New Set Of Sufficient Conditions Research Articles

Approximate controllability for Hilfer fractional stochastic differential systems of order 1

In this paper, we analyse the approximate controllability of Hilfer fractional stochastic differential systems of order 1 < μ < 2 in Hilbert spaces. The primary findings are carried out by using fractional calculus, stochastic analysis theory, cosine family, and Schauder's fixed point theorem. In particular, we draw a new set of sufficient conditions for the approximate controllability of Hilfer fractional stochastic differential equations of order 1 < μ < 2 under the assumption that the corresponding linear system is approximately controllable. In the end, an example is provided to illustrate the derived theory.

Hilfer-Katugampola fractional stochastic differential inclusions with Clarke sub-differential

The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of stochastic Hilfer-Katugampola fractional differential inclusions (SHKFDIs) with non-instantaneous impulsive (NIIs) that is strengthened by Brownian motion (BM) and the Clarke sub-differential. First, we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using stochastic analysis, the Clarke sub-differential's characteristics, and the multi-valued fixed point theorem. Subsequently, by employing Balder's theorem, the existence of optimal control pairs for the considered system is investigated. Eventually, an example is provided to validate the obtained results.

Approximate controllability of impulsive evolution stochastic functional differential equations driven by a fractional Brownian motion

In this paper, we study the approximate controllability of certain class of impulsive evolution stochastic functional differential equations, with variable delays, driven by a fractional Brownian motion in a separable real Hilbert space. We derive a new set of sufficient conditions for approximate controllability using a stochastic analysis of fractional Brownian motion with Hurst parameter H ∈ (1/2,1) and a Schaefer's fixed point theorem. An example is considered at the end of the paper to illustrate the obtained abstract results.

An analysis on asymptotic stability of Hilfer fractional stochastic evolution equations with infinite delay

This article deals with the existence and asymptotic stability in the p-th moment of a mild solution for Hilfer fractional stochastic delay differential equations in Hilbert spaces. Our main results are obtained by fractional calculus, semigroup theory, stochastic analysis, and the Banach fixed point theorem. Further, a new set of sufficient conditions for existence and asymptotic stability in the p-th moment is derived with the help of a fixed point technique. Additionally, we provide an example to demonstrate the reliability of our results.

A study of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1

This paper considers a class of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1 < α < 2 with impulses in a Hilbert space. We study the existence of the mild solution for the cases when the multi-valued map has convex and non-convex values. The results are obtained by combining fixed-point theorems with the fractional order cosine family, semigroup theory, and stochastic techniques. A new set of sufficient conditions is developed to demonstrate the approximate controllability of the system. Finally, an example is given to illustrate the obtained results.

New exploration on approximate controllability of fractional neutral‐type delay stochastic differential inclusions with non‐instantaneous impulse

This paper aims to derive a new set of sufficient conditions for the existence and approximate controllability of neutral‐type fractional stochastic integrodifferential inclusions with infinite delay and non‐instantaneous impulse in a separable Hilbert space using the Atangana–Baleanu Caputo fractional derivative. We investigate the existence of a mild solution for the Atangana–Baleanu Caputo fractional neutral‐type delay integrodifferential stochastic system while taking into account the non‐instantaneous impulses. For this purpose, the Atangana–Baleanu Caputo fractional neutral‐type impulsive delay stochastic system is transferred into an equivalent fixed point problem via an integral operator, and then, the Bohnenblust–Karlin fixed point approach is applied. Further, the approximate controllability results of the proposed nonlinear stochastic impulsive control system are established under the consideration that the corresponding linear system is approximately controllable. The set of sufficient conditions is established by using the concepts of stochastic analysis, fractional calculus, fixed point technique, semigroup theory of bounded linear operators, and the theory of multivalued maps. To illustrate the abstract results, we provide an example at the end of the paper.

A class of time-optimal feedback control for fractional neutral evolution hemivariational inequalities with fixed delay

ABSTRACT In this paper, we study a class of optimal feedback control for a neutral fractional system with hemivariational inequalities. Initially, we derive some existence results of mild solutions for the system by applying the Marteli's fixed point theorem of multivalued maps, properties of generalized Clarke's subdifferential and semigroup operators. Then, by using the Filippov theorem and the Cesari property, a new set of sufficient conditions are formulated to ensure the existence results of a feasible pair for the feedback control systems. Also, we apply our main results to obtain the optimal feedback control pair. Further, we investigate the time-optimal feedback control for our control system. In the end, an example is given to illustrate our theory.

A Study of Multi-Term Time-Fractional Delay Differential System with Monotonic Conditions

In this paper, the existence and uniqueness of mild solution for a class of multi-term time-fractional delay differential system have been discussed in ordered Banach space by enforcing monotone iterative technique. The generalized semigroup theory, fractional calculus and measure of noncompactness have been implemented to obtain the required results. A new set of sufficient conditions with the coefficients in the equations satisfying some monotonic properties has been obtained. Finally, an application is given to illustrate the obtained results.

