Fuzzy Stochastic Systems Research Articles

Stress Monitoring Based on Stochastic Fuzzy Analysis of Heartbeat Intervals

Quantifying stress levels of an individual based on a mathematical analysis of real-time physiological data measurements is challenging. This study suggests a stochastic fuzzy analysis method to evaluate the short time series of R-R intervals (time intervals between consecutive heart beats) for a quantification of the stress level. The 5-min-long series of R-R intervals recorded under a given stress level are modeled by a stochastic fuzzy system. The stochastic model of heartbeat intervals is individual specific and corresponds to a particular stress level. Once the different heartbeat interval models are available for an individual, an analysis of the given R-R interval series generated under an unknown stress level is performed by a stochastic interpolation of the models. The stress estimation method has been implemented in a mobile telemedical application employing an e-health system for an efficient and cost-effective monitoring of patients while at home or at work. The experiments involve 50 individuals whose stress scores were assessed at different times of the day. The subjective rating scores showed a high correlation with the values predicted by the proposed analysis method.

Delay-dependent fuzzy static output feedback control for discrete-time fuzzy stochastic systems with distributed time-varying delays

This paper is concerned with the delay-dependent H∞ fuzzy static output feedback control scheme for discrete-time Takagi–Sugeno (T–S) fuzzy stochastic systems with distributed time-varying delays. To begin with, the T–S fuzzy stochastic system is transformed to an equivalent switching fuzzy stochastic system. Then, based on novel matrix decoupling technique, improved free-weighting matrix technique and piecewise Lyapunov–Krasovskii function (PLKF), a new delay-dependent H∞ fuzzy static output feedback controller design approach is first derived for the switching fuzzy stochastic system. Some drawbacks existing in the previous papers such as matrix equalities constraint, coordinate transformation, the same output matrices, diagonal structure constraint on Lyapunov matrices and BMI problem have been eliminated. Since only a set of LMIs is involved, the controller parameters can be solved directly by the Matlab LMI toolbox. Finally, two examples are provided to illustrate the validity of the proposed method.

Robust [formula omitted] control for T–S fuzzy systems with probabilistic interval time varying delay

In this paper, we are concerned with the problem of robust H∞ control for the Takagi–Sugeno (T–S) fuzzy system with probabilistic interval time-varying state delay. Considering the distribution property of time-varying delay, a new stochastic fuzzy model is first proposed. Then, a delay-distribution-dependent H∞ performance analysis result is established for the closed-loop stochastic fuzzy systems via the Lyapunov–Krasovskii functional method and linear matrix inequality (LMI) technique. Based on the derived H∞ performance analysis results, H∞ controller is designed in terms of LMIs. An illustrative example is proposed to show the effectiveness and feasibility of the proposed method.

Exponential Stability Control for T-S fuzzy Nonlinear Stochastic Networked Control Systems

Exponential Stability Control for T-S fuzzy Nonlinear Stochastic Networked Control Systems

Robust H∞ Filtering for Uncertain Discrete‐Time Fuzzy Stochastic Systems with Sensor Nonlinearities and Time‐Varying Delay

The robust filtering problem for a class of uncertain discrete‐time fuzzy stochastic systems with sensor nonlinearities and time‐varying delay is investigated. The parameter uncertainties are assumed to be time varying norm bounded in both the state and measurement equations. By using the Lyapunov stability theory and some new relaxed techniques, sufficient conditions are proposed to guarantee the robustly stochastic stability with a prescribed H∞ performance level of the filtering error system for all admissible uncertainties, sensor nonlinearities, and time‐varying delays. These conditions are dependent on the lower and upper bounds of the time‐varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two simulation examples are provided to illustrate the effectiveness of the proposed methods.

Energy-to-peak control for a class of discrete stochastic fuzzy systems with time-delay

This paper considers the problem of stochastic stabilization and energy-to-peak control for a class of discrete stochastic fuzzy systems with interval time-delays. The objective is to design a state feedback controller such that the closed-loop system is stochastic stable and satisfies energy-to-peak performance. Based on the idea of interval partitioning, some new sufficient conditions are presented in LMI.

