Trajectory Controllability of Dynamical Systems with Non-instantaneous Impulses

This manuscript considered the system governed by the non-instantaneous impulsive evolution control system and discusses trajectory controllability of the governed system with classical and nonlocal initial conditions over the general Banach space. The results of the trajectory controllability for governed systems are obtained through the concept of operator semigroup and Gronwall’s inequality. This manuscript is also equipped with examples to illustrate the applications of derived results.

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Trajectory Controllability of the Systems Governed by Hilfer Fractional Systems

YMER Digital ◽

10.37896/ymer20.11/5 ◽

2021 ◽

Vol 20 (11) ◽

pp. 37-46

Author(s):

Vishant Shah ◽

Keyword(s):

Differential Equation ◽

Banach Space ◽

Nonlinear System ◽

Differential Equations ◽

Operator Semigroup ◽

Local Conditions ◽

Fractional Systems ◽

Integro Differential Equation ◽

Gronwall’S Inequality ◽

Non Local

In this manuscript, we consider a nonlinear system governed by Hilfer fractional integro-differential equations in a Banach space. Using the concept of operator semigroup and Gronwall’s inequality, we have established the trajectory controllability of the integro-differential equation with local and non-local conditions. Finally, we have given an example to illustrate the application of the derived results

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Semilinear Volterra integrodifferential equations with nonlocal initial conditions

Abstract and Applied Analysis ◽

10.1155/s1085337599000123 ◽

1999 ◽

Vol 4 (2) ◽

pp. 127-139 ◽

Cited By ~ 3

Author(s):

Sergiu Aizicovici ◽

Mark Mckibben

Keyword(s):

Banach Space ◽

Global Existence ◽

Initial Conditions ◽

Mild Solutions ◽

Integrodifferential Equations ◽

Cauchy Problems ◽

Nonlocal Initial Conditions

We establish the global existence of mild solutions to a class of nonlocal Cauchy problems associated with semilinear Volterra integrodifferential equations in a Banach space.

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Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

Abstract and Applied Analysis ◽

10.1155/2012/647103 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 9

Author(s):

Carlos Lizama ◽

Juan C. Pozo

Keyword(s):

Banach Space ◽

Fixed Point ◽

Integrodifferential Equation ◽

Measure Of Noncompactness ◽

Initial Conditions ◽

Mild Solutions ◽

Hausdorff Measure Of Noncompactness ◽

Nonlocal Initial Conditions ◽

Closed Operators ◽

Point Argument

Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditionsu′(t)=Au(t)+∫0tB(t-s)u(s)ds+f(t,u(t)),t∈[0,1],u(0)=g(u), whereA:D(A)⊆X→X, and for everyt∈[0,1]the mapsB(t):D(B(t))⊆X→Xare linear closed operators defined in a Banach spaceX. We assume further thatD(A)⊆D(B(t))for everyt∈[0,1], and the functionsf:[0,1]×X→Xandg:C([0,1];X)→XareX-valued functions which satisfy appropriate conditions.

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Handling Initial Conditions in Vector Fitting for Real Time Modeling of Power System Dynamics

Energies ◽

10.3390/en14092471 ◽

2021 ◽

Vol 14 (9) ◽

pp. 2471

Author(s):

Tommaso Bradde ◽

Samuel Chevalier ◽

Marco De Stefano ◽

Stefano Grivet-Talocia ◽

Luca Daniel

Keyword(s):

Dynamical Systems ◽

Power System ◽

System Dynamics ◽

Real Time ◽

Initial Conditions ◽

Test System ◽

Initial State ◽

Power System Dynamics ◽

Vector Fitting ◽

Time Modeling

This paper develops a predictive modeling algorithm, denoted as Real-Time Vector Fitting (RTVF), which is capable of approximating the real-time linearized dynamics of multi-input multi-output (MIMO) dynamical systems via rational transfer function matrices. Based on a generalization of the well-known Time-Domain Vector Fitting (TDVF) algorithm, RTVF is suitable for online modeling of dynamical systems which experience both initial-state decay contributions in the measured output signals and concurrently active input signals. These adaptations were specifically contrived to meet the needs currently present in the electrical power systems community, where real-time modeling of low frequency power system dynamics is becoming an increasingly coveted tool by power system operators. After introducing and validating the RTVF scheme on synthetic test cases, this paper presents a series of numerical tests on high-order closed-loop generator systems in the IEEE 39-bus test system.

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On some kinds of dense orbits in general nonautonomous dynamical systems

Nonautonomous Dynamical Systems ◽

10.1515/msds-2020-0116 ◽

2020 ◽

Vol 7 (1) ◽

pp. 163-175

Author(s):

Mehdi Pourbarat

Keyword(s):

Dynamical Systems ◽

Initial Conditions ◽

Point Of View ◽

Topological Conjugacy ◽

Topological Transitivity ◽

Nonautonomous Systems ◽

Nonautonomous Dynamical Systems ◽

Sensitive Dependence ◽

Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

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Controllability of impulsive second order semilinear fuzzy integrodifferential control systems with nonlocal initial conditions

Applied Soft Computing ◽

10.1016/j.asoc.2015.10.006 ◽

2016 ◽

Vol 39 ◽

pp. 251-265 ◽

Cited By ~ 3

Author(s):

Mohit Kumar ◽

Sandeep Kumar

Keyword(s):

Control Systems ◽

Initial Conditions ◽

Second Order ◽

Nonlocal Initial Conditions

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Pseudorandom Number Generators Based on Chaotic Dynamical Systems

Open Systems & Information Dynamics ◽

10.1023/a:1011950531970 ◽

2001 ◽

Vol 08 (02) ◽

pp. 137-146 ◽

Cited By ~ 16

Author(s):

Janusz Szczepański ◽

Zbigniew Kotulski

Keyword(s):

Dynamical Systems ◽

Communication Systems ◽

Initial Conditions ◽

Pseudorandom Number ◽

New Approach ◽

Chaotic Dynamical Systems ◽

Pseudorandom Number Generators ◽

Transmission Of Information ◽

Extreme Sensitivity ◽

Contemporary Technology

Pseudorandom number generators are used in many areas of contemporary technology such as modern communication systems and engineering applications. In recent years a new approach to secure transmission of information based on the application of the theory of chaotic dynamical systems has been developed. In this paper we present a method of generating pseudorandom numbers applying discrete chaotic dynamical systems. The idea of construction of chaotic pseudorandom number generators (CPRNG) intrinsically exploits the property of extreme sensitivity of trajectories to small changes of initial conditions, since the generated bits are associated with trajectories in an appropriate way. To ensure good statistical properties of the CPRBG (which determine its quality) we assume that the dynamical systems used are also ergodic or preferably mixing. Finally, since chaotic systems often appear in realistic physical situations, we suggest a physical model of CPRNG.

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