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Controllability for impulsive semilinear functional differential inclusions with a non-compact evolution operator

100%
Benedetti I., Obukhovskii V., Zecca P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2011
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tom 31
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nr 1
39-69
EN
We study a controllability problem for a system governed by a semilinear functional differential inclusion in a Banach space in the presence of impulse effects and delay. Assuming a regularity of the multivalued non-linearity in terms of the Hausdorff measure of noncompactness we do not require the compactness of the evolution operator generated by the linear part of inclusion. We find existence results for mild solutions of this problem under various growth conditions on the nonlinear part and on the jump functions. As example, we consider the controllability of an impulsive system governed by a wave equation with delayed feedback.
2
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Compact Global Chaotic Attractors of Discrete Control Systems

100%
Cheban D.
Nonautonomous Dynamical Systems
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2014
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tom 1
EN
The paper is dedicated to the study of the problem of existence of compact global chaotic attractors of discrete control systems and to the description of its structure. We consider so called switched systems with discrete time xn+1 = fν(n)(xn), where ν : ℤ+ ⃗ {1,2,...,m}. If m ≥ 2 we give sufficient conditions (the family M := {f1,f2,...,fm} of functions is contracting in the extended sense) for the existence of a compact global chaotic attractor. We study this problem in the framework of non-autonomous dynamical systems (cocycles).
3
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On some topological methods in theory of neutral type operator differential inclusions with applications to control systems

84%
Kamenskii M., Obukhovskii V., Yao J.-C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2013
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tom 33
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nr 2
193-204
EN
We consider a neutral type operator differential inclusion and apply the topological degree theory for condensing multivalued maps to justify the question of existence of its periodic solution. By using the averaging method, we apply the abstract result to an inclusion with a small parameter. As example, we consider a delay control system with the distributed control.
4

Existence and density results for retarded subdifferential evolution inclusions

84%
Cardinali T., Pieri S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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1996
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tom 16
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nr 1
53-74
EN
In this paper we study Cauchy problems for retarded evolution inclusions, where the Fréchet subdifferential of a function F:Ω→R∪{+∞} (Ω is an open subset of a real separable Hilbert space) having a φ-monotone subdifferential of oder two is present. First we establish the existence of extremal trajectories and we show that the set of these trajectories is dense in the solution set of the original convex problem for the norm topology of the Banach space C([-r, T₀], Ω) ("strong relaxation theorem"). Then we prove that this density result allows one to establish a nonlinear "bang-bang principle" for a class of control systems with dealy on a nonconvex constraint. We want to observe that the results here extend those of [11] and [13].
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