Fuzzy State Feedback Controller Research Articles

Local Stabilization of Nonlinear Discrete-Time Systems Subject to Amplitude Bounded Disturbances

The stabilization problem of nonlinear discrete-time systems subject to amplitude bounded disturbances by means of Takagi-Sugeno (T-S) fuzzy models is considered in this paper. The linear matrix inequality (LMI) approach is applied to design a state feedback fuzzy controller such that the system trajectories are ultimately bounded, that is, the state trajectory starting in a set of admissible initial conditions is guaranteed to converge in finite time to a nearby region of the state space origin. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems.

Disturbance Rejection of Interval Type-2 Fuzzy Systems Based on Equivalence-Input-Disturbance Approach

This paper focuses on the problem of disturbance rejection for a class of interval type-2 (IT-2) fuzzy systems via equivalence-input-disturbance (EID)-based approach. The main objective of this work is to design a fuzzy state-feedback controller combined with a disturbance estimator such that the output of the fuzzy system perfectly tracks the given reference signal without steady-state error and produces an EID to eliminate the influence of the actual disturbances. By constructing a suitable Lyapunov function and using linear matrix inequality (LMI) technique, a new set of sufficient conditions is established in terms of linear matrix inequalities for the existence of fuzzy controller. Finally, a simple pendulum model is considered to illustrate the effectiveness and applicability of the proposed EID-based control design.

Random fuzzy slow state feedback control for networked two time-scale nonlinear systems with time-delay and data packets dropout

The random fuzzy slow state feedback control approaches based on a standard discrete-time fuzzy singularly perturbed model (SDTFSPM) are investigated for networked two time-scale nonlinear systems (NTTSNSs). A SDTFSPM is constructed firstly to describe considered TTSNSs. Based on the SDTFSPM, random fuzzy slow state feedback controllers (RFSSFCs) with data packets dropout and the RFSSFC with time-delay and data packets dropout for NTTSNSs are designed, respectively. Controller existence conditions described by a set of e-dependent LMIs are provided. Simulation results show that presented methods not only can overcome time-delay and random date packets dropout but also can restrain flexible vibration caused by fast time-scales to stabilise NTTSNSs. In contrast to the existing results, the proposed methods can obtain the higher control performance and handle NTTSNSs with high dimension, so they have better practical value.

T-S Fuzzy Modelling and H∞ Attitude Control for Hypersonic Gliding Vehicles

This paper addresses the T-S fuzzy modelling and H∞ attitude control in three channels for hypersonic gliding vehicles (HGVs). First, the control-oriented affine nonlinear model has been established which is transformed from the reentry dynamics. Then, based on Taylor’s expansion approach and the fuzzy linearization approach, the homogeneous T-S local modelling technique for HGVs is proposed. Given the approximation accuracy and controller design complexity, appropriate fuzzy premise variables and operating points of interest are selected to construct the T-S homogeneous submodels. With so-called fuzzy blending, the original plant is transformed into the overall T-S fuzzy model with disturbance. By utilizing Lyapunov functional approach, a state feedback fuzzy controller has been designed based on relaxed linear matrix inequality (LMI) conditions to stable the original plants with a prescribed H∞ performance of disturbance. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed H∞ T-S fuzzy controller for the original attitude dynamics; the superiority of the designed T-S fuzzy controller compared with other local controllers based on the constructed fuzzy model is shown as well.

Designing a Fuzzy Type-2 Model-based Robust Controller for Ball and Beam System

In the real world an important set of existing systems are inherently non-linear and unstable and essentially require feedback control for effective and safe performance. This paper investigates the designing of an IT-2 fuzzy state feedback control for the ball and beam system. We present the system with an IT-2 fuzzy model and construct an interval fuzzy state feedback controller with an extended dissipativity performance. Finally, the existence conditions, the stability analysis and control design problem are obtained in term of convex optimization problems, which can be solved by standard software. At the end, we present the simulation results.

Delay-dependent stabilization of discrete-time interval type-2 T–S fuzzy systems with time-varying delay

This study focuses on the stabilization problem of discrete-time interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy systems with time-varying delay. A new IT2 fuzzy state feedback controller that does not share the same membership functions and number of rules with the IT2 T–S fuzzy model is designed to close the feedback loop. A novel fuzzy Lyapunov–Krasovskii function (FLKF) is introduced based on the delay partitioning technique to derive the existence conditions of the IT2 fuzzy state feedback controller. The proposed FLKF does not require all the involved symmetric matrices to be positive definite. Several advanced inequalities and the boundary information on membership functions are used to achieve delay-dependent stabilization conditions in terms of linear matrix inequalities. Two numerical examples are provided to show the effectiveness of the proposed approach.

Adaptive Fuzzy Tracking Control Design for SISO Uncertain Nonstrict Feedback Nonlinear Systems

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods.

