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Optimal control of delay systems with differential and algebraic dynamic constraints

Boris S. Mordukhovich, Lianwen Wang (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper concerns constrained dynamic optimization problems governed by delay control systems whose dynamic constraints are described by both delay-differential inclusions and linear algebraic equations. This is a new class of optimal control systems that, on one hand, may be treated as a specific type of variational problems for neutral functional-differential inclusions while, on the other hand, is related to a special class of differential-algebraic systems with a general delay-differential...

Porosity and Variational Principles

Marchini, Elsa (2002)

Serdica Mathematical Journal

We prove that in some classes of optimization problems, like lower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercive function and quasi-convex continuous functions with the topology of the uniform convergence, the complement of the set of well-posed problems is σ-porous. These results are obtained as realization of a theorem extending a variational principle of Ioffe-Zaslavski.

Preface

Zbigniew Bartosiewicz, Ewa Girejko (2006)

Control and Cybernetics

Selection theorem in L¹

Andrzej Nowak, Celina Rom (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.

Solving variational inclusions by a multipoint iteration method under center-Hölder continuity conditions

Catherine Cabuzel, Alain Pietrus (2007)

Applicationes Mathematicae

We prove the existence of a sequence ( x k ) satisfying 0 ∈ f ( x k ) + ∑ i = 1 M a i ∇ f ( x k + β i ( x k + 1 - x k ) ) ( x k + 1 - x k ) + F ( x k + 1 ) , where f is a function whose second order Fréchet derivative ∇²f satifies a center-Hölder condition and F is a set-valued map from a Banach space X to the subsets of a Banach space Y. We show that the convergence of this method is superquadratic.

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