Fuzzy dynamic output‐feedback control of non‐linear networked discrete‐time system with missing measurements

In this article, finite-time control is investigated for multiple time-delayed large-scale nonlinear systems against state and input constraints. There are multiple time-varying delays, intermittent actuator faults, and intermittent sensor faults in this model. Takagi–Sugeno fuzzy model is used to describe the nonlinear system. There are few tries to studying finite-time control for large-scale nonlinear systems. First, a dynamic output feedback controller is designed in this article to make the system finite-time bounded. Then, an augmented closed-loop model is constructed. Sufficient conditions of finite-time control are given by the fuzzy Lyapunov function. Finally, the feasibility of the approach is verified by two simulation examples.

This paper studies the problem of adaptive eventtriggered dynamic output feedback fuzzy control for nonlinear networked control systems. Two crucial factors, packet dropouts and actuator failure, are taken into consideration simultaneously. Takagi-Sugeno fuzzy model is introduced to describe considered systems. The Bernoulli random distribution process is employed to depict the phenomenon of data missing. The actuator failure model is adopted to depict actuator failure. An innovative adaptive event-triggered strategy is built to save computational resource. In the light of Lyapunov stability theory, a fuzzy dynamic output feedback controller is designed to guarantee the stochastic stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for considered systems. Finally, simulation results are provided to demonstrate the usefulness of the proposed control strategy.

This paper addresses stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with parametric uncertainties via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. First, the Takagi-Sugeno (T-S) fuzzy model with parametric uncertainties is used as the model for the uncertain nonlinear system. Based on the fuzzy Lyapunov function approach and a parallel distributed compensation (PDC) scheme, we give stabilization conditions for closed-loop fuzzy systems with parametric uncertainties. Second, all the conditions are formulated in the format of linear matrix inequalities (LMIs) and contain upper bounds of the time derivative of premise membership functions as LMI variables. Finally, the T-S fuzzy model of the chaotic Lorenz system, which has complex nonlinearity, is developed as a test bed. A numerical example of the chaotic Lorenz system is given to illustrate the utility of the fuzzy Lyapunov function approach.

This paper aims to study the robust nonfragile H ∞ controller design problem for a class of uncertain discrete-time nonlinear singular systems. A Takagi-Sugeno (T-S) fuzzy singular model with norm-bounded uncertainties is employed to represent a nonlinear plant. Basing on observers for the fuzzy model, we can construct a fuzzy controller with uncertainties existing in the implementation process. A augmented fuzzy closed-loop system can be obtained by the descriptor systems approach, which can avoid the appearance of coupling terms between matrices of the system model and the controller. Attention of the paper lies in deriving the design conditions of the observer-based controller by choosing a fixed common and fuzzy Lyapunov function, respectively, such that the admissibility and the prescript H ∞ performance of the augmented closed-loop system can be guaranteed. Finally, the simulation results show the validity of the proposed methods.

Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions

This paper investigates the problem of event-triggered dynamic output feedback control for networked Takagi-Sugeno (T-S) fuzzy systems with asynchronous premise variables. Our attention is focused on the design of an event-triggered fuzzy dynamic output feedback controller that guarantees that the closed-loop system is asymptotically stable. First, with consideration of the limited bandwidth and restricted network resource, an event-triggered communication scheme is proposed to save the limited network resource. Second, different from the existing results in the literature, a fuzzy dynamic output feedback controller with asynchronous premise variables is constructed such that the premise membership functions are not necessarily the same as the networked T-S fuzzy systems. Then, by using the Wirtinger inequality and some slack matrices, a less conservative stability and stabilization conditions for the existence of fuzzy dynamic output feedback controller are derived in the form of linear matrix inequalities, which can be solved by the standard MATLAB toolbox. Finally, an example is given to demonstrate the effectiveness of the designed event-triggered fuzzy dynamic output feedback controller.

