FUZZY LOGIC DERIVATION OF NEURAL NETWORK MODELS WITH TIME DELAYS IN SUBSYSTEMS

2005 ◽  
Vol 14 (06) ◽  
pp. 967-974 ◽  
Author(s):  
CHEN-YUAN CHEN ◽  
JOHN RONG-CHUNG HSU ◽  
CHENG-WU CHEN
Keyword(s):  
Time Delays ◽  
Fuzzy Model ◽  
Network Models ◽  
Space Representation ◽  
Linear Matrix ◽  
Neural Network Models ◽  
Lmi Optimization ◽  
Common Solution ◽  
State Space Representation ◽  
The Stability

This paper extends the Takagi-Sugeno (T-S) fuzzy model representation to analyze the stability of interconnected systems in which there exist time delays in subsystems. A novel stability criterion which can be solved numerically is presented in terms of Lyapunov's theory for fuzzy interconnected models. In this paper, we use linear difference inclusion (LDI) state-space representation to represent the fuzzy model. Then, the linear matrix inequality (LMI) optimization algorithm is employed to find common solution and then guarantee the asymptotic stability.

Fuzzy Control for Nonlinear Uncertain T-S Fuzzy Systems with Time-Varying Delays

2013 ◽  
Vol 341-342 ◽  
pp. 668-673
Author(s):  
Yi Min Li ◽  
Yuan Yuan Li
Keyword(s):  
Stability Analysis ◽  
Discrete Time ◽  
Fuzzy Model ◽  
Optimization Techniques ◽  
Linear Matrix ◽  
Time Varying ◽  
Parameter Uncertainties ◽  
Lmi Optimization ◽  
System A ◽  
The Stability

This paper studies the stability analysis of discrete time-varying system with parameter uncertainties and disturbances. The system under consideration is subject to time-varying non-bounded parameter uncertainties in both the state and measured output matrices. To facilitate the stability analysis, the T-S fuzzy model is employed to represent the discrete-time nonlinear system. A fuzzy observer is used to guarantee the Lyapunov stability of the closed-loop system and reduces the effect of the disturbance input on the controlled output to a prescribed level for all admissible uncertainties. The control and observer matrices can be obtained by directly solving a set of linear matrix inequality (LMI) via the existing LMI optimization techniques. Finally, an example is provided to demonstrate the effectiveness of the proposed approach.

LMI Tools for Stability Analysis of Fractional Systems

2005 ◽  
Author(s):  
Mathieu Moze ◽  
Jocelyn Sabatier ◽  
Alain Oustaloup
Keyword(s):  
Geometric Analysis ◽  
Stability Domain ◽  
System Stability ◽  
Necessary Condition ◽  
Space Representation ◽  
Linear Matrix ◽  
Fractional Systems ◽  
State Space Representation ◽  
Classical Stability ◽  
The Stability

The main point when dealing with Linear Matrix Inequalities (LMI) is convexity. However, with state space representation of fractional systems, the stability domain for a fractional order 0 < ν < 1 is not convex. The classical stability condition thus cannot be extended to fractional systems. In this paper, three LMI based methods are used to characterize stability. The first is based on the second Lyapunov method and provides a sufficient but non-necessary condition. The second and new method provides a sufficient and necessary condition, and is based on a geometric analysis of a fractional system stability domain. The third method is more conventional but involves non strict LMI. A comparison of the first two methods is provided.

Quaternionic Neural Networks

2009 ◽  
pp. 411-439 ◽  
Author(s):  
Teijiro Isokawa ◽  
Nobuyuki Matsui ◽  
Haruhiko Nishimura
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Network Models ◽  
Recurrent Network ◽  
Affine Transformations ◽  
Neural Network Models ◽  
Fundamental Properties ◽  
Modern Physics ◽  
The Stability

Quaternions are a class of hypercomplex number systems, a four-dimensional extension of imaginary numbers, which are extensively used in various fields such as modern physics and computer graphics. Although the number of applications of neural networks employing quaternions is comparatively less than that of complex-valued neural networks, it has been increasing recently. In this chapter, the authors describe two types of quaternionic neural network models. One type is a multilayer perceptron based on 3D geometrical affine transformations by quaternions. The operations that can be performed in this network are translation, dilatation, and spatial rotation in three-dimensional space. Several examples are provided in order to demonstrate the utility of this network. The other type is a Hopfield-type recurrent network whose parameters are directly encoded into quaternions. The stability of this network is demonstrated by proving that the energy decreases monotonically with respect to the change in neuron states. The fundamental properties of this network are presented through the network with three neurons.

