Fuzzy Stochastic Systems Research Articles

Event‐triggered integral sliding mode control of Takagi‐Sugeno fuzzy stochastic systems

AbstractThis article analyzes the integral sliding mode control (ISMC) problem for the nonlinear stochastic system by employing the fuzzy approach. Firstly, the Takagi‐Sugeno (T‐S) fuzzy stochastic model with unknown nonlinear function and external disturbance has been developed. Based on the fuzzy model, an observer‐based integral sliding mode fuzzy controller is derived under the event‐triggered scheme (ETS). The Lyapunov‐Krasovskii functionals (LKFs) involving double and triple integral terms are considered and evaluated by applying Writinger inequality lemma and reciprocally convex combination lemma. With the help of matrix's singular value decomposition lemma, the stability conditions have been derived which is in terms of linear matrix inequalities (LMIs) and this can be solved by MATLAB LMI toolbox. Two numerical examples are provided to demonstrate the usefulness of our theoretical conclusions.

Dissipativity analysis on switched uncertain nonlinear T–S fuzzy Systems with stochastic perturbation and time delay

The problem of dissipativity-based filtering for switched time-delayed Takagi–Sugeno (T–S) fuzzy nonlinear systems is investigated. Stochastic perturbation and state-dependent switching are taken into consideration simultaneously. Firstly, the characterized T–S fuzzy systems and designed fuzzy filtering error dynamic system should be mean-square exponential stability with a (ℵ, ℏ, ℓ)-δ-dissipative. This paper dedicates effort to stabilization analysis of continuous T–S fuzzy systems, diminishing the conservatism of stability conditions by means of constructing non-common Lyapunov–Krasovskii functional and employing linear matrix inequalities (LMIs). Secondly, the dissipative control problem for T–S fuzzy stochastic system with time-varying delay and uncertainties via state-dependent switching will be dealt with. Thirdly, Sufficient conditions are proposed to guarantee that the filter-based dynamical error system with time delays and uncertainties is mean-square exponentially stable through dissipativity analysis. Numerical simulation results demonstrate availability and effectiveness of the developed design scheme.

Fault-Tolerant Control for T-S Fuzzy Stochastic Singular Systems

This article investigates the problem of fault estimation and fault-tolerant control for a class of Takagi–Sugeno fuzzy stochastic singular systems. An integral-type sliding-surface-based augmented singular sliding-mode observer, which is applicable to both dual-normalized and nondual-normalized singular systems, is constructed. It is shown that the restrictive rank condition and the equality constraint can be removed. Then, a sufficient condition in terms of linear matrix inequalities is developed to guarantee the asymptotically mean square admissibility of the closed-loop systems such that the fault can be estimated, and the open-loop system can be stabilized. Moreover, a new adaptive sliding-mode controller is designed such that the reachability condition can be guaranteed. Finally, two examples are presented to verify the effectiveness of the proposed method.

Fault Diagnosis and Fault Tolerant Control for T–S Fuzzy Stochastic Distribution Systems Subject to Sensor and Actuator Faults

The problem of fault diagnosis (FD) and fault tolerant control for a class of Takagi–Sugeno (T–S) fuzzy stochastic distribution control systems subject to sensor and actuator faults is discussed in this article. First, fuzzy logic models are used to approximate the output probability density function (PDF). Next, an adaptive augmented state/FD observer is proposed to estimate the system state, sensor and the actuator faults simultaneously. New expected weights based on the sensor fault estimation information and a PI-type fuzzy feedback fault tolerant controller are designed to compensate the effect of sensor fault and actuator fault simultaneously. When the sensor fault occurs, the expected objective is redesigned to compensate the sensor fault. Meanwhile, the PI controller can compensate the effect of actuator fault, and the output PDF of the system can still track the desired PDF after the fault occurs. Finally, an example of quality distribution control in chemical reaction process is given to confirm the effectiveness of the algorithm.

H ∞ fault detection for 2-D T–S discrete stochastic fuzzy systems

ABSTRACT This paper is concerned with fault detection (FD) problem for a class of two-dimensional (2-D) Takagi–Sugeno (T–S) discrete stochastic fuzzy systems. Based on the parallel distributed compensation (PDC), the fuzzy FD filter and the dynamics of FD system are constructed. Since the multiplicative property of the FD system would drastically increase the number of the stability conditions, a method of decoupling based on dimension expansion is used. By decoupling, the number of LMI-based stability conditions is reduced to r from by the conventional method. Then, the fuzzy FD filter is designed. The corresponding fuzzy FD system is proved to be mean-square asymptotically stable and satisfies the attenuation level for all disturbances. In addition, a theorem is proposed to prove that the stability conditions based on decoupling method are equivalent to those of conventional method. Finally, simulation examples are provided to demonstrate the usefulness of the proposed design methods.

