Discrete-time Fuzzy Research Articles

Asynchronous Dissipative Control of Discrete-Time Fuzzy Markov Jump Systems With Dynamic State and Input Quantization

A numerically tractable two-step approach based on backtrack and optimization searches is proposed for asynchronous quantized dissipative control of discrete-time fuzzy Markov jump systems (DFMJSs) under the networked control framework. The asynchrony of modes between the plant and controller is described by a hidden Markov model. Both dynamic state and input quantization are considered. The dynamic zooming factors of the quantizers are designed as piecewise functions with respect to their arguments to avoid division by zero. A fuzzy asynchronous quantized controller is devised to make sure that the closed-loop system is stochastically stable and strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$(\mathcal {Q},\mathcal {S},\mathcal {R})$</tex-math></inline-formula> - dissipative via using a quadratic Lyapunov function and equivalent matrix transformations. Then, the iterative two-step approach is used to determine the optimal dissipativity level and the corresponding control gain and quantization parameters. Analysis and control synthesis for DFMJSs without quantization are also presented, covering some previous results as special cases. Finally, a single-link robot arm system and another numerical example are utilized to validate the present asynchronous dissipative control approaches for the quantization and non-quantization cases, respectively.

Prescribed Performance Discrete-Time Fuzzy Carrier Landing Control of UAV Based on Disturbance Observer

Prescribed Performance Discrete-Time Fuzzy Carrier Landing Control of UAV Based on Disturbance Observer

Quasi-uniform synchronization of fractional fuzzy discrete-time delayed neural networks via delayed feedback control design

This paper is concerned with the quasi-uniform synchronization (Q-US) issues of discrete fractional fuzzy neural networks (DFFNNs) with time delays. Firstly, we analyze the neural network systems with fuzzy time delays in discrete cases, complementing the neglected factors in the current literatures. Secondly, we use discrete fractional calculus including discrete Hölder inequality, discrete Gronwall inequality, and the discrete Lyapunov functional method to enrich the discrete system analysis. In addition, to acquire the Q-US, the designed delay feedback controller has the advantage of handling complex time delays to promote the response of the system. Moreover, the obtained results presented as direct linear matrix inequalities are efficiently verified by the simulation example.

Finite-Time Event-Triggered Stabilization for Discrete-Time Fuzzy Markov Jump Singularly Perturbed Systems.

The finite-time event-triggered stabilization is studied for a class of discrete-time nonlinear Markov jump singularly perturbed models with partially unknown transition probabilities (TPs). T-S fuzzy strategy is adopted to characterize the related nonlinear Markov jump singularly perturbed models. The control objective is to make sure that the system states remain within a bounded domain during a fixed-time interval. First, a mode-dependent event-triggered scheme is constructed to reduce the communication burden and save the network bandwidth. On that basis, by using a new Lyapunov function, a developed finite-time stability criterion is derived for the corresponding system to avoid an ill-conditioned issue due to a small singular perturbation parameter. Moreover, the mode-dependent fuzzy controller gain and the event-triggered parameter are co-designed under the framework of partially unknown TPs. Finally, the feasibility of the main results is provided to verify the finite-time event-triggered control strategy.

Multi-Instant Observer Design of Discrete-Time Fuzzy Systems via An Enhanced Gain-Scheduling Mechanism.

This article is concerned with developing a featured multi-instant Luenberger-like observer of discrete-time Takagi-Sugeno fuzzy systems with unmeasurable state variables, that is, not only to reduce the conservatism but also (at the same time) to alleviate the computational complexity over the recent approach reported in the literature. Contrary to previous approaches, an enhanced gain-scheduling mechanism is proposed for constructing much abundant working modes by online evaluating the updated variation information of normalized fuzzy weighting functions across two adjacent sampling instants and, thus, a different group of observer gain matrices with less conservatism is designed in order to employ the exclusive features for each working mode. Moreover, all the redundant terms containing both surplus and unknown system information are discriminated and removed in this study and, thus, the required computational complexity is reduced to a certain extent than the counterpart one. Finally, numerical examples are provided to illustrate the superiority of the developed approach.

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

Global Exponential Stability and Synchronization of Discrete-Time Fuzzy Bidirectional Associative Memory Neural Networks via Mittag-Leffler Difference Approach

A Mathematical Model of Susceptible Diabetes Complication (SDC) Model in Discrete Time Fuzzy and Crisp Environment

In this study, we examined the mathematical model of the discrete-time equation system with susceptible diabetes complication (SDC), which is known to be caused by environmental and genetic factors in a fuzzy environment. From the diabetes complication (DC) model, the susceptible diabetes complication (SDC) model is being developed. It was obtained using definitions of how the behavior of this model changes in a fuzzy environment. A nonlinear differential equation system transforms the sensitive diabetes complication (SDC) model into a discrete time equation system. Stability analysis of the model with jury criterion was examined. In addition, numerical solutions and graphics of the analysis of the discrete model in fuzzy environment are obtained by using the MATLAB package program.

