Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

2021 ◽  
Vol 26 (2) ◽  
pp. 207-226
Author(s):  
Jiazhe Lin ◽  
Rui Xu ◽  
Liangchen Li
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
Linear Feedback ◽  
Impulsive Effect ◽  
Bidirectional Associative Memory ◽  
Optimal Linear ◽  
Predictor Corrector

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method.

scholarly journals Anti-periodic solutions for fractional-order bidirectional associative memory neural networks with delays

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2169-2177
Author(s):  
Munevver Tuz ◽  
Gulden Suroglu
Keyword(s):  
Neural Networks ◽  
Periodic Solutions ◽  
Fractional Order ◽  
Associative Memory ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Bidirectional Associative Memory ◽  
Inequality Technique ◽  
Lyapunov Functional Method

This paper concerns fractional-order bidirectional associative memory neural networks with distributed delays. Based on inequality technique and Lyapunov functional method, some novel sufficient conditions are obtained for the existence and exponential stability of anti-periodic solutions are established. An example is given to show the feasibility main results.

Robust stability analysis for delayed Cohen-Grossberg-type bidirectional associative memory neural networks with norm-bounded uncertainties

2009 ◽  
Vol 223 (5) ◽  
pp. 693-707
Author(s):  
Y Wang ◽  
P Hu
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Robust Stability ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Bidirectional Associative Memory ◽  
Parameter Uncertainties ◽  
Robust Stability Analysis ◽  
Global Robust Stability ◽  
Bounded Uncertainties

In this paper, the problem of global robust stability is discussed for uncertain Cohen-Grossberg-type (CG-type) bidirectional associative memory (BAM) neural networks (NNs) with delays. The parameter uncertainties are supposed to be norm bounded. The sufficient conditions for global robust stability are derived by employing a Lyapunov-Krasovskii functional. Based on these, the conditions ensuring global asymptotic stability without parameter uncertainties are established. All conditions are expressed in terms of linear matrix inequalities (LMIs). In addition, two examples are provided to illustrate the effectiveness of the results obtained.

scholarly journals On the Stability with Respect to H-Manifolds for Cohen–Grossberg-Type Bidirectional Associative Memory Neural Networks with Variable Impulsive Perturbations and Time-Varying Delays

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 335 ◽  
Author(s):  
Gani Stamov ◽  
Ivanka Stamova ◽  
Stanislav Simeonov ◽  
Ivan Torlakov
Keyword(s):  
Neural Networks ◽  
Associative Memory ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Stability Criteria ◽  
Bidirectional Associative Memory ◽  
The Neural Network ◽  
Lyapunov Function Method ◽  
Impulsive Perturbations ◽  
The Stability

The present paper is devoted to Bidirectional Associative Memory (BAM) Cohen–Grossberg-type impulsive neural networks with time-varying delays. Instead of impulsive discontinuities at fixed moments of time, we consider variable impulsive perturbations. The stability with respect to manifolds notion is introduced for the neural network model under consideration. By means of the Lyapunov function method sufficient conditions that guarantee the stability properties of solutions are established. Two examples are presented to show the validity of the proposed stability criteria.

scholarly journals Stability Analysis of Fractional-Order Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Zhanying Yang ◽  
Jie Zhang
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Fractional Order ◽  
Associative Memory ◽  
Analytical Techniques ◽  
Mean Value Theorem ◽  
Sufficient Condition ◽  
Time Varying ◽  
Bidirectional Associative Memory ◽  
Practical Applications

This paper studies the stability analysis of fractional-order bidirectional associative memory neural networks with mixed time-varying delays. The orders of these systems lie in the interval 1,2. Firstly, a sufficient condition is derived to ensure the finite-time stability of systems by resorting to some analytical techniques and some elementary inequalities. Next, a sufficient condition is obtained to guarantee the global asymptotic stability of systems based on the Laplace transform, the mean value theorem, the generalized Gronwall inequality, and some properties of Mittag–Leffler functions. In particular, these obtained conditions are expressed as some algebraic inequalities which can be easily calculated in practical applications. Finally, some numerical examples are given to verify the feasibility and effectiveness of the obtained main results.

scholarly journals Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes

2017 ◽  
Vol 473 (2204) ◽  
pp. 20170322 ◽  
Author(s):  
Xiaoshuai Ding ◽  
Jinde Cao ◽  
Xuan Zhao ◽  
Fuad E. Alsaadi
Keyword(s):  
Neural Networks ◽  
Fractional Order ◽  
Associative Memory ◽  
State Feedback ◽  
Impulsive Control ◽  
State Feedback Control ◽  
Bidirectional Associative Memory ◽  
Discontinuous Activations ◽  
The Fixed Point Theorem ◽  
Discontinuous Activation Functions

This paper is concerned with the drive–response synchronization for a class of fractional-order bidirectional associative memory neural networks with time delays, as well as in the presence of discontinuous activation functions. The global existence of solution under the framework of Filippov for such networks is firstly obtained based on the fixed-point theorem for condensing map. Then the state feedback and impulsive controllers are, respectively, designed to ensure the Mittag-Leffler synchronization of these neural networks and two new synchronization criteria are obtained, which are expressed in terms of a fractional comparison principle and Razumikhin techniques. Numerical simulations are presented to validate the proposed methodologies.

Sign in / Sign up

Export Citation Format

Share Document