Reliable H∞ guaranteed cost control for uncertain switched fuzzy stochastic systems with multiple time-varying delays and intermittent actuator and sensor faults

In this paper, the issue of delay-dependent passive fault-tolerant control and optimal guaranteed cost control is considered for multiple time-varying delayed switched Takagi–Sugeno (T–S) fuzzy stochastic systems against intermittent actuator and sensor faults, model uncertainties, external disturbances and measurement noise. This is the first attempt to implement H∞ guaranteed cost control for switched T–S fuzzy stochastic systems with intermittent actuator and sensor faults which allows more kinds of faults. Thus, the method has a wider application range. A dynamic output feedback controller is designed. Then, a closed-loop system is constructed. Stability results of reliable H∞ guaranteed cost control are given via piecewise fuzzy Lyapunov function in terms of linear matrix inequalities. Slack matrices are not required at all. The conservatism of this paper is relatively low. At last, the effectiveness of the addressed approach is presented by explanatory examples.

Robust model reference tracking control for interval type‐2 fuzzy stochastic systems

This study considers the uncertainty and disturbance estimator-based control problem for interval type-2 fuzzy stochastic systems with disturbances. The proposed control approach accurately estimates system unknown delays, uncertainties, non-linearities and external disturbances by introducing an appropriate filter. Precisely, the filter's bandwidth is one of the most important parameters in designing and tuning the controller to deal with unknown delays, uncertainties, non-linearities and disturbances. By using the Lyapunov–Krasovskii stability theorem and the linear matrix inequality approach, the required stability conditions and the control gain matrices for the system under consideration are obtained. Further, the effectiveness of the proposed control law is verified using two numerical examples.

H-infinity stability analysis and output feedback control for fuzzy stochastic networked control systems with time-varying communication delays and multipath packet dropouts

The H-infinity stability analysis and delay-dependent Takagi–Sugeno (T–S) fuzzy dynamic output feedback control are proposed for the T–S fuzzy discrete networked control systems with time-varying communication delay and multipath packet dropouts. T–S fuzzy model is employed to approximate the discrete networked control system with time-varying state delay and external disturbance. Stochastic system theory and Bernoulli probability distribution are employed to describe the time-varying communication delay and multipath packet dropouts. Delay-dependent T–S fuzzy dynamic output feedback controller is designed. The delay-dependent T–S fuzzy dynamic output feedback controller is employed to relax the design conditions and enhance the design flexibility. The delay-dependent Lyapunov–Krasovskii functional, stochastic system theory and Bernoulli probability distribution are introduced to guarantee the stochastic mean-square stability and prescribed H-infinity performance. Some slack matrices are introduced to reduce the computation complexity. Finally, simulation examples are presented to show the effectiveness and advantages of the proposed methods.

Multiple intermittent fault estimation and tolerant control for switched T-S fuzzy stochastic systems with multiple time-varying delays

This paper focuses on the observer-based fault estimation (FE) and active dynamic output feedback controller design for switched Takagi–Sugeno (T-S) fuzzy Itô stochastic systems against multiple time-varying delays as well as intermittent actuator faults and sensor faults. External disturbances are also considered. First, a novel descriptor sliding mode observer (SMO) is investigated to establish the error dynamics. Compared with the existing results, the proposed observer could be utilized to more cases and applied to a wider scope. Next, in light of the online FE information, a fault tolerant controller is suggested to make the closed-loop system mean-square exponentially stable. Furthermore, a novel piecewise fuzzy Lyapunov function is depicted and then the delay dependent sufficient conditions can be got by linear matrix inequalities (LMIs). The designed SMO has less conservatism than the existing ones. The reachability of the sliding mode surface in the estimation error space is assured under the adopted method. And the finite-time boundedness (FTB) issue is discussed. At last, a simulation example is acquired to validate the novelty and validity of the method proposed in the paper.

Fault Estimation and Tolerant Control for Discrete-Time Multiple Delayed Fuzzy Stochastic Systems With Intermittent Sensor and Actuator Faults

This article is concerned with observer-based fault estimation (FE) and tolerant controller design for a series of discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems. There exist multiple time-varying state delays, intermittent sensor and actuator faults, nonlinear dynamics, and exogenous disturbances in the systems. Compared with the results of the existence, this approach suggested in this article is more flexible and feasible. By means of the FE information, a novel fuzzy adaptive descriptor observer is developed to obtain the error dynamics. Then, an active observer-based fault-tolerant controller is designed to stabilize the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function with the way of linear matrix inequalities (LMIs), which has less conservatism compared with the ones of the existing observers and fault-tolerant controllers. Finally, a simulation example is shown to illustrate the advantages and effectiveness of this approach depicted in this article.

