H∞ Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model With Unknown Premise Variables via Nonquadratic Lyapunov Function

Membership-function-dependent dynamic output feedback H∞ controller design of continuous-time T-S fuzzy systems via non-quadratic Lyapunov function

The dynamic output feedback H_∞ (DOFH) control under imperfect premise matching (IPM) is studied in this paper for continuous-time Takagi-Sugeno (T-S) fuzzy systems. Different from the existing results, the DOFH switching controller, which enjoys membership functions (MFs) distinct from the fuzzy systems, is designed. First, the non-quadratic Lyapunov function (NQLF) based on MFs is utilized to design the controller. The time derivatives of MFs are addressed by the switching strategy. Second, a method based on linear matrix inequality (LMI) is given to make the controller gains solvable. Third, an improved method is developed to incorporate the more boundary information of MFs into the stability conditions to reduce conservatism. Finally, three examples are used to certify the advantage of the approach.

A novel polynomial membership functions based control method for T-S fuzzy systems

To solve the state feedback stabilization problem for a class of T-S fuzzy systems, a new stability synthesis method is raised to further relax the conservatism existing in the analysis process. First, a series of nonlinear polynomials are used to approximate the system membership functions. And satisfied approximation results can be obtained. Then a polynomials transformation method is raised to change the polynomial membership functions into linear form. This method can facilitate the synthesis process and achieve better approximation precision. Therefore, by a membership function involving stability analysis approach, linear matrix inequality form stability conditions are given. Finally, by presenting and analyzing a numerical and a practical examples, the conservatism reduction effects of the proposed methods are verified.

Membership Function Derivatives Transformation Approach for Stability Analysis and Stabilization Control of T-S Fuzzy Systems

In this text, a membership function derivatives (MFDs) extrema-based method is proposed to relax the conservatism both in stability analysis and synthesis problems of Takagi-Sugeno fuzzy systems. By the designed algorithm, the nonpositiveness of the MFDs extrema is conquered. For an open-loop system, based on certain information of the MFs and derivatives, a series of convex stability conditions is derived. Then, an extremum-based construction method is adopted to involve the MF information. For the shape of MFDs, a coordinate transformation algorithm is proposed to involve it in the stability conditions to achieve local stable effects. For a state-feedback control system, conditions guaranteeing the stability and robustness are listed. Finally, simulation examples and comparisons are carried out to clarify the conservatism reduction results of the raised method.

Smooth Compositions Made Stabilization of Fuzzy Systems: Easy and More Robust

Smooth fuzzy systems are the new structures of the fuzzy system which have recently taken attention for their capacity in system modeling. Hence, this article studies the stability of smooth fuzzy control systems and develops the sufficient conditions of the parameters for the stable closed-loop performance of the system. A major advantage of the presented conditions is that they do not call for a common Lyapunov function and therefore, no LMI is required to be solved to guarantee the stability of the fuzzy model. Besides, although they are the type-1 fuzzy model in nature, however, they show the high level of robustness to the noises and parametric uncertainties, which is comparable to the type-2 fuzzy models. Several comparative simulations demonstrate the capacity of the fuzzy models with the smooth compositions rather than the classical fuzzy models with the min-max or product-sum compositions.

Observer-Based Finite-Time H∞ Control of the Blood Gases System in Extracorporeal Circulation via the T-S Fuzzy Model

This paper studies the problem of the finite-time H∞ control of the blood gases system, presented as a T-S fuzzy model with bounded disturbance during extracorporeal circulation. The aim was to design an observer-based fuzzy controller to ensure that the closed-loop system was finite-time bounded with the H∞ performance. Firstly, different from the existing results, the T-S fuzzy model of a blood gas control system was developed and a new method was given to process the time derivatives of the membership functions. Secondly, based on the fuzzy Lyapunov function, sufficient conditions for the H∞ finite-time boundedness of the system were obtained by using Finsler’s lemma and matrix decoupling techniques. Simulation results are provided to demonstrate the effectiveness of the proposed methodology.