Passive fuzzy controller design for stochastic Takagi—Sugeno fuzzy systems with time-varying delay

This paper discusses the issue of stability and stabilization for the non-linear stochastic systems with time-varying delay subject to passivity performance. Based on the fuzzy modelling approach, the non-linear systems can be represented by a stochastic T—S fuzzy model whose consequent part is described by linear differential equations with a multiplicative noise term. For analysing the stability of the stochastic T—S fuzzy model, the less conservative stability criterion derived by Itô's formula and the Lyapunov—Krasovskii function is proposed as a linear matrix inequality (LMI) problem. Furthermore, the passivity theory is employed to discuss the external disturbance effect on the considered system. Through applying the above techniques, the sufficiency conditions are derived to design fuzzy controllers such that the stochastic T—S fuzzy model with time delay is asymptotically stable and passive in the mean square. Finally, two numerical examples are proposed to show the application and effectiveness of the proposed fuzzy controller design method.

Stabilization for T–S model based uncertain stochastic systems

This paper considers the stabilization problem of a class of uncertain Itô stochastic fuzzy systems driven by a multidimensional Wiener process. The uncertainty modeled in the systems is of the linear fractional type which includes the norm-bounded uncertainty as a special case. The objective is to design a state-feedback fuzzy controller such that the closed-loop system is robustly asymptotically stable under a stochastic setting. By using a stochastic Lyapunov approach, sufficiency conditions for the stability and stabilization of this class of systems are established based on a novel matrix decomposition technique. The derived stability conditions are then employed to design controllers which stabilize the uncertain Itô stochastic fuzzy systems. Two simulation examples are given to illustrate the effectiveness of the approaches proposed.

Filtering For Discrete Fuzzy Stochastic Systems With Sensor Nonlinearities

This paper deals with the filtering problem for discrete-time fuzzy stochastic systems with sensor nonlinearities. There exist time-varying parameter uncertainties and random noise depending on state and external-disturbance. The characteristic of nonlinear sensor is handled by a decomposition method. By means of the parallel distributed compensation technique, the design method of the robust H_ filter is presented. Sufficient conditions for the stochastic stability of the filtering error systems are derived such that the filter parameters can be explicitly obtained. Simulation results are given to illustrate the proposed method.

Robust fuzzy control of nonlinear stochastic delay systems with impulsive effects

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive stochastic systems with time-varying delays is investigated. The nonlinear delay system is represented by the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for mean square exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the applicability of the theoretical results.

Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular fuzzy system with cross-term is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from well-known traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of GMRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to this problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

Robust passivity and passification of stochastic fuzzy time-delay systems

In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi–Sugeno (T–S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter uncertainties and the stochastic disturbances are considered, where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a Brownian motion. We first propose the definition of robust passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the Itô differential rule and the matrix analysis techniques, we establish several sufficient criteria such that, for all admissible parameter uncertainties and stochastic disturbances, the closed-loop stochastic fuzzy time-delay system is robustly passive in the sense of expectation. The derived criteria, which are either delay-independent or delay-dependent, are expressed in terms of linear matrix inequalities (LMIs) that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.

On Passivity and Passification of Stochastic Fuzzy Systems With Delays: The Discrete-Time Case

Takagi-Sugeno (T-S) fuzzy models, which are usually represented by a set of linear submodels, can be used to describe or approximate any complex nonlinear systems by fuzzily blending these subsystems, and so, significant research efforts have been devoted to the analysis of such models. This paper is concerned with the passivity and passification problems of the stochastic discrete-time T-S fuzzy systems with delay. We first propose the definition of passivity in the sense of expectation. Then, by utilizing the Lyapunov functional method, the stochastic analysis combined with the matrix inequality techniques, a sufficient condition in terms of linear matrix inequalities is presented, ensuring the passivity performance of the T-S fuzzy models. Finally, based on this criterion, state feedback controller is designed, and several criteria are obtained to make the closed-loop system passive in the sense of expectation. The results acquired in this paper are delay dependent in the sense that they depend on not only the lower bound but also the upper bound of the time-varying delay. Numerical examples are also provided to demonstrate the effectiveness and feasibility of our criteria.

Fuzzy model-based control of nonlinear stochastic systems with time-delay

This note investigates the problems of robust stabilization and robust H ∞ control for a class of nonlinear stochastic delay systems—stochastic fuzzy delay systems. The purpose of the robust stochastic stabilization problem is the design of a state feedback controller such that the closed-loop system is mean-square exponentially stable for all admissible uncertainties. In the robust H ∞ control problem, in addition, a prescribed H ∞ performance is required to be archived. Sufficient conditions for the solvability of these problems are given in terms of solutions to a set of linear matrix inequalities (LMIs). The developed theory is illustrated by numerical simulation.

