scholarly journals Robust Linear Neural Network for Constrained Quadratic Optimization

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Zixin Liu ◽  
Yuanan Liu ◽  
Lianglin Xiong
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Perturbation Theory ◽  
Optimization Problems ◽  
Quadratic Optimization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Analysis Method ◽  
Linear Neural Network ◽  
Constrained Quadratic Optimization

Based on the feature of projection operator under box constraint, by using convex analysis method, this paper proposed three robust linear systems to solve a class of quadratic optimization problems. Utilizing linear matrix inequality (LMI) technique, eigenvalue perturbation theory, Lyapunov-Razumikhin method, and LaSalle’s invariance principle, some stable criteria for the related models are also established. Compared with previous criteria derived in the literature cited herein, the stable criteria established in this paper are less conservative and more practicable. Finally, a numerical simulation example and an application example in compressed sensing problem are also given to illustrate the validity of the criteria established in this paper.

scholarly journals Dynamics of Uncertain Discrete-Time Neural Network with Delay and Impulses

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xuehui Mei ◽  
Liwei Zhang ◽  
Haijun Jiang ◽  
Zhiyong Yu
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Discrete Time ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Conservative Condition ◽  
Impulsive Delay ◽  
The Stability

The stability of discrete-time impulsive delay neural networks with and without uncertainty is investigated. First, by using Razumikhin-type theorem, a new less conservative condition for the exponential stability of discrete-time neural network with delay and impulse is proposed. Moreover, some new sufficient conditions are derived to guarantee the stability of uncertain discrete-time neural network with delay and impulse by using Lyapunov function and linear matrix inequality (LMI). Finally, several examples with numerical simulation are presented to demonstrate the effectiveness of the obtained results.

Cellular Neural Network Based on Hybrid Linear Matrix Inequality and Particle Swarm Optimization for Noise Removal of Color Image

2011 ◽  
Vol 422 ◽  
pp. 771-774
Author(s):  
Te Jen Su ◽  
Jui Chuan Cheng ◽  
Yu Jen Lin
Keyword(s):  
Neural Network ◽  
Particle Swarm Optimization ◽  
Linear Matrix Inequality ◽  
Color Image ◽  
Particle Swarm ◽  
Cellular Neural Network ◽  
Noise Removal ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Swarm Optimization

This paper presents a color image noise removal technique that employs a cellular neural network (CNN) based on hybrid linear matrix inequality (LMI) and particle swarm optimization (PSO). For designing templates of CNN, the Lyapunov stability theorem is applied to derive the criterion for the uniqueness and global asymptotic stability of the CNN’s equilibrium point. The template design is characterized as a standard LMI problem, and the parameters of templates are optimized by PSO. The input templates are obtained by employing the CNN’s property of saturation nonlinearity, which can be used to eliminate noise from arbitrary corrupted images. The demonstrated examples are compared favorably with other available methods, which illustrate the better performance of the proposed LMI-PSO-CNN methodology.

scholarly journals A Novel Iterative Linear Matrix Inequality Design Procedure for Passive Inter-Substructure Vibration Control

2020 ◽  
Vol 10 (17) ◽  
pp. 5859
Author(s):  
Josep Rubió-Massegú ◽  
Francisco Palacios-Quiñonero ◽  
Josep M. Rossell ◽  
Hamid Reza Karimi
Keyword(s):  
Linear Matrix Inequality ◽  
Vibration Control ◽  
State Feedback ◽  
Optimization Problems ◽  
Seismic Protection ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Static State ◽  
Fluid Viscous Dampers ◽  
Iterative Linear Matrix Inequality

In vibration control of compound structures, inter-substructure damper (ISSD) systems exploit the out-of-phase response of different substructures to dissipate the kinetic vibrational energy by means of inter-substructure damping links. For seismic protection of multistory buildings, distributed sets of interstory fluid viscous dampers (FVDs) are ISSD systems of particular interest. The connections between distributed FVD systems and decentralized static output-feedback control allow using advanced controller-design methodologies to obtain passive ISSD systems with high-performance characteristics. A major issue of that approach is the computational difficulties associated to the numerical solution of optimization problems with structured bilinear matrix inequality constraints. In this work, we present a novel iterative linear matrix inequality procedure that can be applied to obtain enhanced suboptimal solutions for that kind of optimization problems. To demonstrate the effectiveness of the proposed methodology, we design a system of supplementary interstory FVDs for the seismic protection of a five-story building by synthesizing a decentralized static velocity-feedback H∞ controller. In the performance assessment, we compare the frequency-domain and time-domain responses of the designed FVD system with the behavior of the optimal static state-feedback H∞ controller. The obtained results indicate that the proposed approach allows designing passive ISSD systems that are capable to match the level of performance attained by optimal state-feedback active controllers.

