scholarly journals Delay-Dependent Exponential Optimal Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Feng-Hsiag Hsiao
Keyword(s):  
Neural Network ◽  
State Space ◽  
Direct Method ◽  
Exponential Synchronization ◽  
Disturbance Attenuation ◽  
Space Representation ◽  
Linear Matrix ◽  
Multiple Time ◽  
State Space Representation ◽  
Delay Dependent

A novel approach is presented to realize the optimal exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). According to the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal performance by minimizing the disturbance attenuation level at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.

Decentralized Stabilization of Neural Network Linearly Interconnected Systems via T-S Fuzzy Control

2005 ◽  
Vol 129 (3) ◽  
pp. 343-351 ◽  
Author(s):  
Feng-Hsiag Hsiao ◽  
Yew-Wen Liang ◽  
Sheng-Dong Xu ◽  
Gwo-Chuan Lee
Keyword(s):  
Neural Network ◽  
State Space ◽  
Direct Method ◽  
Interconnected Systems ◽  
Space Representation ◽  
Interconnected System ◽  
Decentralized Stabilization ◽  
State Space Representation ◽  
Control Scheme ◽  
Takagi Sugeno

The stabilization problem is considered in this study for a neural-network (NN) linearly interconnected system that consists of a number of NN models. First, a linear difference inclusion (LDI) state-space representation is established for the dynamics of each NN model. Then, based on the LDI state-space representation, a stability criterion in terms of Lyapunov’s direct method is derived to guarantee the asymptotic stability of closed-loop NN linearly interconnected systems. Subsequently, according to this criterion and the decentralized control scheme, a set of Takagi-Sugeno (T-S) fuzzy controllers is synthesized to stabilize the NN linearly interconnected system. Finally, a numerical example with simulations is given to demonstrate the concepts discussed throughout this paper.

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.

Optimal H∞ Fuzzy Control for Nonlinear Interconnected Systems via Genetic Algorithm

2013 ◽  
Vol 459 ◽  
pp. 256-261
Author(s):  
Feng Hsiag Hsiao ◽  
Chien Yu Liu
Keyword(s):  
Genetic Algorithm ◽  
Fuzzy Control ◽  
Direct Method ◽  
Random Search ◽  
Disturbance Attenuation ◽  
Interconnected Systems ◽  
Space Representation ◽  
Multiple Time ◽  
Interconnected System ◽  
Fuzzy Controllers

This paper presents an effective approach for stabilizing nonlinear multiple time-delay (NMTD) interconnected systems via a composite of genetic algorithm (GA) and fuzzy controllers. First, a neural-network (NN) model is employed to approximate each subsystem with multiple time delays. Then, the dynamics of the NN model is converted into a linear differential inclusion (LDI) state-space representation. Next, in terms of Lyapunov's direct method, a delay-dependent stability criterion is derived to guarantee the exponential stability of the NMTD interconnected system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Due to the capability of GA in a random search for global optimization, the lower and upper bounds of the search space can be set so that the GA will seek better feedback gains of fuzzy controllers in order to stabilize more quickly the NMTD interconnected system based on the feedback gains via LMI-based approach. According to the Improved genetic algorithm (IGA), which is demonstrated to have better performance than that of a traditional GA, a robustness design of fuzzy control is synthesized not only to stabilize the NMTD interconnected system but also to achieve optimal H performance by minimizing the disturbance attenuation level.

scholarly journals Robust Control of the Knee Joint Angle of Paraplegic Patients considering Norm-Bounded Uncertainties

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Nilson Moutinho dos Santos ◽  
Ruberlei Gaino ◽  
Márcio Roberto Covacic ◽  
Marcelo Carvalho Minhoto Teixeira ◽  
Aparecido Augusto de Carvalho ◽  
...  
Keyword(s):  
Knee Joint ◽  
State Space ◽  
Control Systems ◽  
Position Control ◽  
Space Representation ◽  
Linear Matrix ◽  
State Space Representation ◽  
The Matrix ◽  
Bounded Uncertainties ◽  
Norm Bounded Uncertainties

A proposal for the knee position control design of paraplegic patients with functional electrical stimulation (FES) using control systems and considering norm-bounded uncertainties is presented. A state-space representation of the knee joint model of the paraplegic patient with its nonlinearity is also demonstrated. The use of linear matrix inequalities (LMIs) in control systems with norm-bounded uncertainties for asymptotic stability is analyzed. The model was simulated in the Matlab environment. The matrixKof state space feedback was obtained through LMIs.

scholarly journals A Novel Approach toℓ2-ℓ∞Filter Design for T-S Fuzzy Systems with Multiple Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Xiaoyu Zhang ◽  
Cheng Gong ◽  
Zhen Zeng
Keyword(s):  
Fuzzy Systems ◽  
Filter Design ◽  
Disturbance Attenuation ◽  
Linear Matrix ◽  
Multiple Time ◽  
Time Varying ◽  
Weighting Matrix ◽  
Novel Approach ◽  
Delay Dependent ◽  
Filtering Problem

This paper investigates theℓ2-ℓ∞filtering problem of T-S fuzzy systems with multiple time-varying delays. First, by the Lyapunov-Krasovskii functional approach and free-weighting matrix method, a delay-dependent sufficient condition onℓ2-ℓ∞-disturbance attenuation is presented, in which both stability and prescribedℓ2-ℓ∞performance are required to be achieved for the filtering-error systems. Then, based on the condition, the full-order and reduced-order delay-dependentℓ2-ℓ∞filter design schemes for T-S fuzzy multiple time-varying delays systems are developed in terms of linear matrix inequality (LMI). Finally, an example is given to illustrate the effectiveness of the result.

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