Displaying similar documents to “Cone-type constrained relative controllability of semilinear fractional systems with delays”

On application of Rothe's fixed point theorem to study the controllability of fractional semilinear systems with delays

Beata Sikora (2019)

Kybernetika

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The paper presents finite-dimensional dynamical control systems described by semilinear fractional-order state equations with multiple delays in the control and nonlinear function f . The relative controllability of the presented semilinear system is discussed. Rothe’s fixed point theorem is applied to study the controllability of the fractional-order semilinear system. A control that steers the semilinear system from an initial complete state to a final state at time t > 0 is presented....

Controllability criteria for time-delay fractional systems with a retarded state

Beata Sikora (2016)

International Journal of Applied Mathematics and Computer Science

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The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient...

Controllability of nonlinear implicit fractional integrodifferential systems

Krishnan Balachandran, Shanmugam Divya (2014)

International Journal of Applied Mathematics and Computer Science

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In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.

Relative controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control

Rajagopal Joice Nirmala, Krishnan Balachandran (2017)

Kybernetika

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This paper describes the controllability of nonlinear fractional delay integrodifferential systems with multiple delays in control. Necessary and sufficient conditions for the controllability criteria for linear fractional delay system are established. Further sufficient conditions for the controllability of nonlinear fractional delay integrodifferential system are obtained by using fixed point arguments. Examples are provided to illustrate the results.

Exact controllability of linear dynamical systems: A geometrical approach

María Isabel García-Planas (2017)

Applications of Mathematics

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In recent years there has been growing interest in the descriptive analysis of complex systems, permeating many aspects of daily life, obtaining considerable advances in the description of their structural and dynamical properties. However, much less effort has been devoted to studying the controllability of the dynamics taking place on them. Concretely, for complex systems it is of interest to study the exact controllability; this measure is defined as the minimum set of controls that...

Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type

Karine Beauchard (2011-2012)

Séminaire Laurent Schwartz — EDP et applications

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The goal of this note is to present the results of the references [5] and [4]. We study the null controllability of the parabolic equations associated with the Grushin-type operator ∂ x 2 + | x | 2 γ ∂ y 2 ( γ > 0 ) in the rectangle ( x , y ) ∈ ( - 1 , 1 ) × ( 0 , 1 ) or with the Kolmogorov-type operator v γ ∂ x f + ∂ v 2 f ( γ ∈ { 1 , 2 } ) in the rectangle ( x , v ) ∈ 𝕋 × ( - 1 , 1 ) , under an additive control supported in an open subset ω of the space domain. We prove that the Grushin-type...

Existence and controllability of fractional-order impulsive stochastic system with infinite delay

Toufik Guendouzi (2013)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper is concerned with the existence and approximate controllability for impulsive fractional-order stochastic infinite delay integro-differential equations in Hilbert space. By using Krasnoselskii's fixed point theorem with stochastic analysis theory, we derive a new set of sufficient conditions for the approximate controllability of impulsive fractional stochastic system under the assumption that the corresponding linear system is approximately controllable. Finally, an example...

On the controllability of fractional dynamical systems

Krishnan Balachandran, Jayakumar Kokila (2012)

International Journal of Applied Mathematics and Computer Science

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This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

On constrained controllability of dynamical systems with multiple delays in control

Beata Sikora (2005)

Applicationes Mathematicae

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Linear, continuous dynamical systems with multiple delays in control are studied. Their relative and absolute controllability with constrained control is discussed. Definitions of various types of constrained relative and absolute controllability for linear systems with delays in control are introduced. Criteria of relative and absolute controllability with constrained control are established. Constraints on control values are considered. Mutual implications between constrained relative...