scholarly journals Fixed-time control of delayed neural networks with impulsive perturbations

2018 ◽  
Vol 23 (6) ◽  
pp. 904-920 ◽  
Author(s):  
Jingting Hu ◽  
Guixia Sui ◽  
Xiaoxiao Lv ◽  
Xiaodi Li
Keyword(s):  
Neural Networks ◽  
Initial Conditions ◽  
Fixed Time ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Time Control ◽  
Analysis Technique ◽  
Lyapunov Function Method ◽  
Impulsive Perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis.

scholarly journals Robust Fixed-Time Synchronization for Coupled Delayed Neural Networks with Discontinuous Activations Subject to a Quadratic Polynomial Growth

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Lina Yu ◽  
Yunfei Ma ◽  
Yuntong Yang ◽  
Jingchao Zhang ◽  
Chunwei Wang
Keyword(s):  
Neural Networks ◽  
Time Synchronization ◽  
Fixed Time ◽  
Functional Method ◽  
Quadratic Polynomial ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Analysis Technique ◽  
Discontinuous Activations ◽  
Discontinuous Activation Functions

In this paper, we focus on the robust fixed-time synchronization for discontinuous neural networks (NNs) with delays and hybrid couplings under uncertain disturbances, where the growth of discontinuous activation functions is governed by a quadratic polynomial. New state-feedback controllers, which include integral terms and discontinuous factors, are designed. By Lyapunov–Krasovskii functional method and inequality analysis technique, some sufficient criteria, which ensue that networks can realize the robust fixed-time synchronization, are addressed in terms of linear matrix inequalities (LMIs). Moreover, the upper bound of the settling time, which is independent on the initial values, can be determined to any desired values in advance by the configuration of parameters in the proposed control law. Finally, two examples are provided to illustrate the validity of the theoretical results.

Improved Results on Finite-Time Stability Analysis of Neural Networks With Time-Varying Delays

2018 ◽  
Vol 140 (10) ◽  
Author(s):  
S. Saravanan ◽  
M. Syed Ali
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Finite Time ◽  
Lyapunov Functional ◽  
Convex Combination ◽  
Linear Matrix ◽  
Time Stability ◽  
Delayed Neural Networks ◽  
Finite Time Stability ◽  
Combination Methods

This paper investigates the issue of finite time stability analysis of time-delayed neural networks by introducing a new Lyapunov functional which uses the information on the delay sufficiently and an augmented Lyapunov functional which contains some triple integral terms. Some improved delay-dependent stability criteria are derived using Jensen's inequality, reciprocally convex combination methods. Then, the finite-time stability conditions are solved by the linear matrix inequalities (LMIs). Numerical examples are finally presented to verify the effectiveness of the obtained results.

scholarly journals Synchronization of Time-Varying Delayed Neural Networks by Fixed-Time Control

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 74240-74246 ◽  
Author(s):  
Yuhua Xu ◽  
Xiaoqun Wu ◽  
Chao Xu
Keyword(s):  
Neural Networks ◽  
Fixed Time ◽  
Time Varying ◽  
Delayed Neural Networks ◽  
Time Control

Sub-fixed-time control for a class of second order system

2020 ◽  
pp. 014233122092100
Author(s):  
Boyan Jiang ◽  
Hua Chen ◽  
Bo Li ◽  
Xuewu Zhang
Keyword(s):  
Initial Conditions ◽  
Equilibrium Points ◽  
Fixed Time ◽  
Second Order ◽  
Order System ◽  
Sufficient Condition ◽  
Time Stability ◽  
Time Control ◽  
Initial States ◽  
The Stability

In this paper, a new concept “sub-fixed-time stability” (SFTS) is proposed and studied, which means the states can converge to a region of equilibrium points in a fixed time for any initial states’ values. Then, a sufficient condition for it is given and proven. Though SFTS is similar to “practical fixed-time stability” (PFTS), they are not the same, and the sufficient condition for SFTS is much clearer and simpler than PFTS. Next, a sub-fixed-time controller is proposed for a class of second order system. The stability analyses are given in the case without disturbance and with disturbance, respectively. Finally, to illustrate the robustness of the proposed sub-fixed-time controller to different initial conditions, 100 numerical simulations are conducted for 100 initial states’ values.

scholarly journals Fixed-Time Stability of the Hydraulic Turbine Governing System

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Caoyuan Ma ◽  
Chuangzhen Liu ◽  
Xuezi Zhang ◽  
Yongzheng Sun ◽  
Wenbei Wu ◽  
...  
Keyword(s):  
Control Strategy ◽  
Finite Time ◽  
Initial Conditions ◽  
Hydraulic Turbine ◽  
Fixed Time ◽  
Time Stability ◽  
Initial State ◽  
Time Control ◽  
Governing System ◽  
Water Turbine

This paper studies the problem of fixed-time stability of hydraulic turbine governing system with the elastic water hammer nonlinear model. To control and improve the quality of hydraulic turbine governing system, a new fixed-time control strategy is proposed, which can stabilize the water turbine governing system within a fixed time. Compared with the finite-time control strategy where the convergence rate depends on the initial state, the settling time of the fixed-time control scheme can be adjusted to the required value regardless of the initial conditions. Finally, we numerically show that the fixed-time control is more effective than and superior to the finite-time control.

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

scholarly journals Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Maoxing Liu ◽  
Jie Wu ◽  
Yong-zheng Sun
Keyword(s):  
Stability Analysis ◽  
Permanent Magnet ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
Fixed Time ◽  
Stability Control ◽  
Time Stability ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors ◽  
Comparison Results

We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document