LMI-Based Robust Fuzzy Model Predictive Control of Discrete-Time Fuzzy Takagi-Sugeno Large-Scale Systems Based on Hierarchical Optimization and H∞ Performance

This paper studies robust fuzzy model predictive control of discrete-time fuzzy Takagi-Sugeno large-scale systems based on hierarchical optimization and H_[Formula: see text] Performance. The considered system in this paper is a large-scale system. So, the Takagi-Sugeno (T-S) fuzzy approach which uses nonlinear local models is applied to estimate the nonlinear system to reduce the burden of modeling. The model predictive control (MPC) is a practical application that is useful for all systems but the problem is the online computational cost. For large-scale systems, this problem is the online computational burden. Besides, it leads to conservative or even no solution. By the proposed method, more relaxed solutions are achieved. First, the T-S system with nonlinear local models is adopted. Second, the hierarchical optimization scheme is considered for the optimization part of the MPC. Third, by inspiring the [Formula: see text] performance, uncertainties and disturbances that are appeared are reduced. Moreover, the linear matrix inequalities (LMIs) are used to solve the proposed method that the computational burden significantly is reduced at the same time. Simulation results are finally presented to show the effectiveness of the proposed controller.

Quadratic Stabilization of Takagi-Sugeno Fuzzy Discrete-time Uncertain Networked Systems

For one class of Takagi-Sugeno uncertain time-delay discrete-time systems this paper proposes an extended way to account related constraints in problem solving of the networked control system quadratic stability reflecting sensor drifts and communication delays. The new design conditions are proposed, exploiting a set of linear matrix inequalities to guaranty the closed-loop system quadratic stability where a specific Lyapunov-Krasovskii functional is exploited. Combining into the functional the disturbance transfer function H∞ norm upper bound, the design task is defined as a multi-objective robust control problem, while only the set of time-invariant control law gains are used in the fuzzy parallel structure of the controller realization. A numerical example is included to assess the feasibility of the technique and its applicability.

Design of an Unmatching Observer-Based Controller for Discrete-Time Fuzzy Systems with Time Delay

The problem of an unmatching observer-based controller design for discrete-time fuzzy systems with time delay is investigated, in which the fuzzy controller shares different membership functions from the fuzzy model. The objective is to design a state observer and unmatching fuzzy controller such that the discrete closed-loop system with time delay is asymptotically stable. A sufficient condition that contains the information of the membership functions of fuzzy model and fuzzy controller for the stabilization via an unmatching observer-based output feedback is presented. The proposed control scheme is well capable of enhancing the design flexibility, and the stability condition is less conservative. Three numerical examples are given to illustrate the effectiveness and advantages of the proposed method.

Finite frequency fault estimation observer design for T-S Fuzzy discrete-time descriptor systems

This paper deals with the problem of fault estimation observer design for T-S fuzzy nonlinear discrete-time descriptor systems in the finite frequency domain. First, a novel fault estimation observer for the augmented descriptor system is given. Based on Parseval's theorem and Lyapunov theory, the performance in the finite frequency domain is derived via time-domain method. Then, new sufficient conditions of admissibility and robust performance index for the dynamic error system are obtained as bilinear matrix inequalities. Meanwhile, an iterative linear matrix inequality algorithm is given to obtain the optimal solution. Finally, an example is given to demonstrate the effectiveness of our method.

Constrained Output-Feedback Control for Discrete-Time Fuzzy Systems With Local Nonlinear Models Subject to State and Input Constraints.

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

Perfect tracking control of discrete-time quadratic TS fuzzy systems via feedback linearisation

ABSTRACTPerfect tracking control is an important and frequently encountered requirement in various industries (e.g. robotic control). We developed a novel systematic framework for designing a fuzzy controller via feedback linearisation to control a class of discrete-time Takagi–Sugeno (TS) fuzzy systems with quadratic rule consequents to achieve such tracking. We established a necessary condition for its local stability and a necessary and sufficient condition for the boundedness of the controller. The feedback linearisation is known to fail to work in certain systems due to the unboundedness of the tracking controller output. To address this issue, we developed a method to check whether any given quadratic TS fuzzy system will cause such a failure. We developed a scheme to ensure that the output of the controller designed for any failure-causing system will be bounded and the resulting controller will attain nearly perfect tracking performance. Applying feedback linearisation to the quadratic fuzzy systems is innovative relative to the literature exclusively dealing with the TS fuzzy systems with linear rule consequents (including our previous results), which are now generalised by the new findings. Two numerical examples are provided to illustrate the effectiveness and utility of our new theoretical results.

