130 research outputs found
Controllability of nonlinear fractional delay dynamical systems with prescribed controls
In this paper, we consider controllability of nonlinear fractional delay dynamical systems with prescribed controls. We firstly give the solution representation of the fractional delay dynamical systems using Laplace transform and Mittag–Leffler functions. Then we give necessary and sufficient conditions for the controllability criteria of linear fractional delay dynamical systems with prescribed controls. Further, we use a fixed point theorem to establish the sufficient condition for the controllability of nonlinear fractional delay dynamical systems with prescribed controls. In particular, we determine several sufficient conditions on the nonlinear function term so that if the linear system is controllable, then the nonlinear system is controllable. Finally, we give two examples to demonstrate the applicability of our obtained results
Controllability of nonlinear fractional Langevin delay systems
In this paper, we discuss the controllability of fractional Langevin delay dynamical systems represented by the fractional delay differential equations of order 0 < α,β ≤ 1. Necessary and sufficient conditions for the controllability of linear fractional Langevin delay dynamical system are obtained by using the Grammian matrix. Sufficient conditions for the controllability of the nonlinear delay dynamical systems are established by using the Schauders fixed-point theorem. The problem of controllability of linear and nonlinear fractional Langevin delay dynamical systems with multiple delays and distributed delays in control are studied by using the same technique. Examples are provided to illustrate the theory
Enlarged Controllability of Riemann-Liouville Fractional Differential Equations
We investigate exact enlarged controllability for time fractional diffusion
systems of Riemann-Liouville type. The Hilbert uniqueness method is used to
prove exact enlarged controllability for both cases of zone and pointwise
actuators. A penalization method is given and the minimum energy control is
characterized.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN
1555-1423, CODEN JCNDDM, available at
[http://computationalnonlinear.asmedigitalcollection.asme.org]. Submitted
10-Aug-2017; Revised 28-Sept-2017 and 24-Oct-2017; Accepted 05-Nov-201
On the constrained and unconstrained controllability of semilinear Hilfer fractional systems
In the paper finite-dimensional semilinear dynamical control systems described by fractional-order state equations with the Hilfer fractional derivative are discussed. The formula for a solution of the considered systems is presented and derived using the Laplace transform. Bounded nonlinear function �� depending on a state and controls is used. New sufficient conditions for controllability without constraints are formulated and proved using Rothe’s fixed point theorem and the generalized Darbo fixed point theorem. Moreover, the stability property is used to formulate constrained controllability criteria. An illustrative example is presented to give the reader an idea of the theoretical results obtained. A transient process in an electrical circuit described by a system of Hilfer type fractional differential equations is proposed as a possible application of the study
Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces
We investigate a class of fractional neutral evolution equations on Banach
spaces involving Caputo derivatives. Main results establish conditions for the
controllability of the fractional-order system and conditions for existence of
a solution to an optimal control problem of minimum energy. The results are
proved with the help of fixed-point and semigroup theories.Comment: This is a preprint of a paper whose final and definite form is
published Open Access in 'Axioms' at [https://doi.org/10.3390/axioms11080379
Controllability of a semilinear neutral dynamic equation on time scales with impulses and nonlocal conditions
In this paper we consider a control system governed by a neutral differential equation on time scales with impulses and nonlocal conditions. We obtain conditions under which the system is approximately controllable, on one hand, and on the other hand, the exactly controllable is also proved. Concretely, first of all, we prove the existence of solutions. After that, we prove approximate controllability assuming that the associated linear system on time scales is exactly controllable, and applying a technique developed by Bashirov et al. [8, 9, 10] where we can avoid fixed point theorems. Next, assuming certain conditions on the nonlinear term, we can apply Banach Fixed Point Theorem to prove exact controllability. Finally, we propose an example to illustrate the applicability of our results.Publisher's Versio
Controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems
Sufficient conditions for controllability of nonlocal impulsive stochastic quasilinear integrodifferential systems in Hilbert spaces are established. The results are obtained by using evolution operator, semigroup theory and fixed point technique. As an application, an example is provided to illustrate the obtained result
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