Optimization of third-order discrete and differential inclusions described by polyhedral set-valued mappings

2015 ◽  
Vol 95 (9) ◽  
pp. 1831-1844 ◽  
Author(s):  
Elimhan N. Mahmudov ◽  
Sevilay Demir ◽  
Özkan Değer
Keyword(s):  
Differential Inclusions ◽  
Third Order ◽  
Polyhedral Set ◽  
Set Valued Mappings

Preliminaries from set-valued analysis

2012 ◽  
Author(s):  
Rafal Goebel ◽  
Ricardo G. Sanfelice ◽  
Andrew R. Teel
Keyword(s):  
Hybrid Systems ◽  
Differential Inclusions ◽  
Set Valued Mapping ◽  
Continuity Properties ◽  
Set Valued Mappings

This chapter includes the necessary background on further developments in the theory of hybrid systems. It first presents the notion of convergence for a sequence of sets and how it generalizes the notion of convergence of a sequence of points. The chapter then deals with set-valued mappings and their continuity properties. Given a set-valued mapping M : ℝᵐ ⇉ ℝⁿ, the chapter defines the range of M as the set rgeM = {‎y ∈ ℝⁿ : Ǝx ∈ ℝᵐ such that y ∈ M(x)}‎; and the graph of M as the set gphM = {‎(x,y) ∈ ℝᵐ × ℝⁿ : y ∈ M(x)}‎. The chapter also specializes some of the concepts, such as graphical convergence, to hybrid arcs and provides further details in such a setting. Finally, the chapter discusses differential inclusions.

Filippov Lemma for certain differential inclusion of third order

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
Grzegorz Bartuzel ◽  
Andrzej Fryszkowski
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Third Order

AbstractWe propose a version of the Filippov Lemma for differential inclusions of the type

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