Switched Fuzzy Systems Research Articles

Robust Control for a Class of Uncertain Switched Fuzzy Systems with Saturating Actuators

AbstractThis paper investigates the robust control problem for a class of uncertain switched fuzzy systems with saturating actuators. The asymptotical stability for fuzzy subsystems subject to actuator saturation is not assumed. Based on the multiple Lyapunov functions method, we design a switching law and a state feedback control law such that the closed‐loop system is asymptotically stable. Additionally, the estimation of the domain of attraction is presented by solving an optimization problem. Finally, simulation results verify the feasibility and effectiveness of the proposed method.

Design of Output Feedback Controller for Switched Fuzzy Systems with Time-Delay

This paper investigates the problems of stabilization and control for time-delay switched fuzzy systems using output feedback controller. Based on the linear matrix inequality (LMI) technique, multiple Lyapunov method is used to obtain a sufficient condition for the existence of the controller for the output feedback. Then an algorithm is constructed to transform the sufficient condition into a LMI form, thus obtaining a method for designing the controller. The designed controller guarantees the closed-loop system to be asympototically stable. A numerical example is given to show the effectiveness of our method.

Tracking Control for a Class of Switched Fuzzy Systems

This paper investigates the problems of tracking control for switched fuzzy systems. Based on the state-dependent switching method, sufficient conditions for the solvability of the tracking control problem are given. We use single Lyapunov function technique to design a tracking control law. The controller design problem can be solved efficiently. A numerical example is given to show the effectiveness of our method.

Robust $$H_{\infty }$$ H ∞ Control for Networked Switched Fuzzy Systems with Network-Induced Delays and Packet Dropout

A networked switched fuzzy system, as a special networked control system, is studied. Such a system with network-induced delays and packet dropout is represented as a switched fuzzy system with time-varying delays. For this system, we investigate a robust $$H_{\infty }$$ H ? control problem. The solvability for the $$H_{\infty }$$ H ? control problem of each fuzzy subsystem is not assumed. Based on the multiple Lyapunov functions method, a state feedback control law and a switching law are designed such that the robust $$H_{\infty }$$ H ? control problem of the closed-loop system is solvable. Meanwhile, Lyapunov---Krasovskii functionals and free-weighting matrices are taken to deal with the induced delay and packet dropout caused by network. Finally, an example is given to verify the effectiveness of the proposed approach.

Observer-based tracking control for a class of switched fuzzy systems with fast switching controller

Observer-based robust tracking control for a class of switched fuzzy (SF) systems with time delay is investigated in this paper. An SF system, which differs from the existing systems, is first employed to describe a non-linear system. Next, a fast switching controller consisting of a number of simple sub-controllers is proposed. The designed controller based on measured output instead of the state information integrates the advantages of both the linear and switching state-feedback controllers but eliminates their disadvantages. Tracking hybrid control schemes, which are based upon a combination of the H∞ tracking theory, fast switching control algorithm and switching law design, are developed such that the observer-based H∞ model reference tracking performance is guaranteed. Sufficient conditions for the solvability of the tracking control problem are given for the case in which the state of system is not available. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are performed to demonstrate the effectiveness of the proposed control design approach.

Switching Control for a Class of Discrete-Time Switched Fuzzy Systems Based on LMI

Switching control and stability issues for discrete-time switched systems whose subsystems are all discrete-time fuzzy systems are studied and new results derived. Innovated representation models for switched fuzzy systems are proposed. The common Lyapunov function method has been adopted to study the stability of this class of switched fuzzy systems. Sufficient conditions for asymptotic stability are presented. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

Switching Control for a Class of Switched Fuzzy Systems

A switching control of uncertain switched fuzzy systems is presented. In this model, each subsystem of switched system is an uncertain fuzzy system. Using Multiple Lyapunov function method and switching technique, the relevant closed-loop system is asymptotically stable for all allowable uncertainties. Moreover, switching strategy achieving system global asymptotic stability of the uncertain switched fuzzy system is given. The main condition is given in form of LMI which are more solvable. A simulation shows the feasibility and the effectiveness of the method.

