Fuzzy Stochastic Systems Research Articles

Adjustable order fault estimation observer based fault-tolerant control for switched fuzzy stochastic systems

Based on fault estimation, fault-tolerant control problem of switching stochastic nonlinear systems with actuator fault and sensor fault are studied. The fuzzy models are invited to solve the nonlinear problems of the systems. The fault estimation observer is designed to estimate the system states, actuator and sensor faults. The order of observer can be adjusted, which can improve the design flexibility and realize a compromise between the estimated cost and estimated accuracy. Unlike some classical results, the output differential is not required in the observer, which increases the application range. Based on the observer, the fault-tolerant controller is proposed, besides, the sufficient condition is achieved to ensure that the closed-loop system is mean-squared exponential stability. Finally, the feasibility is verified by two simulations.

Fault Tolerant Control of Fuzzy Stochastic Distribution Systems With Packet Dropout and Time Delay

The fault diagnosis (FD) and fault tolerant control (FTC) problem of the fuzzy stochastic distribution system (SDS) over packet dropout and time delay is studied. Firstly, the static model of linear fuzzy logic system that approximates the output PDF and the dynamic model with the multiplicative fault in a fuzzy system are established. The random packet dropout and time delay caused by the network are described in a unified framework, in which the lost data is compensated with the latest data received by the buffer. On this basis, an adaptive observer is devised to estimate the unknown multiplicative fault. The design of sliding mode predictive fault tolerant controller is discussed to ensure that the system still has good tracking performance after the fault occurs. Numerical simulations on a molecular weight distribution control system are supplied to prove the effectiveness of the presented scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The motivation of this paper is to improve the reliability of the fuzzy stochastic distribution system with packet dropout and time delay. This kind of stochastic distribution systems is described by the relationship between the input and the output PDF rather than the normal relationship between the input and the output. When the multiplicative fault occurs in the system, the design of fault diagnosis strategy and fault-tolerant controller becomes an important challenge, especially when the system is subject to packet dropout and time delay. To address the above problems, a new fault diagnosis and fault-tolerant control scheme is proposed, which can accurately estimate the time and size of the fault and obtain the satisfactory fault-tolerant control effect.

Disturbance estimation-based resilient control design for interval type-2 fuzzy stochastic systems under multiple disturbance observer

This research endeavour's primary attention is on the problems of stabilization and multiple disturbance rejection for a class of interval type-2 fuzzy stochastic systems that are prone to parameter uncertainties and multiple disturbances. Specifically, the multiple disturbances are classified into two aspects: the first aspect is matched disturbances, which emanate from an exogenous system, while the second aspect is norm-bounded mismatched disturbances. Further, to provide a precise estimation of the matched disturbances, a fuzzy rule-based multiple disturbance observer is built. Based on the estimated information from the framed observer, a disturbance estimation-based resilient control is devised that can withstand the effects of disturbances. Besides, the footprints of mismatched kind of disturbances are handled by employing the ( Q , S , R ) − ς ~ dissipative performance. Moreover, to insure the attainment of the foremost objective of this analysis, a collection of suitable criteria has been developed by means of linear matrix inequalities with the satisfied disturbance attenuation index through Lyapunov's theory of stability. In addition, under the lighting of adequate conditions, the gain matrices of the configured controller and the framed observer can be determined. Finally, two simulation examples are supplied as a conclusion to the examination, each serving to illustrate the potency and viability of the designed control scheme and the presented theoretical findings.

Intermediate observer based integrated fault estimation and fault-tolerant control for switched fuzzy stochastic systems

This paper studies the fault-tolerant control (FTC) of switched fuzzy stochastic systems (SFSS) in the presence of actuator and sensor faults, disturbance and noise. The dynamic intermediate observers (IOs) are designed to reconstruct the system states and faults, simultaneously, where the output estimation error feedback term and its derivative are considered, simultaneously, which can reduce the effect of the fast time-varying fault. The integrated fault estimation (FE) and FTC design method is considered to ensure the systems are mean-square exponential stability (MSES) with the weighted H∞ performance index, and the integrated design technique avoids the FE error influencing the closed-loop systems. The single-step linear matrix inequality (LMI) conditions are obtained to calculate the observer and controller gain matrices, simultaneously, which overcomes the coupling of the observer and controller gains. Finally, two simulations are offered to show the effectiveness of the proposed technique.