Results on the existence and approximate controllability of neutral‐type delay integro‐differential system with noninstantaneous impulse

This manuscript aims to establish a new set of sufficient conditions for the existence and approximate controllability of a neutral‐type fractional integro‐differential system employed with noninstantaneous impulse and finite delay in Hilbert space. In order to bring off the main results, the author used fractional calculus, semigroup theory, and Schauder's fixed‐point theorem. At the end, we provide an example to illustrate the main results.

Fractional neutral stochastic integrodifferential equations with Caputo fractional derivative: Rosenblatt process, Poisson jumps and Optimal control

The objective of this paper is to investigate the existence of mild solutions and optimal controls for a class of fractional neutral stochastic integrodifferential equations driven by Rosenblatt process and Poisson jumps in Hilbert spaces. First we establish a new set of sufficient conditions for the existence of mild solutions of the aforementioned fractional systems by using the successive approximation approach. The results are formulated and proved by using the fractional calculus, solution operator and stochastic analysis techniques. The existence of optimal control pairs of system governed by fractional neutral stochastic differential equations driven by Rosenblatt process and poisson jumps is also been presented. An example is provided to illustrate the theory.

Existence and approximate controllability results for second-order impulsive stochastic neutral differential systems

This paper focuses on the existence and approximate controllability of second-order non-autonomous impulsive stochastic neutral differential systems in Hilbert spaces. First, by using Schauder's fixed-point theorem, stochastic analysis theory, and evolution operators, a new set of sufficient conditions are formulated, and we prove the existence of mild solutions of second-order non-autonomous impulsive stochastic neutral differential systems. Further, the result is extended to study the approximate controllability results for second-order non-autonomous impulsive stochastic neutral differential systems. Then, a set of sufficient conditions are derived for the approximate controllability of second-order non-autonomous impulsive stochastic neutral differential system by assuming the associated linear system is approximately controllable. The results are obtained with the help of Krasnoselskii's fixed point theorem. Finally, an example is given to illustrate our obtained results.

Computing Sum of Sources Over a Classical-Quantum MAC

We consider the task of communicating a generic bivariate function of two classical correlated sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. We first propose a coding scheme based on asymptotically good algebraic structured codes, in particular, nested coset codes, and provide a set of sufficient conditions for the reconstruction of the function of the sources over a CQ-MAC. The proposed technique enables the decoder to recover the desired function without recovering the sources themselves. We further improve this by employing a coding scheme based on a classical superposition of algebraic structured codes and unstructured codes. This coding scheme allows exploiting the symmetric structure common amongst the sources and also leverage the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources whose function can be reconstructed over any given CQ-MAC, and identify examples demonstrating the same. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

Approximate Controllability of Non-Instantaneous Impulsive Stochastic Evolution Systems Driven by Fractional Brownian Motion with Hurst Parameter H∈(0,12)

This paper initiates a study on the existence and approximate controllability for a type of non-instantaneous impulsive stochastic evolution equation (ISEE) excited by fractional Brownian motion (fBm) with Hurst index 0&lt;H&lt;1/2. First, to overcome the irregular or singular properties of fBm with Hurst parameter 0&lt;H&lt;1/2, we define a new type of control function. Then, by virtue of the stochastic analysis theory, inequality technique, the semigroup approach, Krasnoselskii’s fixed-point theorem and Schaefer’s fixed-point theorem, we derive two new sets of sufficient conditions for the existence and approximate controllability of the concerned system. In the end, a concrete example is worked out to demonstrate the applicability of our obtained results.

Robust Asynchronous Filtering for Discrete-Time T–S Fuzzy Complex Dynamical Networks Against Deception Attacks

In this article, the robust asynchronous filtering problem is investigated for a class of discrete-time T–S fuzzy complex dynamical networks subjected to random coupling delays and deception attacks. Specifically, the deception attacks are considered in the filter, where the adversary attempts to inject some false information data in the measurement output to modify the transmitted signal in the communication networks. We introduce, respectively, two sets of stochastic variables satisfying the Bernoulli distribution to depict the probability of the data transmitted by the network being subjected to time-varying coupling delays and deception attacks. By using Lyapunov–Krasovskii stability theory and Abel lemma-based finite-sum inequality, a new set of sufficient conditions is established, which ensures the stochastic stability of the resulting error system with a prescribed mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> and passivity performance index. The proposed filter parameters are obtained by solving linear matrix inequalities. Ultimately, both the effectiveness and advantages of the proposed asynchronous filter with deception attacks are verified by two numerical examples including a tunnel diode circuit model.