Observer-Based Control of a Class of Switched Fuzzy Systems

For the non-measurable states, a control of switched fuzzy systems is presented based on observer. Using switching technique and multiple Lyapunov function method, the fuzzy observer is built to ensure that for all allowable external disturbance the relevant closed-loop system is asymptotically stable. Moreover, switching strategy achieving system global asymptotic stability of the switched fuzzy system is given. In this model, a switching state feedback controller is presented. A simulation shows the feasibility and the effectiveness of the method.

Stability of a Class of Discrete-Time Switched Fuzzy Systems by Arbitrary Switching

This paper investigates a representation model, namely, a discrete-time switched fuzzy system. In this model, a system is a switched system whose subsystems are all discrete-time Takagi-Sugeno (T-S) fuzzy systems. For the proposed discrete-time switched fuzzy system is built to ensure that the relevant system is asymptotically stable by Arbitrary Switching and the Lyapunov functions method. The main conditions are given in form of linear matrix inequalities (LMIs), which are easily solvable. The elaborated illustrative examples and the respective simulation experiments demonstrate the effectiveness of the proposed method.

Output Feedback Control for a Class of Switched Fuzzy Systems

The output feedback control problem is addressed for a class of switched fuzzy Systems. Using multiple Lyapunov function method and switching law, the relevant closed-loop system is asymptotically stable, with the switching law designed to implement the global asymptotic stability. The sufficient conditions to ensure the output feedback asymptotically stable output feedback control of closed-loop system are studied. The sufficient condition is transformed into Linear Matrix Inequality (LMI) problem which are more solvable. Finally, a numerical simulation example is employed to illustrate the effectiveness and the convergence of the design methodologies.

Petri Net Representation of Switched Fuzzy Systems

Switched fuzzy systems can be used to describe the hybrid systems with fuzziness. However, the languages to describe the switching logic and the fuzzy subsystems are, in general, different, and this difference makes the system analysis and implementation hard. In this paper, we use differential Petri net (DPN) as a unified model to represent both the discrete logic and fuzzy dynamic processes. To exam the rationality of the representation, we prove the correctness of the representation for the discrete part and estimate the approximation accuracy of the representation for the dynamic part. Our work provides a way to analyze the switched fuzzy systems by checking the PN and to use the PN model for further system implementation. We demonstrate the benefits of our work via a case study.

Reliable Control for Time-Varying Delay Switched Fuzzy Systems with Faulty Actuators Based on Observers Switching Method

This paper deals with the reliable control problem of nonlinear systems represented by switched fuzzy systems (SFS) with time-varying delay, where each subsystem of switched system is a time-varying delay fuzzy system. A switched fuzzy system with a Takagi and Sugeno (T-S) fuzzy model, which differs from existing ones, is firstly employed to describe a nonlinear system. When the actuators are serious failure, the residual part of actuators cannot make original system stability, using switching technique depends on the states of observers, and the fuzzy reliable controller based on measured observers states instead of the original system states information is built. The stabilization criterion of the reliable control problem is given for the case that the state of original system is unmeasurable. The multi-Lyapunov functions method is utilized to the stability analysis and controller design for time-varying delay switched fuzzy systems with faulty actuators. Moreover, observers switching strategy achieving estimation errors decreasing uniformly asymptotically to zero of the switched fuzzy systems is considered. Finally, the stabilization criterion is transformed into the solvability of sufficient linear matrix inequality (LMI) conditions. To illustrate the effectiveness of the proposed stabilization criterion and controller design approaches, a designed numerical example is studied, and some simulations are provided.