A New Stochastic Sliding-Mode Design for Descriptor Fuzzy Systems With Time-Varying Delay.

In this article, by use of sliding-mode control, a descriptor stochastic fuzzy system with time-varying delay is considered. First, a new sliding-mode surface is proposed. By use of it, the fuzzy system with different input matrices could be studied. At the same time, the controlled system still has strong robustness to external disturbance. Second, since time delay is variable, there is not the time-delay term in the function of the new sliding-mode surface. It makes the controller construct hard. Third, the process of constructing the controller is different from the traditional method. The process of designing the controller does not use the border of external disturbance. Using a new self-adaptive method, the considered system reaches and is kept on the surface. Unlike the earlier sliding-mode controller, the virtue of this controller is that the fluctuation of the controller is small. Finally, two simulations are given to illustrate the effect of this method.

Finite-time non-fragile [formula omitted] sampled-data control for uncertain T-S fuzzy system with time-varying delay and nonlinear perturbation subject to Markovian jump

This paper focuses on studying the finite-time non-fragile H∞ sampled-data control of uncertain T-S fuzzy time-varying delay system with nonlinear perturbation and Markovian jump parameters. We first construct a different Lyapunov-Krasovskii functional that plays a key role to fully capture the available characteristics of sampling period. Second, based on the Lyapunov-Krasovskii functional approach, free weighting matrix method and a novel efficient inequality technique, less conservative sufficient conditions are established, which make stochastic fuzzy system achieve finite-time boundedness and finite-time H∞ boundedness with an optimized performance. Then, the desired multiplicative non-fragile sampled-data control gains can be obtained by solving the linear matrix inequalities. Finally, three numerical examples are given to illustrate the effectiveness of the proposed method.

Aperiodic sampled-data robust [formula omitted] control for delayed stochastic fuzzy systems with quasi-periodical multi-rate approach

This paper considers the robust H∞ problem of delayed stochastic T–S fuzzy systems with aperiodic sampled-data. In order to represent the sawtooth structure of sampled-data more vividly, we reconstruct the continuous time-varying delayed stochastic T–S fuzzy model with discrete feedback as an impulsive control model. Then, the quasi-periodical time-varying Lyapunov function method is introduced to cope with the mean-squared exponential stability of the multi-rate aperiodic sampling control problem and its H∞ performance. Otherwise, for the sake of determining the exact matrices Pm and Pm+1 of delayed matrix function P(t−d(t)), we design a new algorithm. Next, two theorems with the information of maximum and minimum sampling length and the size of time-delay are proposed to realize the H∞ performance. Since the single-rate controllers are the special case of the multi-rates’, the obtained results are less conservative than previous ones. Finally, a numerical example is given to illustrate our results.

Networked H∞ filtering for Takagi–Sugeno fuzzy systems under multi-output multi-rate sampling

This paper studies networked H∞ filtering for Takagi–Sugeno fuzzy systems with multi-output multi-sensor asynchronous sampling. Different output variables in a dynamic system are sampled by multiple sensors with different sampling rates. To estimate the signals of such a system, a continuous multi-rate sampled-data fusion method is proposed to design a novel networked filter. By considering a class of decentralized event-triggered transmission schemes, multi-channel network-induced delays, and the updating modes of the MOMR sampled-data, a networked jumping fuzzy filter is proposed to estimate system signals based on the transmitted multi-rate sampled-data of fuzzy system and the multi-rate sampled states of filter, and the jumping among filter modes is governed by a Markov process which depends on the arrival times of sampled output sub-vectors. To deal with asynchronous membership functions, the networked fuzzy filtering system is modeled as an uncertain fuzzy stochastic system with membership function deviation bounds. Based on stability and H∞ performance analysis, several membership-function-dependent conditions are presented to co-design the event-triggered transmission schemes and the fuzzy filter such that the filtering error system is robustly mean-square exponentially stable with a prescribed H∞ attenuation level. Finally, the improvement in estimation performance and comparison with the existing filtering methods are discussed through simulation examples.

Adaptive sliding mode control for interval type-2 stochastic fuzzy systems subject to actuator failures

ABSTRACTThis paper investigates the problem of adaptive sliding mode control for a class of interval type-2 Itô stochastic fuzzy systems, where the actuator failures may happen. The sliding function is firstly constructed, whose key feature is its dependence on the upper membership functions. And then, an adaptive scheme is proposed to estimate the effectiveness lose values of faulty actuators, and a sliding mode controller based on estimating scheme is designed such that the reachability of the specified sliding surface can be guaranteed even in the presence of actuator failures, in which the lower and upper membership functions are involved. Moreover, the stability conditions of sliding mode dynamics are derived, which involve some coupling terms of Lyapunov matrix and the sliding matrix. By introducing additional matrix variables and employing the cone complementary linearisation algorithm, the above nonlinear stability criterions are decoupled and lastly converted to a minimisation problem with linear constraints. Finally, a numerical example demonstrates the validity of the proposed method.