Antidisturbance Control Design for Interval Type-2 Fuzzy Stochastic Systems With Input Quantization

Quantized anti-disturbance control design problem is presented for a class of interval type-2 (IT2) fuzzy stochastic systems subject to time delays and multiple disturbances. The inherent uncertain nonlinear and hybrid characteristics of the concerned system make it difficult to design a stable anti-disturbance controller. In order to properly reflect the characteristics of IT2 fuzzy stochastic models with multiple disturbances, a new fuzzy disturbance observer is proposed to estimate the disturbances generated by a fuzzy exogenous system. Furthermore, a quantized fuzzy anti-disturbance control scheme is synthesized by fusing the estimation of the multiple disturbances. With the support of Lyapunov functional method, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$It{\hat{o}}$</tex-math></inline-formula> 's formula and auxiliary function-based integral inequality, the resulting IT2 fuzzy stochastic systems are proved to be robustly stochastically stable with mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> /passivity performance index. The design methods of the fuzzy disturbance observer and quantized anti-disturbance controller are formulated in the form of linear matrix inequalities so that the corresponding gain matrices can be easily obtained. Finally, simulation studies on three examples are provided to justify the efficiency of the designed control strategy.

Multiple interval delay-dependent finite-time control of fuzzy stochastic systems

This work is concerned with multiple interval delay-dependent stochastic finite-time boundedness as well as input-output finite-time mean square stabilization for fuzzy plants against state constraints as well as input constraints. Nonlinear dynamics, intermittent actuator faults, exogenous disturbances, model uncertainties and intermittent sensor faults appear in the multiplicative form in these systems. The switching between the faulty and healthy conditions is described via semi-Markov chain. First, a semi-Markovian fault-tolerant controller is researched. Next, the closed-loop model is gathered. The issue of robust stochastic finite-time boundedness as well as input-output finite-time mean square stabilization against H∞ performance is realized via fuzzy stochastic Lyapunov function. Meanwhile, sufficient conditions are presented with linear matrix inequalities. At last, this validity of this approach in this paper is proved by two examples.

Robust [formula omitted] sliding mode control for uncertain polynomial fuzzy stochastic singular systems

This paper considers the robust H∞ sliding mode control (SMC) problem for uncertain polynomial fuzzy stochastic singular systems. The interest is focused on designing a polynomial fuzzy sliding mode controller, and two assumptions in most integral SMC methods for fuzzy stochastic systems are removed. By constructing an integral sliding surface, the equivalent control law is obtained, and the sliding mode dynamics is derived. With the help of the sum-of-squares method, for sliding mode dynamics, the mean-square admissibility and the H∞ performance are guaranteed. Furthermore, the sliding mode controller is established. The effectiveness and advantages of the proposed design method are finally revealed via a practical example of the modified bio-economic model and a numerical example.

Approximating solutions of fuzzy stochastic fractional integro-evolution equations with the Averaging Principle: Theory and Applications

This paper introduces the averaging principle (AP) as a method for solving fuzzy stochastic fractional integro-evolution equations (FSFIEEs). By making certain assumptions, the solutions of FSFIEEs can be estimated as mean square solutions of averaged fuzzy stochastic systems. This technique simplifies the analysis and comprehension of complex systems that are subject to both randomness and uncertainty.

Asynchronous robust dynamic output feedback $$H_{\infty }$$ control for fuzzy stochastic hybrid systems subject to time-varying delays and hidden Markov model

Asynchronous robust dynamic output feedback $$H_{\infty }$$ control for fuzzy stochastic hybrid systems subject to time-varying delays and hidden Markov model

Dissipativity-Based Intermittent Fault Detection and Tolerant Control for Multiple Delayed Uncertain Switched Fuzzy Stochastic Systems With Unmeasurable Premise Variables.

This study focuses on dissipativity-based fault detection for multiple delayed uncertain switched Takagi-Sugeno fuzzy stochastic systems with intermittent faults and unmeasurable premise variables. Nonlinear dynamics, exogenous disturbances, and measurement noise are also considered. In contrast to the existing study works, there is a wider range of applications. An observer is explored to detect faults. A controller is studied to stabilize the considered system. A piecewise fuzzy Lyapunov function is collected to obtain delay-dependent sufficient conditions by means of linear matrix inequalities. The designed observer has less conservatism. In addition, the strict [Formula: see text]dissipativity performance is achieved in the residual dynamic. Besides, the elaborate H∞ performance and the elaborate H_ performance are also acquired. Finally, the availability of the method in this study is verified through two simulation examples.