scholarly journals Stability and stabilizability of dynamical systems with multiple time-varying delays: delay-dependent criteria

2003 ◽  
Vol 2003 (4) ◽  
pp. 137-152 ◽  
Author(s):  
D. Mehdi ◽  
E. K. Boukas
Keyword(s):  
Time Delays ◽  
Uncertain Systems ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
The Stability ◽  
Delay Dependent ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

This paper deals with the class of uncertain systems with multiple time delays. The stability and stabilizability of this class of systems are considered. Their robustness are also studied when the norm-bounded uncertainties are considered. Linear matrix inequality (LMIs) delay-dependent sufficient conditions for both stability and stabilizability and their robustness are established to check if a system of this class is stable and/or is stabilizable. Some numerical examples are provided to show the usefulness of the proposed results.

Stability analysis for discrete-time stochastic neural networks with mixed time delays and impulsive effects

2010 ◽  
Vol 88 (12) ◽  
pp. 885-898 ◽  
Author(s):  
R. Raja ◽  
R. Sakthivel ◽  
S. Marshal Anthoni
Keyword(s):  
Neural Networks ◽  
Equilibrium Point ◽  
Discrete Time ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Linear Matrix ◽  
Stochastic Neural Networks ◽  
Mixed Time Delays ◽  
The Stability

This paper investigates the stability issues for a class of discrete-time stochastic neural networks with mixed time delays and impulsive effects. By constructing a new Lyapunov–Krasovskii functional and combining with the linear matrix inequality (LMI) approach, a novel set of sufficient conditions are derived to ensure the global asymptotic stability of the equilibrium point for the addressed discrete-time neural networks. Then the result is extended to address the problem of robust stability of uncertain discrete-time stochastic neural networks with impulsive effects. One important feature in this paper is that the stability of the equilibrium point is proved under mild conditions on the activation functions, and it is not required to be differentiable or strictly monotonic. In addition, two numerical examples are provided to show the effectiveness of the proposed method, while being less conservative.

scholarly journals Neural-Network-Based Discrete-Time Fuzzy Control of Continuous-Time Nonlinear Systems with Dither

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Zhi-Ren Tsai ◽  
Jiing-Dong Hwang
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Discrete Time ◽  
Continuous Time ◽  
Fuzzy Controller ◽  
Sampling Frequency ◽  
Space Representation ◽  
Linear Matrix ◽  
State Space Representation ◽  
Ct System

This study presents an effective approach to stabilizing a continuous-time (CT) nonlinear system using dithers and a discrete-time (DT) fuzzy controller. A CT nonlinear system is first discretized to a DT nonlinear system. Then, a Neural-Network (NN) system is established to approximate a DT nonlinear system. Next, a Linear Difference Inclusion state-space representation is established for the dynamics of the NN system. Subsequently, a Takagi-Sugeno DT fuzzy controller is designed to stabilize this NN system. If the DT fuzzy controller cannot stabilize the NN system, a dither, as an auxiliary of the controller, is simultaneously introduced to stabilize the closed-loop CT nonlinear system by using the Simplex optimization and the linear matrix inequality method. This dither can be injected into the original CT nonlinear system by the proposed injecting procedure, and this NN system is established to approximate this dithered system. When the discretized frequency or sampling frequency of the CT system is sufficiently high, the DT system can maintain the dynamic of the CT system. We can design the sampling frequency, so the trajectory of the DT system and the relaxed CT system can be made as close as desired.

