown to possess a robustness...
An optimal control problem is studied, in which the state is required
to remain in a
compact set . A control feedback law is constructed which, for
given ε > 0, produces -optimal trajectories that satisfy the
state constraint universally with respect to all initial conditions
in .
The construction relies upon a constraint removal technique which
utilizes geometric properties of inner approximations of and a
related trajectory tracking result.
The control feedback is shown to possess a robustness...
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