Fuzzy SMC for Quantized Nonlinear Stochastic Switching Systems With Semi-Markovian Process and Application.

This article is concerned with the issue of quantized sliding-mode control (SMC) design methodology for nonlinear stochastic switching systems subject to semi-Markovian switching parameters, T-S fuzzy strategy, uncertainty, signal quantization, and nonlinearity. Compared with the previous literature, the quantized control input is first considered in studying T-S fuzzy stochastic switching systems with a semi-Markovian process. A mode-independent sliding surface is adopted to avoid the potential repetitive jumping effects. Then, by means of the Lyapunov function, stochastic stability criteria are proposed to be dependent of sojourn time for the corresponding sliding-mode dynamics. Furthermore, the fuzzy-model-based SMC law is proposed to ensure the finite-time reachability of the sliding-mode dynamics. Finally, an application example of a modified series dc motor model is provided to demonstrate the effectiveness of the theoretical findings.

Reduced-order intermediate variable observer based fault estimation and fault-tolerant control for fuzzy stochastic systems with exogenous disturbance

This paper studies fault estimation and fault-tolerant control problems for fuzzy systems with exogenous disturbance and stochastic noise. The fuzzy reduced-order intermediate variable observers and the disturbance observers are proposed to reconstruct the sensor fault, the actuator fault and the disturbance. According to the estimated results, the observer based fault-tolerant controllers are devised. Compared with the full-order observer design method, the designed reduced-order observers are with lower dimensions and less cost. Different from the classic intermediate observer, the feedback term of the output estimation error is introduced into our observers, which increases the design freedom. And the obtained linear matrix inequality conditions can ensure that the whole closed-loop systems are mean-square exponentially stable. Finally, two examples are offered to verify the feasibility of the proposed method.

Adaptive fuzzy observer-based mismatched faults and disturbance design for singular stochastic T-S fuzzy switched systems

This paper deals with the problem of observer-based mismatched faults for switched singular fuzzy systems subject to disturbances. First, in order to obtain the estimation of unmeasurable or partially measurable states, fuzzy adaptive observer is obtained, eliminating the influence of external disturbances and mismatched faults, simultaneously. Second, by constructing appropriate piecewise Lyapunov functions and average dwell time, the switched singular fuzzy stochastic system with external parameter perturbations and faults is guaranteed to be robustly stable Further, by solving the linear matrix inequalities a sufficient condition to maintain the stability of error dynamic system is presented. Finally, to illustrate the proposed method is available, numerical examples are presented.

Observer-based sliding mode control for fuzzy stochastic switching systems with deception attacks

This paper discusses the issue of observer-based sliding mode control for fuzzy stochastic semi-Markov switching systems (S-MSSs) under cyber attacks. The underlying control signal is vulnerable to the deception attacks, in which the opponents inject fake data into the signal in a probabilistic way. Inspired by the unmeasurable states, an integral sliding surface dependent on a fuzzy observer is designed. Then, in consideration of the deception attacks, the conditions are established to achieve the stochastic stability for fuzzy sliding mode dynamics. Moreover, the proposed observer-based sliding mode control law guarantees the reachability of the sliding region. In the end, the simulation study on a single-link robot arm model is given to demonstrate the availability of the given results.

Novel Delay-Dependent Stabilization for Fuzzy Stochastic Systems with Multiplicative Noise Subject to Passivity Constraint

A novel delay-dependent stability criterion for Takagi-Sugeno (T-S) fuzzy systems with multiplicative noise is addressed in this paper subject to passivity performance. The general case of interval time-varying delay is considered for the practical control issue. For the criterion, an integral Lyapunov-Krasovskii function is proposed to derive some sufficient relaxed conditions and to avoid the derivative of the membership function. Moreover, a free-matrix inequality is adopted to deal with the delay terms such that the available derivative of time-varying delay is bigger than one. In order to employ a convex optimization algorithm to find the control gain, a projection lemma is applied to acquire the Linear Matrix Inequality (LMI) form of the sufficient conditions. With the obtained gains, a fuzzy controller is designed by the concept of Parallel Distributed Compensation (PDC) such that the delayed T-S fuzzy systems with multiplicative noise are asymptotically stable and passive in the mean square. Finally, a stabilization problem of the ship’s autopilot dynamic system and some comparisons are discussed during the simulation results.

