Robust Controller Design of a Class of Uncertain Switched Fuzzy Systems with Delays

The robust control problem for a class of uncertain switched fuzzy systems with delays is investigated. Firstly,the model of the switched fuzzy system is presented and the parallel distributed compensation( PDC) technology is employed to design fuzzy controllers. Then, based on the convex combination method, a sufficient condition for robust stabilization in terms of linear matrix inequalities( LMIs) is obtained and a switching law is presented.Meanwhile,the Lyapunov-Krasovskii functional is taken to deal with time varying delays. Moreover,an algorithm is applied to finding a solution for a group of convex combination coefficient. Finally,a numerical example is given to demonstrate the effectiveness of the proposed method.

Delay-dependent robust H_∞control of convex polyhedral uncertain fuzzy systems

The robust H∞ control problem for a class of uncertain Takagi-Sugeno fuzzy systems with timevarying state delays is studied. The uncertain parameters are supposed to reside in a polytope. Based on the delay-dependent Lyapunov functional method, a new delay-dependent robust H∞ fuzzy controller, which depends on the size of the delays and the derivative of the delays, is presented in term of linear matrix inequalities （LMIs）. For all admissible uncertainties and delays, the controller guarantees not only the asymptotic stability of the system but also the prescribed H∞ attenuation level. In addition, the effectiveness of the proposed design method is demonstrated by a numerical example.

On Methodology of Fuzzy Systems

Fuzziness is one of the general characteristics of human thinking and objective things.Fuzzy systems are efficient tools to simulate human thinking and execute fuzzy information processing. This paper discusses several fundamental problems on methodology of fuzzy systems briefly,including generalized fuzzy entropy, generalized defuzzification strategies and fuzzy consistent relation.

Guaranteed cost control for T-S fuzzy systems with time-varying delays

This paper deals with the problem of guaranteed cost control for nonlinear systems with time-varying delays which is represented by Takagi-Sugeno （T-S） fuzzy models with time-varying delays.The derivatives of time-varying delay are not necessary to be bounded.Based on the free weighting matrix method,sufficient conditions for the existence of fuzzy guaranteed cost controller via state feedback are given in terms of linear matrix inequalities （LMIs）.A minimizing method is also proposed to search the suboptimal upper bound of the guaranteed cost function.The results are delay-dependent but contain delay-independent criteria as a special case.A numerical example is presented to demonstrate the effectiveness and less conservativeness of our work.

Robust passive control for discrete-time T-S fuzzy systems with delays

This article deals with the robust stability analysis and passivity of uncertain discrete-time Takagi- Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy model with parametric uncertainties can approximate nonlinear uncertain systems at any precision. A sufficient condition on the existence of robust passive controller is established based on the Lyapunov stability theory. With the help of linear matrix inequality （LMI） method, robust passive controllers are designed so that the closed-loop system is robust stable and strictly passive. Furthermore, a convex optimization problem with LMI constraints is formulated to design robust passive controllers with the maximum dissipation rate. A numerical example illustrates the validity of the proposed method.

Robust control for a class of uncertain switched fuzzy systems

A model of uncertain switched fuzzy systems whose subsystems are uncertain fuzzy systems is presented. Robust controllers for a class of switched fuzzy systems are designed by using the Lyapunov function method. Stability conditions for global asymptotic stability are developed and a switching strategy is proposed. An example shows the effectiveness of the method.

Relaxed delay-dependent stabilization criteria for discrete-time fuzzy systems based on a switching fuzzy model and piecewise Lyapunov functions

This paper presents delay-dependent stability analysis and controller synthesis methods for discrete-time Takagi-Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, the delay-dependent stabilization criteria are derived for the switching fuzzy system based on the piecewise Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered in each subregion, and accordingly the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, a design example is given to show the validity of the proposed method.

GH_2 Control for Uncertain Discrete-time-delay Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function

Generalized H2 （GH2） stability analysis and controller design of the uncertain discrete-time Takagi-Sugeno （T-S） fuzzy systems with state delay are studied based on a switching fuzzy model and piecewise Lyapunov function. GH2 stability sufficient conditions are derived in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered. Therefore, the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. To illustrate the validity of the proposed method, a design example is provided.