SYNCHRONIZATION OF TIME-DELAYED T–S FUZZY CHAOTIC SYSTEMS VIA SCALAR OUTPUT VARIABLE

2005 ◽  
Vol 15 (08) ◽  
pp. 2593-2601 ◽  
Author(s):  
JAE-HUN KIM ◽  
HYUNSEOK SHIN ◽  
EUNTAI KIM ◽  
MIGNON PARK
Keyword(s):  
Time Delay ◽  
Fuzzy Model ◽  
Order System ◽  
Linear Matrix ◽  
Output Variable ◽  
First Order ◽  
Scalar Output ◽  
The Stability ◽  
Takagi Sugeno ◽  
System With Time Delay

It has been known that very complex chaotic behaviors can be observed in a simple first-order system with time-delay. This paper presents a fuzzy model-based approach for synchronization of time-delayed chaotic system via a scalar output variable. Takagi–Sugeno (T–S) fuzzy model can represent a general class of nonlinear system and we employ it for fuzzy modeling of the chaotic drive and response system with time-delay. Since only a scalar output variable is available for synchronization, a fuzzy observer based on T–S fuzzy model is designed and applied to chaotic synchronization. We analyze the stability of the overall fuzzy synchronization system by applying Lyapunov–Krasovskii theory and derive stability conditions by solving linear matrix inequalities (LMI's) problem. A numerical example is given to demonstrate the validity of the proposed synchronization approach.

Multifunctional Electrical Prosthetic Hand -Development of Tendon-driven Mechanism and Controller

2002 ◽  
Vol 14 (6) ◽  
pp. 557-564 ◽  
Author(s):  
Wenwei Yu ◽  
◽  
Daisuke Nishikawa ◽  
Yasuhiro Ishikawa ◽  
Hiroshi Yokoi ◽  
...  
Keyword(s):  
Neural Network ◽  
Time Delay ◽  
Recurrent Neural Network ◽  
Network Models ◽  
Joint Torque ◽  
Prosthetic Hand ◽  
Neural Network Models ◽  
Nonlinear Properties ◽  
The Stability

The purpose of this research was to develop a tendondriven electrical prosthetic hand, which is characterized by its mechanical torque-velocity converter and a mechanism that can assist proximal joint torque by distal actuators. To cope with time-delay and nonlinear properties of the prosthetic hand, a controller based on a Jordan network, recurrent neural network models, is proposed. The results of experiments on the stability of the controller are confirmed when tracking static wire tensions. Finally, the next prototype of prosthetic hand based on these methods is introduced.

A LEARNING ALGORITHM FOR OPTIMAL REPRESENTATION OF EXPERIMENTAL DATA

1994 ◽  
Vol 04 (02) ◽  
pp. 311-326 ◽  
Author(s):  
JOSEPH L. BREEDEN ◽  
NORMAN H. PACKARD
Keyword(s):  
Experimental Data ◽  
Time Delays ◽  
Optimality Criterion ◽  
Learning Algorithm ◽  
Space Representation ◽  
Coordinate Systems ◽  
State Space Representation ◽  
Optimal Representation ◽  
Definition Of ◽  
General Tool

We have developed a procedure for finding optimal representations of experimental data. Criteria for optimality vary according to context; an optimal state space representation will be one that best suits one’s stated goal for reconstruction. We consider an ∞-dimensional set of possible reconstruction coordinate systems that include time delays, derivatives, and many other possible coordinates; and any optimality criterion is specified as a real valued functional on this space. We present a method for finding the optima using a learning algorithm based upon the genetic algorithm and evolutionary programming. The learning algorithm machinery for finding optimal representations is independent of the definition of optimality, and thus provides a general tool useful in a wide variety of contexts.

L2 gain state derivative feedback control of uncertain vehicle suspension systems

2017 ◽  
Vol 24 (16) ◽  
pp. 3779-3794 ◽  
Author(s):  
Hakan Yazici ◽  
Mert Sever
Keyword(s):  
Ride Comfort ◽  
Controller Design ◽  
Parametric Uncertainty ◽  
Feedback Controller ◽  
Vehicle Suspension ◽  
Space Representation ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
State Space Representation ◽  
Tire Stiffness

This paper is concerned with the design of a robust L2 gain state derivative feedback controller for an active suspension system. An uncertain quarter vehicle model is used to analyze vehicle suspension performance. Parametric uncertainty is assumed to exist in sprung mass, tire stiffness and suspension damping coefficients. Polytopic type state space representation is used to enable robust controller design via a linear matrix inequalities (LMIs) framework. Then nominal and robust L2 gain state derivative feedback controllers having bounded controller gains and robust L2 gain state feedback controllers are tested against ISO2631 random road disturbances with different road grades and vehicle horizontal velocities. Simulation results show that the proposed robust L2 gain state derivative feedback controller is very effective in improving ride comfort without deterioration on road holding ability.

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