(2010-6217) Solvability of fuzzy fractional stochastic Pantograph differential system

In this paper, a new type of equation namely fuzzy fractional stochastic Pantograph delay differential system (FSPDDS) is proposed. In our previous work, a first extension of fuzzy stochastic differential system into fuzzy fractional stochasticdifferential system by using Granular differentiability has been established. Here we study the existence and uniqueness results for the fuzzy FSPDDS which are obtained by using generalized Granular differentiability and contraction principlewith weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.

Sliding-Mode Control for Fuzzy Stochastic Systems With Different Local-Input Matrices

By use of the method of sliding-mode control, the stabilization of the T-S fuzzy stochastic system with time delay is considered in this article. The characteristic of the proposed method is that the input matrices of the fuzzy system are not common. And the proposed control method of this article can resist the disturbance. First, a novel sliding-mode surface is introduced. Using the new surface, the stability of the fuzzy system can be studied even if the input matrices are not common. Second, a new lemma is given to judge if the surface can be utilized in the considered system. Third, a new control law is constructed according to the new sliding-mode surface. The control law is designed to deal with the problems produced by time delay and stochastic systems. At last, two simulations are provided. In this part, the input matrices of fuzzy systems are different from each other and there is a disturbance in this considered system. From the simulations, the results illustrate the validity of the proposed method.

Finite-Time Admissibility and Controller Design for T-S Fuzzy Stochastic Singular Systems with Distinct Differential Term Matrices

The finite-time admissibility analysis and controller design issues for extended T-S fuzzy stochastic singular systems (FSSSs) with distinct differential term matrices and Brownian parameter perturbations are discussed. When differential term matrices are allowed to be distinct in fuzzy rules, such fuzzy models can describe a wide class of nonlinear stochastic systems. Using fuzzy Lyapunov function (FLF), a new and relaxed sufficient condition is proposed via strict linear matrix inequalities (LMIs). Different from the existing stability conditions by FLF, the derivative bounds of fuzzy membership functions are not required in this condition. Based on admissibility analysis results, a design method for parallel distribution compensation (PDC) controller of FSSSs is given to guarantee the finite-time admissibility of the closed-loop system. Finally, the feasibility and effectiveness of the proposed methods in this article are illustrated with three examples.

Composite fault-tolerant and anti-disturbance control for switched fuzzy stochastic systems

This paper investigates the issue of fault-tolerant and anti-disturbance attenuation for a two-dimensional modified repetitive control system (2D MRCS) which is described by switched fuzzy systems with multiple disturbances. In particular, the multiple disturbances contain an exogenous disturbance and standard Wiener noise. Specifically, a generalized extended state observer (GESO) is incorporated with the 2D MRCS to estimate both fault and exogenous multiple disturbances so that the disturbances and faults can be attenuated in the control input. Further, the improved 2D MRCS relaxes the stability condition and provides an enhanced tracking performance. Based on the Lyapunov function approach, pole placement technique and average dwell time approach, the stability criteria for the considered system is developed in terms of linear matrix inequality (LMI). Then an algorithm for designing a GESO-based 2D MRC design is developed based on the obtained LMIs. Further, the results developed are validated in the simulation section through three numerical examples.

Fuzzy Static Output Control of T–S Fuzzy Stochastic Systems via Line Integral Lyapunov Function

Considering some unmeasurable states, a fuzzy static output control problem of nonlinear stochastic systems is discussed in this paper. Based on a modelling approach, a Takagi–Sugeno (T–S) fuzzy system, constructed by a family of stochastic differential equations and membership functions, is applied to represent nonlinear stochastic systems. Parallel distributed compensation (PDC) technology is used to construct the static output controller. A line-integral Lyapunov function (LILF) is used to derive some sufficient conditions for guaranteeing the asymptotical stability in the mean square. From the LILF, a potential conservatism produced by the derivative of the membership function is eliminated to increase the relaxation of sufficient conditions. Furthermore, those conditions are transferred into linear matrix inequality (LMI) form via projection lemma. According to the convex optimization algorithm, the feasible solutions are directly obtained to establish the static output fuzzy controller. Finally, a numerical example is applied to demonstrate the effectiveness and usefulness of the proposed design method.