Feng-Hsiag Hsiao

T-S fuzzy controllers for nonlinear interconnected systems with multiple time delays

This paper investigates the effectiveness of a passive tuned mass damper (TMD) and fuzzy controller in reducing the structural responses subject to the external force. In general, TMD is good for linear systems. We proposed here an approach of Takagi-Sugeno (T-S) fuzzy controller to deal with the nonlinear system. To overcome the effect of modeling error between nonlinear multiple time-delay systems and T-S fuzzy models, a robustness design of fuzzy control via model-based approach is proposed in this paper. A stability criterion in terms of Lyapunovs direct method is derived to guarantee the stability of nonlinear multiple time-delay interconnected systems. Based on the decentralized control scheme and this criterion, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay interconnected system and the H/sup /spl infin// control performance is achieved at the same time. Finally, the proposed methodology is illustrated by an example of a nonlinear TMD system.

Robust stabilization of nonlinear multiple time-delay large-scale systems via decentralized fuzzy control

To overcome the effect of modeling errors between nonlinear multiple time-delay subsystems and Takagi-Sugeno (T-S) fuzzy models with multiple time delays, a robustness design of fuzzy control is proposed in This work. In terms of Lyapunovs direct method, a delay-dependent stability criterion is hence derived to guarantee the asymptotic stability of nonlinear multiple time-delay large-scale systems. Based on this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear multiple time-delay large-scale system. Finally, a numerical example with simulations is given to demonstrate the concepts discussed throughout This work.

Stability analysis of T-S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi-Sugeno (T-S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunovs direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.

Fuzzy controllers for nonlinear interconnected tmd systems with external force

Abstract This paper investigates the effectiveness of a passive tuned mass damper (TMD) and active fuzzy controllers in reducing structural responses under external forces. In general, TMD is good for linear systems. We propose here a fuzzy controller to deal with nonlinear systems. For the fuzzy controller, a stability criterion in terms of Lyapunovs direct method is derived to guarantee the stability of interconnected TMD systems. Based on decentralized control and this criterion, a set of model‐based fuzzy controllers are then synthesized via the technique of parallel distributed compensation (PDC) to stabilize the nonlinear interconnected TMD system. Finally, an example is given to illustrate the concepts discussed throughout this paper.

APPLICATION AND ROBUSTNESS DESIGN OF FUZZY CONTROLLER FOR RESONANT AND CHAOTIC SYSTEMS WITH EXTERNAL DISTURBANCE

A robustness design of fuzzy control via model-based approach is proposed in this paper to overcome the effect of approximation error between nonlinear system and Takagi-Sugeno (T-S) fuzzy model. T-S fuzz model is used to model the resonant and chaotic systems and the parallel distributed compensation (PDC) is employed to determine structures of fuzzy controllers. Linear matrix inequality (LMI) based design problems are utilized to find common definite matrices P and feedback gains K satisfying stability conditions derived in terms of Lyapunov direct method. Finally, the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic and resonant systems.

Stability analysis of fuzzy large-scale systems

This paper is concerned with the stability problem of fuzzy large-scale systems. Each of them consists of J interconnected subsystems which are represented by Takagi-Sugeno fuzzy models. A stability criterion in terms of Lyapunovs direct method is proposed to guarantee the asymptotic stability of fuzzy large-scale systems. Finally, an example is given to demonstrate the results.

Robust Kalman Filter Synthesis for Uncertain Multiple Time-Delay Stochastic Systems

The problem of robust Kalman filter synthesis is considered in this present study for discrete multiple time-delay stochastic systems with parametric and noise uncertainties. A discrete multiple time-delay uncertain stochastic system can be transformed into another uncertain stochastic system with no delay by properly defining state variables. Minimax theory and Bellman-Gronwall lemma are employed on the basis of the upper norm-bounds of parametric uncertainties and noise uncertainties. A robust criterion can consequently be derived which guarantees the asymptotic stability of the uncertain stochastic system. Designed procedures are finally elaborated upon with an illustrative example.

Robustness Design of Fuzzy Control for Nonlinear Multiple Time-Delay Large-Scale Systems via Neural-Network-Based Approach

The stabilization problem is considered in this correspondence for a nonlinear multiple time-delay large-scale system. First, the neural-network (NN) model is employed to approximate each subsystem. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of each NN model. According to the LDI state-space representation, a robustness design of fuzzy control is proposed to overcome the effect of modeling errors between subsystems and NN models. Next, in terms of Lyapunovs direct method, a delay-dependent stability criterion is derived to guarantee the asymptotic stability of nonlinear multiple time-delay large-scale systems. Finally, based on this criterion and the decentralized control scheme, a set of fuzzy controllers is synthesized to stabilize the nonlinear multiple time-delay large-scale system.

Fuzzy Control for Nonlinear Systems via Neural-Network-Based Approach

The stabilization problem is considered in this study for a nonlinear system. It is shown that the stability analysis of nonlinear systems can be reduced into linear matrix inequality (LMI) problems. First, the neural-network (NN) model is employed to approximate a nonlinear system via the backpropagation algorithm. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. In terms of Lyapunovs direct method, a sufficient condition is provided to guarantee the stability of nonlinear systems. Based on this criterion, a model-based fuzzy controller is then designed to stabilize the nonlinear system and the H∞ control performance is achieved at the same time. Finally, two examples with numerical simulations are given to illustrate the control methodology.

Stabilization of Nonlinear Singularly Perturbed Multiple Time-Delay Systems by Dither

Dither is a high frequency signal injected into nonlinear systems for the purpose of improving their performance. Stability of the dithered nonlinear singularly perturbed multiple time-delay reduced-order model and by using the relaxed method to analyze stability of the dithered reduced-order model when the frequency of dither is sufficient high. Moreover, if the singular perturbation parameter is sufficiently small, then stability of the relaxed model would imply stability in finite time of the dithered nonlinear singularly perturbed multiple time-delay system.