Further Study on Observer Design for Continuous-Time Takagi-Sugeno Fuzzy Model With Unknown Premise Variables via Average Dwell Time

This article further studies the problem of observer design for the continuous-time Takagi-Sugeno (T-S) fuzzy system with unmeasurable premise variables. A membership function-dependent Lyapunov function is designed to obtain the observer-based controller. Different from the existing results, a switching method is proposed to deal with the time derivative of membership functions. Several problems such as, too many parameters, and the small local stabilization region in the existing papers are solved by applying the switching method. In addition, two algorithms are designed to obtain the controller gains and observer gains. In the end, two examples are provided to demonstrate the effectiveness of the proposed approach.

A Review of Convex Approaches for Control, Observation and Safety of Linear Parameter Varying and Takagi-Sugeno Systems

This paper provides a review about the concept of convex systems based on Takagi-Sugeno, linear parameter varying (LPV) and quasi-LPV modeling. These paradigms are capable of hiding the nonlinearities by means of an equivalent description which uses a set of linear models interpolated by appropriately defined weighing functions. Convex systems have become very popular since they allow applying extended linear techniques based on linear matrix inequalities (LMIs) to complex nonlinear systems. This survey aims at providing the reader with a significant overview of the existing LMI-based techniques for convex systems in the fields of control, observation and safety. Firstly, a detailed review of stability, feedback, tracking and model predictive control (MPC) convex controllers is considered. Secondly, the problem of state estimation is addressed through the design of proportional, proportional-integral, unknown input and descriptor observers. Finally, safety of convex systems is discussed by describing popular techniques for fault diagnosis and fault tolerant control (FTC).

Dynamic Boundary Fuzzy Control Design of Semilinear Parabolic PDE Systems With Spatially Noncollocated Discrete Observation

The problem of dynamic boundary fuzzy control design is investigated in this paper for nonlinear parabolic partial differential equation (PDE) systems with spatially noncollocated discrete observation. Two cases of noncollocated discrete observation in space (i.e., pointwise observation in space and local piecewise uniform observation in space) are considered, respectively. The spatially noncollocated discrete observation makes the control design very difficult. Such design difficulty can be surmounted by an observer-based feedback control technique. It is assumed that the semilinear PDEs are accurately represented by a Takagi-Sugeno fuzzy PDE model. On the basis of the obtained fuzzy PDE model, a fuzzy Luenberger-type PDE state observer with above two cases of noncollocated discrete observation in space is first proposed for exponential estimation of the PDE system state. An observer-based dynamic fuzzy controller is then constructed such that the resulting closed-loop system is exponentially stable. Sufficient conditions on existence of such fuzzy controller are developed by Lyapunov technique with variations of vector-valued Poincaré-Wirtinger inequality, and presented in terms of linear matrix inequalities. Finally, extensive numerical simulation results of two examples are provided to support the proposed design method.

Robust Fault Estimation Design for Discrete-Time Nonlinear Systems via A Modified Fuzzy Fault Estimation Observer

The paper provides relaxed designs of fault estimation observer for nonlinear dynamical plants in the Takagi-Sugeno form. Compared with previous theoretical achievements, a modified version of fuzzy fault estimation observer is implemented with the aid of the so-called maximum-priority-based switching law. Given each activated switching status, the appropriate group of designed matrices can be provided so as to explore certain key properties of the considered plants by means of introducing a set of matrix-valued variables. Owing to the reason that more abundant information of the considered plants can be updated in due course and effectively exploited for each time instant, the conservatism of the obtained result is less than previous theoretical achievements and thus the main defect of those existing methods can be overcome to some extent in practice. Finally, comparative simulation studies on the classical nonlinear truck-trailer model are given to certify the benefits of the theoretic achievement which is obtained in our study.

Adaptive Fuzzy Output-Constrained Fault-Tolerant Control of Nonlinear Stochastic Large-Scale Systems With Actuator Faults

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example.