Fault Estimation and Fault-Tolerant Control for Switched Fuzzy Stochastic Systems

This paper addresses the problems of fault estimation and fault-tolerant control for switched fuzzy stochastic systems with actuator fault and sensor fault. A novel observer is proposed to estimate the system states, actuator, and sensor faults, simultaneously. The proposed observer can be treated as an extension of the traditional proportional-integral observer. The estimation information is utilized to design the fault-tolerant controller. Based on the piecewise Lyapunov function and the average dwell time, a set of linear matrix inequalities can be achieved, which ensure that the closed-loop system is mean-square exponentially stable with a weighted $H_\infty$ performance level. At last, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

Robust Fuzzy Filter Design for Nonlinear Parabolic Partial Differential Systems with Continuous Wiener Noise and Discontinuous Poisson Noise

This paper addresses a robust \(H_{\infty }\) fuzzy filter design problem for nonlinear stochastic partial differential systems (NSPDSs) with continuous random fluctuation, discontinuous Poisson jumping noise, random external disturbance and measurement noise in the spatiotemporal domain. For NSPDSs, the robust \(H_{\infty }\) filter design problem through a measurement output needs to solve a complex second-order Hamilton Jacobi integral inequality. In order to simplify the design procedure, a fuzzy stochastic partial differential system based on a fuzzy interpolation approach is proposed to approximate the NSPDS. Then, the robust \(H_{\infty }\) fuzzy filter design problem can be reformulated as a diffusion matrix inequality (DMI) problem. Since the DMI problem is difficult to be solved via traditional algebraic techniques, we utilize the divergence theorem and Poincare inequality to transform the DMIs to a set of linear matrix inequalities (LMIs) which could be easily solved with the help of MATLAB LMI Toolbox. Finally, a robust state estimation problem of an ecology system with intrinsic spatiotemporal continuous Wiener noise and discontinuous Poisson jump fluctuation is provided as an example to illustrate the design procedure and to confirm the \(H_{\infty }\) filtering performance of the proposed \(H_{\infty }\) fuzzy filter design method.

EID-based sliding mode investment policy design for fuzzy stochastic jump financial systems

This paper proposes a sliding mode investment policy design for nonlinear stochastic financial systems which can be represented by the well-known Takagi–Sugeno fuzzy model. When modeling the financial systems, it is more important to consider the unpredictable investment changes and worldwide unpredictable events which can be regarded as external disturbances. The equivalent-input-disturbance (EID) approach combined with sliding mode investment policy design is implemented to reject the unpredictable investment changes for having better investment. Moreover, the Luenberger state observer is constructed for the addressed financial system to estimate the unpredictable investment changes and worldwide unpredictable events. More precisely, a sliding mode investment policy design is developed by solving the obtained linear matrix inequality (LMI)-based constrained algorithm. Finally, the obtained results of the addressed fuzzy stochastic financial system are verified through numerical simulation to show efficiency of the proposed sliding mode investment policy design.

Adaptive Event-Triggered Fault Detection for Fuzzy Stochastic Systems With Missing Measurements

This paper discusses adaptive event-triggered fault detection filter design for fuzzy stochastic models with missing measurements. First, a novel event-triggered strategy is introduced, while an adaptive law is provided to adjust communication threshold dynamically. Compared with traditional event-triggered methods with fixed threshold, the proposed strategy is more effective on saving network communication resources. Second, a Bernoulli stochastic process is proposed to describe the measurement missing phenomenon, which always appears in real network environment. Then, an integrated fault detection model for fuzzy stochastic systems is constructed by taking network-induced delays, adaptive event-triggered strategy and missing measurements into account. A new method is provided to achieve mean-square asymptotical stability of residual model with one desired fault detection objective. Finally, simulation cases are introduced to verify the validity of the designed strategy.

L2 – L∞ reduced-order filter design for T-S fuzzy stochastic discrete systems

ABSTRACTThis paper investigates the problem of the filtering for discrete-time Takagi–Sugeno fuzzy stochastic systems. The objective is to find new filter design conditions ensuring both the mean square asymptotic stability and prescribed performance of the filtering error system. By means of a fuzzy Lypunov function and by introducing some slack variables through an appropriate use of the projection lemma, new analysis conditions of performance are proposed. Then, the full and reduced-order filter design conditions are proposed in Linear Matrix Inequality form. Finally, to illustrate the proposed approach, simulation and comparison with existing results in the literature are given.