Passivity and Passification of Uncertain Fuzzy Systems with Impulse

The passivity and feedback passification problems of fuzzy systems with parameter uncertainties and impulse are first presented in this paper. Based on the parallel distributed compensation （PDC） technique, some passivity and passification conditions are proposed in terms of linear matrix inequalities （LMIs）. Numerical examples are given to show the correctness and effectiveness of our theoretical results.

Computation Tree Logic Model Checking of Multi-Agent Systems Based on Fuzzy Epistemic Interpreted Systems

Model checking is an automated formal verification method to verify whether epistemic multi-agent systems adhere to property specifications.Although there is an extensive literature on qualitative properties such as safety and liveness,there is still a lack of quantitative and uncertain property verifications for these systems.In uncertain environments,agents must make judicious decisions based on subjective epistemic.To verify epistemic and measurable properties in multi-agent systems,this paper extends fuzzy computation tree logic by introducing epistemic modalities and proposing a new Fuzzy Computation Tree Logic of Knowledge(FCTLK).We represent fuzzy multi-agent systems as distributed knowledge bases with fuzzy epistemic interpreted systems.In addition,we provide a transformation algorithm from fuzzy epistemic interpreted systems to fuzzy Kripke structures,as well as transformation rules from FCTLK formulas to Fuzzy Computation Tree Logic(FCTL)formulas.Accordingly,we transform the FCTLK model checking problem into the FCTL model checking.This enables the verification of FCTLK formulas by using the fuzzy model checking algorithm of FCTL without additional computational overheads.Finally,we present correctness proofs and complexity analyses of the proposed algorithms.Additionally,we further illustrate the practical application of our approach through an example of a train control system.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

A Stable Fuzzy-Based Computational Model and Control for Inductions Motors

In this paper,a stable and adaptive sliding mode control(SMC)method for induction motors is introduced.Determining the parameters of this system has been one of the existing challenges.To solve this challenge,a new self-tuning type-2 fuzzy neural network calculates and updates the control system parameters with a fast mechanism.According to the dynamic changes of the system,in addition to the parameters of the SMC,the parameters of the type-2 fuzzy neural network are also updated online.The conditions for guaranteeing the convergence and stability of the control system are provided.In the simulation part,in order to test the proposed method,several uncertain models and load torque have been applied.Also,the results have been compared to the SMC based on the type-1 fuzzy system,the traditional SMC,and the PI controller.The average RMSE in different scenarios,for type-2 fuzzy SMC,is 0.0311,for type-1 fuzzy SMC is 0.0497,for traditional SMC is 0.0778,and finally for PI controller is 0.0997.

Event-triggered fault detection for T-S fuzzy systems with local nonlinear models in finite-frequency domain

This article investigates the issue of event-triggered fault detection(FD)filter design for T-S fuzzy systems with local nonlinear models.A novel H−/H∞FD filter subject to the event triggering transmission mechanism is designed in finite-frequency domain.Then,a novel lemma,in which the nonlinear part and the event triggering mechanism are dealt appropriately,is presented to capture the sensitivity and robustness performances.In addition,the slack matrices are utilised to derive optimal filter parameters by solving a convex optimisation problem.The less conservative FD method can get better detection performances than those entire-frequency methods.Finally,an example is introduced to verify the new results.

Delay-dependent Robust Stabilization and H_∞ Control for Uncertain Stochastic T-S Fuzzy Systems with Discrete Interval and Distributed Time-varying Delays

In this paper, delay-dependent robust stabilization and H∞ control for uncertain stochastic Takagi-Sugeno （T-S） fuzzy systems with discrete interval and distributed time-varying delays are discussed. The purpose of the robust stochastic stabilization problem is to design a memoryless state feedback controller such that the closed-loop system is mean-square asymptotically stable for all admissible uncertainties. In the robust H∞ control problem, in addition to the mean-square asymptotic stability requirement, a prescribed H∞ performance is required to be achieved. Sufficient conditions for the solvability of these problems are proposed in terms of a set of linear matrix inequalities （LMIs） and solving these LMIs, a desired controller can be obtained. Finally, two numerical examples are given to illustrate the effectiveness and less conservativeness of our results over the existing ones.

