Control Problems for Evolutionary Differential Inclusions

2018 ◽  
pp. 307-332
Author(s):  
Dumitru Motreanu
Keyword(s):  
Differential Inclusions ◽  
Control Problems

INVARIANCE PROPERTY WITH APPLICATION TO SOLVING CONTROL PROBLEMS

2014 ◽  
Vol 16 (02) ◽  
pp. 1440013
Author(s):  
V. N. USHAKOV ◽  
S. A. BRYKALOV ◽  
A. R. MATVIYCHUK ◽  
A. V. USHAKOV
Keyword(s):  
Phase Space ◽  
Finite Time ◽  
Differential Inclusions ◽  
Time Moment ◽  
Invariance Property ◽  
Control Problems ◽  
Time Interval ◽  
Controlled System ◽  
Controlled Systems ◽  
Target Set

We consider controlled systems and differential inclusions on a bounded time interval. The investigated problem brings the controlled system to a fixed compact target set in the phase space at a finite time moment. It is known that integral funnels of controlled systems and differential inclusions satisfy the invariance property. We discuss application of the invariance property to constructing approximations to integral funnels. Examples of nonlinear controlled systems are considered in which the proposed algorithm is realized.

scholarly journals Well-posed control problems related to second-order differential inclusions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Doria Affane ◽  
Mustapha Fateh Yarou
Keyword(s):  
Differential Inclusions ◽  
Optimal Control Problems ◽  
Dimensional Space ◽  
Maximal Monotone ◽  
Second Order ◽  
Control Problems ◽  
Finite Dimensional Space ◽  
Finite Dimensional ◽  
Quadratic Optimal Control ◽  
Well Posed

<p style='text-indent:20px;'>The paper deals with quadratic optimal control problems, we study the equivalence between well-posed problems and affinity on the control for a second-order differential inclusions with two-points conditions, governed by a maximal monotone operator in a finite dimensional space.</p>

scholarly journals Differential inclusions and abstract control problems

1996 ◽  
Vol 53 (1) ◽  
pp. 109-122 ◽  
Author(s):  
Mieczyław Cichoń
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Banach Spaces ◽  
Differential Inclusions ◽  
Evolution Operator ◽  
Linear Operators ◽  
Control Problems ◽  
Theory Of Optimal Control ◽  
Integral Solutions

We prove an existence theorem for differential inclusions in Banach spaces. Here {A (t): t ∈ [0,T]} is a family of linear operators generating a continuous evolution operator K (t, s). We concentrate on maps F with F (t,·) weakly sequentially hemi-continuous.Moreover, we show a compactness of the set of all integral solutions of the above problem. These results are also applied to a semilinear optimal control problem. Some corollaries, important in the theory of optimal control, are given too. We extend in several ways theorems existing in the literature.

scholarly journals Existence and Controllability Results for Nonlocal Fractional Impulsive Differential Inclusions in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
JinRong Wang ◽  
Ahmed G. Ibrahim
Keyword(s):  
Banach Spaces ◽  
Caputo Derivative ◽  
Infinitesimal Generator ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Linear Part ◽  
Sufficient Conditions ◽  
Control Problems ◽  
Compactness Property ◽  
Impulsive Differential Inclusions

We firstly deal with the existence of mild solutions for nonlocal fractional impulsive semilinear differential inclusions involving Caputo derivative in Banach spaces in the case when the linear part is the infinitesimal generator of a semigroup not necessarily compact. Meanwhile, we prove the compactness property of the set of solutions. Secondly, we establish two cases of sufficient conditions for the controllability of the considered control problems.

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