Relaxed LMI Conditions for Local Stability and Local Stabilization of Continuous-Time Takagi-Sugeno Fuzzy Systems

Inner-Estimating Domains of Attraction for Nonpolynomial Systems With Polynomial Differential Inclusions

In this article, based on polynomial differential inclusions, we propose a heuristic iterative approach for estimating the domains of attraction for nonpolynomial systems. First, we use the fuzzy model to construct a polynomial differential inclusion for the nonpolynomial system, which can be equivalently written as a time-invariant uncertain polynomial system. Then, beginning with an initial inner estimation, we present an iterative approach to enlarge this initial inner estimation by calculating common Lyapunov-like functions. Furthermore, the domains of attraction are estimated by combining this iterative approach with heuristic construction of differential inclusions. In the end, our heuristic iterative approach is implemented with linear semidefinite programming and then tested on some nonpolynomial examples with comparisons to the existing methods in the literature.

Observer-Based Output Feedback MPC for T-S Fuzzy System With Data Loss and Bounded Disturbance

This paper investigates the output feedback model predictive control (OFMPC) for Takagi-Sugeno fuzzy networked control systems with bounded disturbance, where data quantization and data loss occur simultaneously. The quantization error is treated as sector bound uncertainties by using the sector bound approach and the data loss process is modeled as a time-homogeneous Markov chain. Invoking S -procedure and the notion of quadratic boundedness which can specify closed-loop stability for system with disturbance, the state observer is offline designed and the networked output feedback model predictive controller is provided which explicitly considers the satisfaction of input constraints. Two online synthesis algorithms of OFMPC are presented, one parameterizing the infinite horizon control moves into a single feedback law, the other into one free control move followed by the single feedback law based on the state observer. A new formula is introduced to refresh the ellipsoidal bound of estimation error which can guarantee the recursive feasibility of optimization problem. An example is given to demonstrate the effectiveness of the proposed new design techniques.

Reduced-order multiple observer for Takagi-Sugeno systems with unknown inputs

The paper discusses a niche area problem - the design of reduced-order multiple observers which can achieve the finite-time state reconstruction for Takagi-Sugeno multiple models with unknown inputs. The new reduced-order multiple observer obtained in this paper is only the second ever designed, the author of this paper continuing his work started one year ago with the introduction of the reduced-order multiple observer concept. The obtaining of the new reduced-order multiple observer is achieved by combining two classical reduced-order observers for linear time-invariant multivariable systems with unknown inputs and a full-order multiple observer for Takagi-Sugeno systems. The main innovative idea behind the design of the reduced-order multiple observer for Takagi-Sugeno systems described by the multiple models is the split of the multiple model into two subsystems: an unknown-input-free subsystem and an unknown-input-depending subsystem. The unknown-input-free subsystem is brought to the form of a standard multiple model and, in this situation, any algorithm to design full-order multiple observers can be used in the design of reduced-order multiple observers. The steps of the design procedure have been summarized and software implemented; then, the validation of the suggested algorithm has been done for two concrete cases associated to the motion of an aircraft during its landing.

An alternative LMI static output feedback control design for discrete-time nonlinear systems represented by Takagi-Sugeno models

This paper presents a static output feedback controller design for discrete-time nonlinear systems exactly represented by Takagi-Sugeno models. By introducing past states in the control law as well as in the Lyapunov function, more relaxed results are obtained. Different conditions in terms of linear matrix inequalities are provided. The proposed conditions are less demanding than the ones in the literature. This is illustrated via numerical examples.

Local Model Predictive Control for T-S Fuzzy Systems

In this paper, a new linear matrix inequality-based model predictive control (MPC) problem is studied for discrete-time nonlinear systems described as Takagi-Sugeno fuzzy systems. A recent local stability approach is applied to improve the performance of the proposed MPC scheme. At each time k , an optimal state-feedback gain that minimizes an objective function is obtained by solving a semidefinite programming problem. The local stability analysis, the estimation of the domain of attraction, and feasibility of the proposed MPC are proved. Examples are given to demonstrate the advantages of the suggested MPC over existing approaches.

Fault Estimation Observer Design for Discrete-Time Takagi-Sugeno Fuzzy Systems Based on Homogenous Polynomially Parameter-Dependent Lyapunov Functions

This paper investigates the problem of robust fault estimation (FE) observer design for discrete-time Takagi-Sugeno fuzzy systems via homogenous polynomially parameter-dependent Lyapunov functions. First, a novel framework of the fuzzy FE observer is established with the help of a maximum-minimum-priority-based switching mechanism. Then, for every activated switching case, a targeted result is achieved by the aid of exploring an important property of improved homogenous polynomials. Since the helpful information of the underlying system can be duly updated and effectively utilized at every sampled point, the conservatism of previous results is availably reduced. Furthermore, the proposed result is further improved by eliminating those redundant terms of the introduced matrix-valued variables. Simulation results based on a discrete-time nonlinear truck-trailer model are provided to show the advantages of the theoretic result that is developed in this paper.

