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

Abstract

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.

Stubborn state estimation for nonlinear distributed parameter systems subject to measurement outliers

“…Different sensor deployment may generate different measurement models. For example, in References 25,26, sensors have been deployed within the whole space domain which leads to the continuous or piecewise measurement in space. In References 27,28, sensors have been deployed on the boundary of space domain and a boundary measurement model has been provided.…”

Synthesis of a Dynamical Output ${H}_{\infty}$ Controller for the Fuzzy Input-Output Model

“…On the other hand, the classical linear model can be regarded as a special kind of T-S fuzzy model with all the local linear models chosen to be the same. Within the framework of the T-S fuzzy model, numerous fuzzy control issues, such as stability analysis [8]- [12], systematic controller design [12]- [16], robustness analysis [17]- [20], have been extensively investigated. In effect, the T-S fuzzy system based research still remains one of the hot topics in the field of nonlinear control [21]- [28].…”