Fuzzy filtering of nonlinear fuzzy stochastic systems with time-varying delay

This paper is concerned with the H ∞ filtering problem for nonlinear stochastic Takagi–Sugeno (T–S) fuzzy systems with time-varying delay, where the nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of both the fuzzy-rule-independent and the fuzzy-rule-dependent filters that guarantee a prescribed noise attenuation level in an H ∞ sense. To reduce the conservatism, a delay-dependent approach developed to derive the main results in terms of linear matrix inequalities (LMIs). When the fuzzy-rule-independent filter is applied, a sufficient condition is first proposed to ensure that the filtering error system is stochastically stable with an H ∞ performance. The corresponding solvability condition for a desired fuzzy-rule-independent filter is established by casting the fuzzy-rule-independent filter design into a convex optimization problem. Then, the parallel results are obtained for the case when the fuzzy-rule-dependent filter is used, and these results have less conservatism than those for the fuzzy-rule-independent filter design case. Finally, a numerical example is provided to illustrate the effectiveness of the proposed theory.

Delay-dependent robust control of uncertain stochastic fuzzy systems with time-varying delay

The problem of delay-dependent robust fuzzy control for stochastic nonlinear systems with parameter uncertainties and time-varying delay is considered. A generalised Takagi-Sugeno fuzzy model is introduced to represent a stochastic nonlinear system in which the consequent parts are composed of a set of uncertain stochastic time-varying delay systems. Delay-dependent stability criterion is first obtained such that for all admissible uncertainties, the overall fuzzy system is asymptotically stable in the mean square. Then, based on the stability criterion and the parallel distributed compensation scheme, a state feedback fuzzy controller is proposed to guarantee the asymptotical stability in the mean square for the closed-loop system. These conditions are expressed in terms of linear matrix inequalities, and are dependent on the size of the time delay and on the size of the derivative of time delay. Finally, a simulation example is given to illustrate the effectiveness of the developed method.

Delay-dependent stabilization for stochastic fuzzy systems with time delays

This paper is concerned with the delay-dependent stabilization problem for a class of time-delay stochastic fuzzy systems. The time delays are assumed to appear in both the state and the control input. The purpose is the design of a state-feedback fuzzy controller such that the resulting closed-loop system is asymptotically stable in the mean square. A delay-dependent condition for the solvability of this problem is obtained in terms of relaxed linear matrix inequalities (LMIs). By solving these LMIs, a desired controller can be obtained. Finally, a numerical example is given to demonstrate the effectiveness of the present results.

Guaranteed cost control for uncertain stochastic fuzzy systems with time delay

This paper studies a delay-dependent guaranteed cost control problem for a class of uncertain nonlinear stochastic systems with time delay represented by the Takagi-Sugeno (T-S) fuzzy model with uncertain parameters. The descriptor system method and Gu's inequality are employed to obtain delay-dependent sufficient conditions such that the closed-loop system is asymptotically stable with a certain guaranteed cost control performance. The effectiveness of the proposed method is shown by a simulation example.

05/02693 Fuzzy control with random delays using invariant cones and its application to control of energy processes in microelectromechanical motion devices

In this paper, a class of microelectromechanical systems described by nonlinear differential equations with random delays is examined. Robust fuzzy controllers are designed to control the energy conversion processes with the ultimate objective to guarantee optimal achievable performance. The fuzzy rule base used consists of a collection of r fuzzy IF-THEN rules defined as a function of the conditional variable. The method of the theory of cones and Lyapunov functionals is used to design a class of local fuzzy control laws. A verifiably sufficient condition for stochastic stability of fuzzy stochastic microelectromechanical systems is given. As an example, we have considered the design of a fuzzy control law for an electrostatic micromotor.

Approximation of stochastic processes by T–S fuzzy systems

Fuzzy systems can provide us with universal approximation models of deterministic input–output relationships, but in the stochastic environment few achievements related to the subject have so far achieved. In the paper a novel stochastic Takagi–Sugeno (T–S) fuzzy system is introduced to represent approximately existing randomness in many real-world systems. By recapitulating the general architecture of the stochastic T–S fuzzy rule-based system, we analyze systematically approximating capability of the stochastic system to a class of stochastic processes. By the canonical representation of the stochastic processes, the stochastic fuzzy system is capable of with arbitrary accuracy providing the approximation to the stochastic processes in mean square sense. Finally, an efficient algorithm for the stochastic T–S fuzzy system is developed. A simulation example demonstrates how a stochastic T–S fuzzy system can be constructed to realize the given stochastic process, approximately.