Stochastic Dynamics of Discrete-Time Fuzzy Random BAM Neural Networks with Time Delays

By using the semidiscrete method of differential equations, a new version of discrete analogue of stochastic fuzzy BAM neural networks was formulated, which gives a more accurate characterization for continuous-time stochastic neural networks than that by the Euler scheme. Firstly, the existence of the 2p-th mean almost periodic sequence solution of the discrete-time stochastic fuzzy BAM neural networks is investigated with the help of Minkowski inequality, Hölder inequality, and Krasnoselskii’s fixed point theorem. Secondly, the 2p-th moment global exponential stability of the discrete-time stochastic fuzzy BAM neural networks is also studied by using some analytical skills in stochastic theory. Finally, two examples with computer simulations are given to demonstrate that our results are feasible. The main results obtained in this paper are completely new, and the methods used in this paper provide a possible technique to study 2p-th mean almost periodic sequence solution and 2p-th moment global exponential stability of semidiscrete stochastic fuzzy models.

Observer-Based State Estimation of Discrete-Time Fuzzy Systems Based on a Joint Switching Mechanism for Adjacent Instants.

The problem of observer-based state estimation of discrete-time fuzzy systems is investigated by constructing a joint switching mechanism for adjacent instants. Thanks to the usage of both the proposed spatial partitioning method and a set of new free matrix-valued variables, abundant information about size differences of all the normalized fuzzy weighting functions for adjacent instants can be interactively integrated into the fuzzy observer design for the first time. Compared with the recent result from three important aspects (conservatism level, online computational burden, and offline computational burden), three positive results can be obtained: 1) it provides a chance for reducing the conservatism by a large margin; 2) the required online computational burden remains unchanged as referred ones; and 3) as a tradeoff, the required offline computational burden increases to some extent but is still affordable from the view of complexity analysis. Finally, two numerical simulations have been given to validate the effectiveness of our developed theoretical results.

Decentralized Control Design for Switching Fuzzy Large-Scale T–S Systems by Switched Lyapunov Function with $$H_\infty $$ H ∞ Performance

This paper investigates the $$H_{\infty }$$ control design for switched fuzzy discrete-time interconnected systems. This type of systems contains nonlinear interconnected subsystems. Every subsystem has different switching modes described by a T–S fuzzy model. Less conservative sufficient conditions are proposed and formulated in terms of LMIs obtained using Switched Lyapunov functions and parallel distributed compensation (PDC) controllers. The design is allowed by $$H_{\infty }$$ technique and a relaxed method is presented. Two numerical examples are developed to illustrate the effectiveness of the obtained results.

Regularization and Stabilization for Rectangular T–S Fuzzy Discrete-Time Systems With Time Delay

This paper is concerned with the regularization and stabilization problems for rectangular discrete-time fuzzy systems with time delay. A dynamic compensation is designed to ensure that the close-loop system is square, and a necessary and sufficient condition is proposed to guarantee the existence of a dynamic compensation with which the close-loop system is regular and causal. Moreover, sufficient conditions are derived in terms of bilinear matrix inequalities to guarantee the admissibility of the closed-loop system. We present an efficient algorithm which is proved to be convergent to solve the conditions. Two examples are given to show the effectiveness and efficiency of the proposed method.

Feedback-linearization-based control of discrete-time quadratic TS fuzzy systems with disturbances

Feedback-linearization-based control of discrete-time quadratic TS fuzzy systems with disturbances

On Dynamical Behavior of Discrete Time Fuzzy Logistic Equation

The aim of this paper is to investigate the dynamical behavior of the following model which describes the logistic difference equation taking into account the subjectivity in the state variables and in the parameters. xn+1=Axn(1~-xn), n=0,1,2,⋯, where {xn} is a sequence of positive fuzzy numbers. A,1~ and the initial value x0 are positive fuzzy numbers. The existence and uniqueness of the positive solution and global asymptotic behavior of all positive solution of the fuzzy logistic difference equation are obtained. Moreover, some numerical examples are presented to show the effectiveness of results obtained.

Observer Design of Discrete-Time Fuzzy Systems Based on an Alterable Weights Method

This paper proposes an improvement on observer design of discrete-time fuzzy systems based on an alterable weights method. Different from the recent result, a more effective ranking-based switching mechanism is developed by introducing a bank of alterable weights for the sake of making use of the size difference information of the normalized fuzzy weighting functions more freely than before. Therefore, a positive result can be provided in this paper, that is, less conservative conditions of designing feasible fuzzy observers can be obtained than those existing results, while the computational cost of designing feasible fuzzy observers is even less than the up-to-date one. Finally, two numerical examples are given to show the progressiveness of the proposed method.