Observer-Based Robust Control of Uncertain Switched Fuzzy Systems with Combined Switching Controller

The observer-based robust control for a class of switched fuzzy (SF) time-delay systems involving uncertainties and external disturbances is investigated in this paper. A switched fuzzy system, which differs from existing ones, is firstly employed to describe a nonlinear system. Next, a combined switching controller is proposed. The designed controller based on the observer instead of the state information integrates the advantages of both the switching controllers and the supplementary controllers but eliminates their disadvantages. The proposed controller provides good performance during the transient period, and the chattering effect is removed when the system state approaches the origin. Sufficient condition for the solvability of the robust control problem is given for the case that the state of system is not available. Since convex combination techniques are used to derive the delay-independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are conducted to demonstrate the effectiveness of the proposed control design approach.

Robust Reliable Control for a Class of Uncertain Time-Delay Switched Fuzzy Systems Based on Observers Switching

It is presented a model of uncertain time-delay switched fuzzy systems, which each subsystem of switched system is an uncertain time-delay fuzzy system. The robust reliable control problem is studied by multi-Lyapunov functions. When the actuators are serious failure – the residual part of actuators can not make original system stability, using switching technique depend on the states of observers, robust fuzzy reliable controller is built to ensure the relevant closed-loop system is asymptotic stability. The results for example are used to illustrate the feasibility and the effectiveness of the method.

Robust Tracking Control for Switched Fuzzy Systems with Fast Switching Controller

This paper addresses the problem of designing robust tracking controls for a class of switched fuzzy (SF) systems with time delay. A switched fuzzy system, which differs from existing ones, is firstly employed to describe a nonlinear system. Next, a fast switching controller consisting of a number of simple subcontrollers is proposed. The smooth transition is governed by using the fast switching controller. Tracking hybrid control schemes which are based upon a combination of the H∞ tracking theory, fast switching control algorithm, and switching law design are developed such that the H∞ model referent tracking performance is guaranteed. Since convex combination techniques are used to derive the delay independent criteria, some subsystems are allowed to be unstable. Finally, various comparisons of the elaborated examples are conducted to demonstrate the effectiveness of the proposed control design approach. All results illustrate good control performances as desired.

Nonfragile control for a class of uncertain switching fuzzy time-delay systems

A sufficient condition for the existence of nonfragile state-feedback controllers and a switching law for a class of uncertain switching fuzzy time-delay systems are proposed based on the multiple Lyapunov functions technique, under the assumption that the controller gain to be designed has variations. The corresponding results are all formulated in terms of linear matrix inequalities (LMIs). Simulation results show the effectiveness of the design method.

Delay-dependent H∞ Control for T-S Fuzzy Systems Based on a Switching Fuzzy Model and Piecewise Lyapunov Function

This paper studies the problem of H ∞ control 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 with H ∞ performance are derived for the switching fuzzy systems 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. Finally, a design example is given to show the validity of the proposed method.

Reliable Adaptive Control for Switched Fuzzy Systems

A model of a kind of uncertain switched fuzzy systems is presented first, in which each subsystem is an uncertain fuzzy system. Then the robust stabilization problem to the system is studied and a solution proposed. When the upper bounds of the disturbances are unknown, and the actuator is serious failure and the residual part of actuator can not make original system stable, a reliable robust adaptive controller is constructed to guarantee the closed-loop system is uniformly ultimately bounded via using switching technique and multiple Lyapunov function approach. The switching strategy achieving system uniformly ultimately bounded of the uncertain switched fuzzy system is given. An illustrative example is given that demonstrates the feasibility and the effectiveness of the proposed method.

Robust Output Feedback Control for a Class of Uncertain Switching Fuzzy Systems

Abstract The problem of robust output-feedback control for a class of uncertain switching fuzzy control systems is investigated. Asymptotic stability of the observer, based on the error equation, is obtained by using the switching technique and the common Lyapunov function method. Switching laws are also designed via using single Lyapunov function method for observer equation such that the closed-loop system is asymptotically stable. The sufficient condition for the asymptotic stability of the uncertain switching fuzzy control system is transformed into standard solvable LMIs. An illustrative example along with the respective simulation results is give to demonstrate the effectiveness of the proposed design synthesis.