Cancellation-Based Nonquadratic Controller Design for Nonlinear Systems via Takagi-Sugeno Models

This paper is concerned with nonquadratic conditions for stabilization of continuous-time nonlinear systems via exact Takagi-Sugeno models and generalized fuzzy Lyapunov functions. The approach hereby proposed feedback to the time derivatives of the membership functions through a multi-index control law that cancels out the terms responsible of former a priori local conditions. Thus, a nonquadratic controller design in the form of linear matrix inequalities is achieved; it does not require bounds on the time derivatives nor any extra parameters. The examples included are shown to outperform former approaches.

Control Synthesis of Discrete-Time T-S Fuzzy Systems: Reducing the Conservatism Whilst Alleviating the Computational Burden

The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi-Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix approach in the literature, we aim to design a more efficient slack variable approach under a general framework of homogenous matrix polynomials. Thanks to the introduction of a new extended representation for homogeneous matrix polynomials, related matrices with the same coefficient are collected together into one sole set and thus those redundant terms of the augmented multi-indexed matrix approach can be removed, i.e., the computational burden can be alleviated in this paper. More importantly, due to the fact that more useful information is involved into control design, the conservatism of the proposed approach as well is less than the counterpart of the augmented multi-indexed matrix approach. Finally, numerical experiments are given to show the effectiveness of the proposed approach.

Novel Fuzzy Modeling and Synchronization of Chaotic Systems With Multinonlinear Terms by Advanced Ge-Li Fuzzy Model

Ge and Li proposed an alternative strategy to model and synchronize two totally different nonlinear systems in the end of 2011, which provided a new version for fuzzy modeling and has been applied to several fields to simplify their modeling works and solve the mismatch problems [1]-[17]. However, the proposed model limits the number of nonlinear terms in each equation so that this model could not be used in all kinds of nonlinear dynamic systems. As a result, in this paper, a more efficient and comprehensive advanced-Ge-Li fuzzy model is given to further release the limitation and improve the effectiveness of the original one. The novel fuzzy model can be applied to all kinds of complex nonlinear systems--this is the universal strategy and only m x 2 fuzzy rules as well as two linear subsystems are needed to simulate nonlinear behaviors (m is the number of states in a nonlinear dynamic system), whatever the nonlinear terms are copious or complicated. Further, the fuzzy synchronization of two nonlinear dynamic systems with totally distinct structures can be achieved via only two sets of control gains designed through the novel fuzzy model as well as its corresponding fuzzy synchronization scheme. Two complicated dynamic systems are designed to be the illustrations, Mathieu-Van der pol system with uncertainties and Quantum-cellular neural networks nano system with uncertainties, to show the effectiveness and feasibility of the novel fuzzy model.

Robust Frequency-Domain Constrained Feedback Design via a Two-Stage Heuristic Approach

Based on a two-stage heuristic method, this paper is concerned with the design of robust feedback controllers with restricted frequency-domain specifications (RFDSs) for uncertain linear discrete-time systems. Polytopic uncertainties are assumed to enter all the system matrices, while RFDSs are motivated by the fact that practical design specifications are often described in restricted finite frequency ranges. Dilated multipliers are first introduced to relax the generalized Kalman-Yakubovich-Popov lemma for output feedback controller synthesis and robust performance analysis. Then a two-stage approach to output feedback controller synthesis is proposed: at the first stage, a robust full-information (FI) controller is designed, which is used to construct a required output feedback controller at the second stage. To improve the solvability of the synthesis method, heuristic iterative algorithms are further formulated for exploring the feedback gain and optimizing the initial FI controller at the individual stage. The effectiveness of the proposed design method is finally demonstrated by the application to active control of suspension systems.

Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems

This paper investigates the problems of universal fuzzy model and universal fuzzy controller for discrete-time nonaffine nonlinear systems (NNSs). It is shown that a kind of generalized T-S fuzzy model is the universal fuzzy model for discrete-time NNSs satisfying a sufficient condition. The results on universal fuzzy controllers are presented for two classes of discrete-time stabilizable NNSs. Constructive procedures are provided to construct the model reference fuzzy controllers. The simulation example of an inverted pendulum is presented to illustrate the effectiveness and advantages of the proposed method. These results significantly extend the approach for potential applications in solving complex engineering problems.

On fuzzy sampled-data control of chaotic systems via a time-dependent Lyapunov functional approach

In this paper, a novel approach to fuzzy sampled-data control of chaotic systems is presented by using a time-dependent Lyapunov functional. The advantage of the new method is that the Lyapunov functional is continuous at sampling times but not necessarily positive definite inside the sampling intervals. Compared with the existing works, the constructed Lyapunov functional makes full use of the information on the piecewise constant input and the actual sampling pattern. In terms of a new parameterized linear matrix inequality (LMI) technique, a less conservative stabilization condition is derived to guarantee the exponential stability for the closed-loop fuzzy sampled-data system. By solving a set of LMIs, the fuzzy sampled-data controller can be easily obtained. Finally, the chaotic Lorenz system and Rössler's system are employed to illustrate the feasibility and effectiveness of the proposed method.