scholarly journals Improved Results on Finite-Time Passivity and Synchronization Problem for Fractional-Order Memristor-Based Competitive Neural Networks: Interval Matrix Approach

2022 ◽  
Vol 6 (1) ◽  
pp. 36
Author(s):  
Pratap Anbalagan ◽  
Raja Ramachandran ◽  
Jehad Alzabut ◽  
Evren Hincal ◽  
Michal Niezabitowski
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Initial Conditions ◽  
Interval Matrix ◽  
Linear Matrix ◽  
Parameter Mismatch ◽  
Synchronization Problem ◽  
State Dependent

This research paper deals with the passivity and synchronization problem of fractional-order memristor-based competitive neural networks (FOMBCNNs) for the first time. Since the FOMBCNNs’ parameters are state-dependent, FOMBCNNs may exhibit unexpected parameter mismatch when different initial conditions are chosen. Therefore, the conventional robust control scheme cannot guarantee the synchronization of FOMBCNNs. Under the framework of the Filippov solution, the drive and response FOMBCNNs are first transformed into systems with interval parameters. Then, the new sufficient criteria are obtained by linear matrix inequalities (LMIs) to ensure the passivity in finite-time criteria for FOMBCNNs with mismatched switching jumps. Further, a feedback control law is designed to ensure the finite-time synchronization of FOMBCNNs. Finally, three numerical cases are given to illustrate the usefulness of our passivity and synchronization results.

Finite-time synchronization for fractional-order memristor-based neural networks with discontinuous activations and multiple delays

2020 ◽  
Vol 34 (15) ◽  
pp. 2050162
Author(s):  
Dawei Ding ◽  
Ziruo You ◽  
Yongbing Hu ◽  
Zongli Yang ◽  
Lianghui Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Multiple Delays ◽  
Multiple Time ◽  
Set Valued Mapping ◽  
Synchronization Problem ◽  
Discontinuous Activations ◽  
The Stability

This paper addresses the finite-time synchronization problem for fractional-order memristor-based neural networks (FMNNs) with discontinuous activations, in which multiple delays are considered. Firstly, on the basis of set-valued mapping as well as differential inclusions theory, the synchronization issue of drive-response systems is considered as the stabilization of the error system. Then, the state feedback controllers, which contain both discontinuous part and time-delayed part, are designed to analyze the finite-time synchronization of the concerned network model. Making use of the stability theorem of fractional-order systems with multiple time delays, some fractional derivative inequalities and comparison theorem, several sufficient criteria are established for confirming that the synchronization error of the concerned system can reach zero within a limited time. Additionally, the settling time can be optimized by adjusting controller parameter. Finally, the effectiveness of synchronization strategies is validated through the simulation results.

Finite-time synchronization for fuzzy inertial cellular neural networks with time-varying delays via integral inequality

2021 ◽  
pp. 1-14
Author(s):  
Zhenjie Wang ◽  
Wenxia Cui ◽  
Wenbin Jin
Keyword(s):  
Neural Networks ◽  
Integral Inequality ◽  
Finite Time ◽  
Time Synchronization ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Synchronization Problem ◽  
Inequality Techniques

This paper mainly considers the finite-time synchronization problem of fuzzy inertial cellular neural networks (FICNNs) with time-varying delays. By constructing the suitable Lyapunov functional, and using integral inequality techniques, several sufficient criteria have been proposed to ensure the finite-time synchronization for the addressed (FICNNs). Without applying the known finite-time stability theorem, which is widely used to solve the finite-time synchronization problems for (FICNNs). In this paper, the proposed method is relatively convenient to solve finite-time synchronization problem of the addressed system, this paper extends the research works on the finite-time synchronization of (FICNNs). Finally, numerical simulations illustrated verify the effectiveness of the proposed results.

scholarly journals New Methods of Finite-Time Synchronization for a Class of Fractional-Order Delayed Neural Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Weiwei Zhang ◽  
Jinde Cao ◽  
Ahmed Alsaedi ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Interval ◽  
Finite Time Interval ◽  
Delayed Neural Networks ◽  
New Methods ◽  
Theoretical Results

Finite-time synchronization for a class of fractional-order delayed neural networks with fractional order α, 0<α≤1/2 and 1/2<α<1, is investigated in this paper. Through the use of Hölder inequality, generalized Bernoulli inequality, and inequality skills, two sufficient conditions are considered to ensure synchronization of fractional-order delayed neural networks in a finite-time interval. Numerical example is given to verify the feasibility of the theoretical results.

Finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks

2020 ◽  
pp. 2150032
Author(s):  
Dawei Ding ◽  
Ziruo You ◽  
Yongbing Hu ◽  
Zongli Yang ◽  
Lianghui Ding
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Finite Time ◽  
Time Synchronization ◽  
Linear Part ◽  
State Feedback Control ◽  
Razumikhin Technique ◽  
Quaternion Multiplication ◽  
Control Schemes ◽  
The Stability

This paper mainly concerns with the finite-time synchronization of delayed fractional-order quaternion-valued memristor-based neural networks (FQVMNNs). First, the FQVMNNs are studied by separating the system into four real-valued parts owing to the noncommutativity of quaternion multiplication. Then, two state feedback control schemes, which include linear part and discontinuous part, are designed to guarantee that the synchronization of the studied networks can be achieved in finite time. Meanwhile, in terms of the stability theorem of delayed fractional-order systems, Razumikhin technique and comparison principle, some novel criteria are derived to confirm the synchronization of the studied models. Furthermore, two methods are used to obtain the estimation bounds of settling time. Finally, the feasiblity of the synchronization methods in quaternion domain is validated by the numerical examples.

Sign in / Sign up

Export Citation Format

Share Document