On the approximate controllability results for fractional integrodifferential systems of order [formula omitted] with sectorial operators

In this paper, we investigate the approximate controllability for fractional integrodifferential inclusions of order r∈(1,2) in Banach space with sectorial operators. In particular, we obtain a new set of sufficient conditions for the approximate controllability of nonlinear fractional integrodifferential inclusions of order r∈(1,2) under the assumption that the corresponding linear system is approximately controllable. In addition, we establish the approximate controllability results for the Sobolev type fractional control system with nonlocal conditions. The results are obtained with the help of fractional derivatives, sectorial operators of type (P,η,r,γ), multivalued functions, and Bohnenblust-fixed Karlin’s point theorem. Moreover, an example is also provided to illustrate the effectiveness of the results.

Design of [formula omitted]/passive state feedback control for delayed fractional order gene regulatory networks via new improved integral inequalities

This work deals with H∞/passivity analysis and control design for fractional-order gene regulatory networks (FOGRNs) with delays. The results are derived by structuring a new class of Lyapunov Krasovskii functional (LKF). To deal with these LKF and time delay terms, two new fractional-order integral inequalities (FOIIs) are established. Firstly, a fractional-order free weighting matrix based integral inequality (FOFMBII) is derived. This FOFMBII includes fractional-order Wirtinger’s integral inequality (FOWII) as a particular case. Secondly, another improved FOII is constructed to facilitate the estimation of the fractional derivative of Lyapunov functional. Then, using the derived FOIIs and constructed LKF, a new set of sufficient conditions is established in terms of linear matrix inequalities (LMIs) for ensuring the stability of FOGRNs with a prescribed mixed H∞/passivity or H∞ or passivity level. The theoretical results are validated on a genetic network model. Three control gain matrices for the considered model are calculated based on H∞, passivity, and mixed H∞/passivity performances. The efficiencies of these three controllers are compared. Finally, the simulation results are given to exhibit the validity of the proposed results.

Practical Stability Analysis and Switching Controller Synthesis for Discrete-time Switched Affine Systems via Linear Matrix Inequalities

This paper considers the practical asymptotic stabilization of adesired equilibrium point in discrete-time switched affine systems.The main purpose is to design a state feedback switching rule forthe discrete-time switched affine systems whose parameters can beextracted with less computational complexities. In this regard,using switched Lyapunov functions, a new set of sufficientconditions based on matrix inequalities are developed to solve thepractical stabilization problem. For any size of the switched affinesystem, the derived matrix inequalities contain only one bilinearterm as a multiplication of a positive scalar and a positivedefinite matrix. It is shown that the practical stabilizationproblem can be solved via a few convex optimization problems,including Linear Matrix Inequalities (LMIs) through gridding of ascalar variable interval between zero and one. The numericalexperiments on an academic example and a DC-DC buck-boost converter,as well as comparative studies with the existing works, prove thesatisfactory operation of the proposed method in achieving betterperformances and more tractable numerical solutions.

A note concerning to approximate controllability of Atangana-Baleanu fractional neutral stochastic systems with infinite delay

In this paper, we investigate the approximate controllability results of Atangana-Baleanu fractional neutral stochastic systems with infinite delay. Using principles and ideas from stochastic analysis, the theory of multivalued maps, fractional calculus, and Bohnenblust-Karlin fixed point theorem, a new set of sufficient conditions are formulated and proved for the approximate controllability of the fractional stochastic control system. We then apply our findings to the theory of nonlocal conditions. Finally, an example is given to illustrate the theory.

Guaranteed cost leaderless consensus for uncertain Markov jumping multi-agent systems

ABSTRACT This paper proposes an approach for the solvability of multi-agent systems with Markov jumps subject to time-varying delay and uncertainties. The primary concern of this paper is to construct a state feedback control design with a guaranteed cost function which not only ensures consensus but also assures certain amount of energy consumption. This cost function is designed with the aid of control inputs of all agents and state error among neighbouring agents. A new set of sufficient conditions for the guaranteed cost consensus of the considered Markov jumping multi-agent system (MAS) is derived in terms of linear matrix inequalities (LMIs) by constructing suitable Lyapunov-Krasovskii functional (LKF) and with the aid of Kronecker product properties. Finally, a numerical example is given to illustrate the effectiveness of the developed theoretical results.

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

The exponential stability of semi-linear stochastic partial differential equations (SPDEs) involving L&#x00E8;vy type noise is investigated in this paper. By constructing an appropriate Lyapunov function, a new set of sufficient conditions are established in terms of linear matrix inequalities (LMIs) which ensures the mean-square exponentially stability (MSES) of given system with Neumann boundary conditions. Then the <i>H</i>_&#x221E; performance index is introduced to eliminate the disturbance which occurs in the considered system. The boundary control gain is obtained by solving the LMI conditions using the standard MATLAB software. Finally, a numerical example is provided to demonstrate the usefulness of the proposed methods.