scholarly journals Robust boundary tracking for reachable sets of nonlinear differential inclusions

2014 ◽  
Vol 15 (5) ◽  
pp. 1129-1150 ◽  
Author(s):  
Janosch Rieger
Keyword(s):  
Differential Inclusions ◽  
Reachable Sets ◽  
Boundary Tracking ◽  
Nonlinear Differential Inclusions

Reachable Sets and Integral Funnels of Differential Inclusions Depending on a Parameter

2021 ◽  
Vol 104 (1) ◽  
pp. 200-204
Author(s):  
V. N. Ushakov ◽  
A. A. Ershov
Keyword(s):  
Differential Inclusions ◽  
Reachable Sets

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.  

Uncertainty in public health models treated by differential inclusions

2020 ◽  
Vol 11 (04) ◽  
pp. 2050040
Author(s):  
Stanislaw Raczynski
Keyword(s):  
Public Health ◽  
Differential Inclusion ◽  
Differential Inclusions ◽  
Epidemic Models ◽  
Reachable Sets ◽  
Model Construction ◽  
Model Parameters ◽  
Uncertain Parameters ◽  
Epidemic Spread ◽  
Epidemic Modeling

An application of differential inclusions in the epidemic spread models is presented. Some mostly used epidemic models are discussed here, and a brief survey of epidemic modeling is given. Most of the models are some modifications of the Susceptible–Infected–Recovered model. Simple simulations are carried out. Then, we consider the influence of some uncertain parameters. It is pointed out that the presence of some fluctuating model parameters can be treated by differential inclusions. The solution to such differential inclusion is given in the form of reachable sets for model variables. Here, we focus on the differential inclusion application rather than the model construction.

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.

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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