In this paper, the issue of human behavior learning (HBL) is addressed for a class of nonlinear human-in-the-loop (HiTL) systems where the human operator is viewed as a nonlinear optimal controller. Owing to its outstanding interpretability and strong nonlinear representation capability, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear HiTL control system and approximate the unknown human control law based on the parallel distributed compensation (PDC) scheme. A quadratic-like cost function with fuzzy weighting matrices is built to depict the human behavior, which conforms to human thinking and is unknown to the machine. The aim of the HBL is to retrieve the fuzzy weighting matrices such that the human control law will be optimal in the sense of minimizing the retrieved cost function. In the proposed HBL scheme, the state-dependent Riccati equation (SDRE) based nonlinear optimal control technique plays an important role, which has a similar structure to the linear quadratic regulator (LQR) theory and thus is of low computational complexity. With the help of the PDC based fuzzy approximator for the unknown human control law, a two-step procedure is proposed for the HBL. First, a filter-based adaptive law is developed to learn the gain matrices of the fuzzy approximator using the system state data only. The convergence analysis of the adaptive estimator is also given. Then, a semidefinite programming (SDP) problem with the quadratic objective function can be set up for determining the fuzzy weighting matrices of the cost function. The simulation study on a steering control system of the intelligent vehicle is given to show the effectiveness and applicability of the developed approach.

This paper deals with the problem of output feedback control for a class of discrete-time nonlinear quadratic systems with quantization effects and missing measurements. The measured output of system is quantized by a logarithmic quantizer. Moreover, the missing measurements are modeled by introducing a diagonal matrix composed of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval [0 1]. In this paper, the output feedback controller design method, which guarantees the zero equilibrium point of the closed-loop system is stochastic stable, is provided. By using LMI technique, the sufficient condition is derived for computing the desired controller gain matrix and observer gain matrix of the system. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.

Takagi-Sugeno (T-S) fuzzy model is a system described by a set of fuzzy if-then rules which give local linear representations of the underlying nonlinear system. Usually, a fuzzy control law is constructed by a set of controllers for each local linear representation to carry out the control of a T-S fuzzy system. While, simultaneous control addresses the stability and performance of multiple plants under a single feedback controller. In this paper, simultaneous linear control for nonlinear uncertain systems described by general T-S fuzzy model is considered. A procedure for simultaneous control of T-S fuzzy systems with parametric uncertainties is presented, by which robust reliability method is adopted to deal with uncertainties. Simultaneously linear controller design for an uncertain T-S fuzzy system is carried out by solving a problem of robust reliability based optimization, in which, both the robustness with respect to uncertainties and the control cost can be taken into account simultaneously. It is demonstrated by numerical simulation of the chaotic Lorenz system control that the presented method is effective and feasible.

Tins paper is concerned with a class of nonlinear networked control systems with network-induced delay shorter than one sample period. Based on the assumptions that the actuator node is time-driven and the controller node is event-driven, a Takagi-Sugeno (T-S) fuzzy model is used to approximate the nonlinear networked systems with delay. By means of Lyapunov functions, a method for designing a fuzzy state feedback controller to satisfy the prescribed H/sub /spl infin// performance index is proposed. The results are presented in terms of linear matrix inequalities (LMIs) which can be solved by LMI toolbox in Matlab 6.5. Finally, a numerical example is given to validate the proposed method.

In this paper, optimal fuzzy observer is developed for discrete time nonlinear stochastic system based on Takagi-Sugeno (TS) fuzzy model. We design a optimal fuzzy observer using the mathematical duality and by extending the nonlinear Bayesian estimation using Gaussian sum approach to the TS fuzzy model.

This paper reviews the development of fuzzy systems and the problem of time delay control in nonlinear systems. Based on this review, a fuzzy Lyapunov method defined in fuzzy blending quadratic Lyapunov functions is proposed from which to derive stability conditions. In the controller procedure, a parallel distributed compensation (PDC) scheme is utilized to construct a global fuzzy logic controller (FLC) by blending all linear local state feedback controllers. Furthermore, the multiple time-delay interconnected systems are considered in the nonlinear fuzzy systems. Key words: Interconnected systems, fuzzy Lyapunov method, linear matrix inequality.

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In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS) was proposed by Okubo (1985). In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k))║≤α + β║v (k)║^γ , where α≥0, β≥0, 0≤γ≤1. When 0≤γ<1. It is easy to extend the method to discrete time systems. But in the case γ = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.

The H∞ dynamic output feedback control problem for a class of discrete‐time switched time‐delay systems under asynchronous switching is investigated in this paper. Sensor nonlinearity and missing measurements are considered when collecting output knowledge of the system. Firstly, when there exists asynchronous switching between the switching modes and the candidate controllers, new results on the regional stability and l2 gain analysis for the underlying system are given by allowing the Lyapunov‐like function (LLF) to increase with a random probability. Then, a mean square stabilizing output feedback controller and a switching law subject to average dwell time (ADT) are obtained with a given disturbance attenuation level. Moreover, the mean square domain of attraction could be estimated by a convex combination of a set of ellipsoids, the number of which depends on the number of switching modes. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.