Fuzzy inference systems with no any rule base and linearly parameter growth

A class of new fuzzy inference systems New-FISs is presented.Compared with the standard fuzzy system, New-FIS is still a universal approximator and has no fuzzy rule base and linearly parameter growth. Thus, it effectively overcomes the second "curse of dimensionality":there is an exponential growth in the number of parameters of a fuzzy system as the number of input variables,resulting in surprisingly reduced computational complexity and being especially suitable for applications,where the complexity is of the first importance with respect to the approximation accuracy.

Robust H_∞ control for fuzzy descriptor systems with state delay

The problem of robust H ∞ fuzzy state feedback control for uncertain fuzzy descriptor systems with state delay is solved. In the case that time-varying uncertainties are in all parameter matrices, sufficient conditions for the existence of fuzzy state feedback controller are presented in terms of linear matrix inequality (LMI). The proposed robust H ∞ control laws guarantee that the resulting closed-loop system is regular, impulse free, and stable with prescribed H ∞ norm bounded constraint for all admissible uncertainties. Finally, a numerical example is provided to demonstrate the validity of the proposed method.

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.

New approaches to relaxed stabilization conditions and H-infinity control designs for T-S fuzzy systems

This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems. New methods of stabilization design and H-infinity control are derived based on a relaxed approach in which both fuzzy Lyapunov functions and staircase membership functions are used. Through the staircase membership functions approx- imating the continuous membership functions of the given fuzzy model, the membership functions can be brought into the design conditions of fuzzy systems, thereby significantly reducing the conservativeness in the recent fuzzy controller design methods. Unlike some previous fuzzy Lyapunov function approaches reported in the literatures, the proposed design techniques of stabilization and H-infinity control do not depend on the time-derivative of the membership functions that may be pointed out as the main source of conservatism when considering fuzzy Lyapunov functions analysis. Moreover, conditions for the solvability of the controller design given here are written in the form of linear matrix inequalities, but not bilinear matrix inequalities, which are easier to be solved by convex optimization techniques. Simulation examples are given to demonstrate the validity and applicability of the proposed approaches.

Stability analysis of T-S fuzzy control systems with interval plants

The stability of a type of Takagi-Sugeno ( T-S) fuzzy control systems is considered. The plant of T-S fuzzy system has parameter uncertainties. By using the off-axis circle criterion and Kharitonov Theorem,a sufficient condition is derived to analyze the global asymptotic stability of T-S fuzzy control system. The proposed method has a graphical explanation which facilitates stability analysis. A numerical example is also given to demonstrate how to use our approach in analyzing certain T-S fuzzy control systems.

Non-fragile memory feedback control for uncertain time-varying delay switched fuzzy systems with unknown nonlinear disturbance

Currently,the feedback control rate of most nonlinear systems is realised by the memoryless state feedback controller which cannot affect the impact of time delay on the systems,and the general processing method of the Lyapunov–Krasovskii functional for the time-varying delay switched fuzzy systems(SFS)is more conservative.Therefore,this paper addresses the problem of nonfragile robust and memory state feedback control for switched fuzzy systems with unknown nonlinear disturbance.Non-fragile memory state feedback robust controller which has two controller gains different from each other,and switching law are designed to keep the proposed systems asymptotically stable for all admissible parameter uncertainties.Delay-dependent less conservative sufficient conditions are obtained through using the Lyapunov–Krasovskii functional method and free-weighting matrices depending on Leibniz–Newton,guaranteeing that the SFS can be asymptotically stable.A numerical example is given to illustrate the proposed controller performs better than the classic memoryless state feedback controller.