Pattern Recognition Controller Based on Fuzzy Neural Network

2014 ◽  
Vol 915-916 ◽  
pp. 1140-1143
Author(s):  
Liang Cheng
Keyword(s):  
Neural Network ◽  
Numerical Simulation ◽  
Pattern Recognition ◽  
Fuzzy Neural Network ◽  
Feasible Solution ◽  
Fuzzy Theory ◽  
Network Design Problem ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Fuzzy Neural

A class of fuzzy neural network design problem H controller. By TS fuzzy theory, a model of nonlinear complex systems. Then, based on Lyapunov-Krasovskii functional and LMI technique, gives the design an H controller. By using the Matlab LMI toolbox, we can get the corresponding feasible solution of linear matrix inequalities. Finally, a numerical simulation examples are given to prove the correctness of the H controller.

Structural Damage Detection Using Linear Matrix Inequality Methods

2000 ◽  
Vol 122 (4) ◽  
pp. 448-455 ◽  
Author(s):  
M. O. Abdalla ◽  
K. M. Grigoriadis ◽  
D. C. Zimmerman
Keyword(s):  
Experimental Data ◽  
Linear Matrix Inequality ◽  
Damage Detection ◽  
Structural Damage ◽  
Optimization Problems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Structural Damage Detection ◽  
Test Bed ◽  
Stiffness Reduction

In this work, linear matrix inequality (LMI) methods are proposed for computationally efficient solution of damage detection problems in structures. The structural damage detection problem that is considered consists of estimating the existence, location, and extent of stiffness reduction in structures using experimental modal data. This problem is formulated as a convex optimization problem involving LMI constraints on the unknown structural stiffness parameters. LMI optimization problems have low computational complexity and can be solved efficiently using recently developed interior-point methods. Both a matrix update and a parameter update formulation of the damage detection is provided in terms of LMIs. The presence of noise in the experimental data is taken explicitly into account in these formulations. The proposed techniques are applied to detect damage in simulation examples and in a cantilevered beam test-bed using experimental data obtained from modal tests. [S0739-3717(00)00104-5]

EXPONENTIAL STABILITY FOR STOCHASTIC NEURAL NETWORKS OF NEUTRAL TYPE WITH IMPULSIVE EFFECTS

2010 ◽  
Vol 24 (11) ◽  
pp. 1099-1110 ◽  
Author(s):  
RATHINASAMY SAKTHIVEL ◽  
R. SAMIDURAI ◽  
S. MARSHAL ANTHONI
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Exponential Stability ◽  
Stochastic Analysis ◽  
Lyapunov Functional ◽  
Neutral Type ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Matrix Inequality

This paper is concerned with the exponential stability of stochastic neural networks of neutral type with impulsive effects. By employing the Lyapunov functional and stochastic analysis, a new stability criterion for the stochastic neural network is derived in terms of linear matrix inequality. A numerical example is provided to show the effectiveness and applicability of the obtained result.

scholarly journals Stability Analysis Based on Caputo-Type Fractional-Order Quantum Neural Networks

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yumin Dong ◽  
Xiang Li ◽  
Wei Liao ◽  
Dong Hou
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Learning Algorithm ◽  
Activation Function ◽  
Linear Matrix ◽  
Mixed Delays ◽  
Sigmoid Function ◽  
Matrix Inequality ◽  
Fractional Quantum ◽  
Quantum Neural Network

In this paper, a quantum neural network with multilayer activation function is proposed by using multilayer Sigmoid function superposition and learning algorithm to adjust quantum interval. On this basis, the quasiuniform stability of fractional quantum neural networks with mixed delays is studied. According to the order of two different cases, the conditions of quasi uniform stability of networks are given by using the techniques of linear matrix inequality analysis, and the sufficiency of the conditions is proved. Finally, the feasibility of the conclusion is verified by experiments.

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