Fuzzy Boundary Control Design for a Class of Nonlinear Parabolic Distributed Parameter Systems

Wu, Huai‐Ning; Wang, Junwei; Li, Han-Xiong

doi:10.1109/tfuzz.2013.2269698

Cited by 160 publications

(70 citation statements)

References 43 publications

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“…with the initial values Finally, Figures 1-4 show the error dynamical system of the controlled delayed PDSs given by (33), which is globally exponentially stabilized. Network (33) is globally exponentially synchronized, which supports the proposed methods.…”

Section: Illustrative Examplementioning

confidence: 99%

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Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

et al. 2017

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This paper is concerned with the exponential synchronization for a class of -coupled complex partial differential systems (PDSs) with time-varying delay. The synchronization error dynamic of the PDSs is defined in the -dimensional spatial domain. To achieve synchronization, we added a linear feedback controller. A sufficient condition is derived to ensure the exponential synchronization of the proposed networks using the Lyapunov-Krasovskii stability approach and matrix inequality technology. The proposed system has broad applications. Two example applications are presented in the final section of this paper to verify the proposed theoretical result.

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Section: Illustrative Examplementioning

confidence: 99%

“…These phenomena are generally modeled in partial differential systems (PDSs). Therefore, increasing concerns have risen on the study of PDSs [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]. A significant part of research is based on reaction-diffusion neural network models, such as [25,[34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

et al. 2017

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“…In [43], the utilization of NN control is presented to efficiently compensate for the modeling errors for a flexible multilink system. For control of the distributed parameter system, adaptive boundary control [44], [45] and fuzzy boundary control [46]- [48] are also used and have obtained an effective performance. Fuzzy logic control is a powerful method for handling the system uncertainties [49]- [59].…”

Section: Introductionmentioning

confidence: 99%

Neural Network Control of a Flexible Robotic Manipulator Using the Lumped Spring-Mass Model

Sun

Hong

2017

IEEE Trans. Syst. Man Cybern, Syst.

276

109

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Adaptive neural networks (NNs) are employed for control design to suppress vibrations of a flexible robotic manipulator. To improve the accuracy in describing the elastic deflection of the flexible manipulator, the system is modeled via the lumped spring-mass approach. Full-state feedback control as well as output feedback control are proposed separately. Aiming at achieving the control objective, uniform ultimate boundedness of the closed-loop system is ensured. Numerical simulations for the lumped model of the flexible robotic system are carried out to verify the performance of the NN control. Finally, the experiments are given to further validate the feasibility of the proposed NN controllers on the Quanser platform.

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“…Similarly, the distributed fuzzy proportional-spatial derivative state feedback control design was proposed [36] to exponentially stabilize the 1-dimensional nonlinear parabolic PDS with the Neumann boundary condition via a recursive LMI algorithm. In addition, an optimal control design [37] and a fuzzy boundary control design [38] for 1-dimensional parabolic PDSs can be found. In relation to the stochastic case, the robust H ∞ filter design was realized for the 2-dimensional nonlinear stochastic PDS with the Dirichlet boundary condition through the finite difference method [39].…”

Section: Introductionmentioning

confidence: 99%

Robust Fuzzy $H_{\infty }$ Estimator-Based Stabilization Design for Nonlinear Parabolic Partial Differential Systems With Different Boundary Conditions

Chen

2016

IEEE Trans. Fuzzy Syst.

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In this paper, a new robust fuzzy H∞ estimatorbased stabilization design for a class of N -dimensional nonlinear parabolic partial differential systems (PDSs) with either the Dirichlet or Neumann boundary conditions is proposed. First, an N -dimensional parabolic Takagi-Sugeno (T-S) fuzzy PDS is used to approximate the N -dimensional nonlinear parabolic PDS via the knowledge-based T-S fuzzy system technique. Second, based on the N -dimensional parabolic T-S fuzzy PDS, a robust fuzzy estimator-based controller is employed not only to stabilize the PDS, but also to attenuate the effects of external and measurement noises on the PDS in the spatio-temporal domain below a prescribed attenuation level. The robust fuzzy H∞ estimator-based stabilization design problem can be formulated as a diffusion matrix inequality (DMI) problem. To solve DMIs via the traditional algebraic matrix techniques, we utilize the divergence theorem and the Poincaré inequality to transform the DMIs into bilinear matrix inequalities (BMIs) with a Poincaré constant defined according to the spatial domain of the corresponding PDS. Finally, the robust fuzzy H∞ estimator-based stabilization design problem can be effectively solved by a set of linear matrix inequalities (LMIs) instead of the BMIs with the help of the proposed decoupled method. Additionally, an optimal robust fuzzy H∞ estimator-based stabilization design can be realized via minimizing the noise attenuation level. A simulation example is provided to illustrate the design procedure and verify the performance of the proposed optimal design.Index Terms-Fuzzy estimator-based control design; Ndimensional parabolic fuzzy partial differential system; Ndimensional parabolic nonlinear partial differential system; Robust fuzzy H∞ stabilization; Spatio-temporal random noise.

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Fuzzy Boundary Control Design for a Class of Nonlinear Parabolic Distributed Parameter Systems

Cited by 160 publications

References 43 publications

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

Exponential Synchronization of a Class of N-Coupled Complex Partial Differential Systems with Time-Varying Delay

Neural Network Control of a Flexible Robotic Manipulator Using the Lumped Spring-Mass Model

Robust Fuzzy $H_{\infty }$ Estimator-Based Stabilization Design for Nonlinear Parabolic Partial Differential Systems With Different Boundary Conditions

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