Decidability of hybrid systems with linear and nonlinear differential inclusions

1997 ◽  
pp. 77-92
Author(s):  
M. Broucke ◽  
P. Varaiya
Keyword(s):  
Hybrid Systems ◽  
Differential Inclusions ◽  
Nonlinear Differential Inclusions ◽  
Linear And Nonlinear

scholarly journals Solvability of control problem for fractional nonlinear differential inclusions with nonlocal conditions

2019 ◽  
Vol 24 (4) ◽  
Author(s):  
Alka Chadha ◽  
Rathinasamy Sakthivel ◽  
Swaroop Nandan Bora
Keyword(s):  
Differential Inclusions ◽  
Approximate Controllability ◽  
Measure Of Noncompactness ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Fractional Differential Inclusions ◽  
Multivalued Maps ◽  
Nonlinear Differential Inclusions ◽  
Approximately Controllable ◽  
Fractional Differential

In this paper, we study the approximate controllability of nonlocal fractional differential inclusions involving the Caputo fractional derivative of order q ∈ (1,2) in a Hilbert space. Utilizing measure of noncompactness and multivalued fixed point strategy, a new set of sufficient conditions is obtained to ensure the approximate controllability of nonlocal fractional differential inclusions when the multivalued maps are convex. Precisely, the results are developed under the assumption that the corresponding linear system is approximately controllable.  

scholarly journals Evolution Inclusions in Banach Spaces under Dissipative Conditions

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 750
Author(s):  
Tzanko Donchev ◽  
Shamas Bilal ◽  
Ovidiu Cârjă ◽  
Nasir Javaid ◽  
Alina I. Lazu
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Qualitative Properties ◽  
Evolution Inclusions ◽  
Fully Nonlinear ◽  
Limit Solution ◽  
Nonlinear Differential Inclusions ◽  
Limit Solutions ◽  
Lipschitz Conditions ◽  
Integral Solutions

We develop a new concept of a solution, called the limit solution, to fully nonlinear differential inclusions in Banach spaces. That enables us to study such kind of inclusions under relatively weak conditions. Namely we prove the existence of this type of solutions and some qualitative properties, replacing the commonly used compact or Lipschitz conditions by a dissipative one, i.e., one-sided Perron condition. Under some natural assumptions we prove that the set of limit solutions is the closure of the set of integral solutions.

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.

Near viability for fully nonlinear differential inclusions

2014 ◽  
Vol 12 (10) ◽  
Author(s):  
Irina Căpraru ◽  
Alina Lazu
Keyword(s):  
Differential Inclusion ◽  
Differential Inclusions ◽  
Existence Of Solutions ◽  
Null Controllability ◽  
Dissipative Operator ◽  
Nonlinear Case ◽  
Tangency Condition ◽  
Gronwall’S Lemma ◽  
Nonlinear Differential Inclusions ◽  
Near Viability

AbstractWe consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness theorem, which are extensions to the nonlinear case of similar results for semilinear differential inclusions. As an application, we give an approximate null controllability result.

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