AQM scheme design for TCP network via Takagi‐Sugeno fuzzy method

This paper proposes a novel T‐S fuzzy control method instead of the traditional linear system control method to improve the TCP network performance. Thus a TCP network can be modeled as a T‐S fuzzy system, and by use of linear matrix inequality method and cone complementarity linearization algorithm, a fuzzy state feedback controller is provided while considering the problem of the asynchronous membership grades between the controller and the plant. Simulation results are presented to show that the proposed control approach can guarantee the asymptotical stability of the studied system and the desired queue size. © 2016 Wiley Periodicals, Inc. Complexity 21: 606–612, 2016

Imperfect premise matching controller design for T-S fuzzy systems under network environments

This paper focuses on an imperfect premise matching controller design for T-S fuzzy systems under network environments. Different with the traditional parallel distribution compensation (PDC) method, the same premises between the PDC controller and the T-S fuzzy systems are no longer needed again in the proposed method. Under consideration of the unmatched grades of membership in the networked T-S fuzzy systems, a unified T-S fuzzy model is firstly proposed, in which a networked state-feedback fuzzy controller with communication delays is used to reconstruct the system. Then, based on the constructed model and by use of the Wirtinger-based inequality technique to deal with the cross items, two less conservative stability and stabilization criteria are derived to enhance the design flexibility. Finally, two numerical examples are used to show the effectiveness of proposed method.

T-S fuzzy model based adaptive fuzzy current tracking control of three-phase active power filter

This paper proposed an adaptive fuzzy state feedback controller for a three-phase active power filter (APF) based on a Takagi-Sugeno (T-S) fuzzy model. The T-S fuzzy model is based on the APF dynamic model in the dq frame, which ensures that the current control dynamic and DC capacitor voltage dynamic become decoupled. By using the parallel distributed compensation (PDC), local linear state feedback controller could be designed for each T-S fuzzy sub-model. To deal with the parametric uncertainties and external disturbances, a parameter estimation scheme for tuning the parameters of T-S fuzzy model is designed and the parameters are adjusted online by the adaptive law derived from the Lyapunov stability analysis. Simulation studies demonstrate that the proposed control method exhibit excellent performance in both steady state and transient operation during balanced and unbalanced load, and source voltage.

An Optimal Divisioning Technique to Stabilization Synthesis of T-S Fuzzy Delayed Systems.

This paper investigates the problem of stability analysis and stabilization for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay. By using appropriately chosen Lyapunov-Krasovskii functional, together with the reciprocally convex a new sufficient stability condition with the idea of delay partitioning approach is proposed for the delayed T-S fuzzy systems, which significantly reduces conservatism as compared with the existing results. On the basis of the obtained stability condition, the state-feedback fuzzy controller via parallel distributed compensation law is developed for the resulting fuzzy delayed systems. Furthermore, the parameters of the proposed fuzzy controller are derived in terms of linear matrix inequalities, which can be easily obtained by the optimization techniques. Finally, three examples (one of them is the benchmark inverted pendulum) are used to verify and illustrate the effectiveness of the proposed technique.

Nonquadratic Lyapunov Functions for Nonlinear Takagi-Sugeno Discrete Time Uncertain Systems Analysis and Control

This paper deals with the analysis and design of the state feedback fuzzy controller for a class of discrete time Takagi -Sugeno (T-S) fuzzy uncertain systems. The adopted framework is based on the Lyapunov theory and uses the linear matrix inequality (LMI) formalism. The main goal is to reduce the conservatism of the stabilization conditions using some particular Lyapunov functions. Four nonquadratic Lyapunov Functions are used. This Lyapunov function represent an extention from two Lypaunov functions existing in the literature. Their influence in the stabilization region (feasible area of stabilization) is shown through examples, the stabilization conditions of controller for discrete time T-S parametric uncertain systems is demonstrated with the variation of the lyapunov functions between (k, k+1) and (k, k+t) sample times. The controller gain can be obtained via solving several linear matrix inequalities (LMIs). Through the examples and simulations, we demonstrate their uses and their robustness. Comparative study verify the effectiveness of the proposed methods.

State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions

This paper is concerned with the problems of state and output feedback control for interval type-2 (IT2) fuzzy systems with mismatched membership functions. The IT2 fuzzy model and the IT2 state and output feedback controllers do not share the same membership functions. A novel performance index, which is expressed as an extended dissipativity performance, is introduced to be a generalization of $H_{\infty }$ , $L_{2}$ – $L_{\infty }$ , passive, and dissipativity performances indexes. First, the IT2 Takagi–Sugeno fuzzy model and the controllers are constructed by considering the mismatched membership functions. Second, on the basis of Lyapunov stability theory, the IT2 fuzzy state and output feedback controllers are designed, respectively, to guarantee that the closed-loop system is asymptotically stable with extended dissipativity performance. The existence conditions of the two kinds of controllers are obtained in terms of convex optimization problems, which can be solved by standard software. Finally, simulation results are provided to illustrate the effectiveness of the proposed methods.

Interval Type-2 Fuzzy Model Predictive Control of Nonlinear Networked Control Systems

In this paper, the problem of fuzzy predictive control of nonlinear networked control systems subject to parameter uncertainties and defective communication links is studied. Stochastic variables with Bernoulli random binary distribution are used to represent the defective communication links with packets loss occurring intermittently between the controller and the physical plant. An interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model is employed to describe the nonlinear plant subject to parameter uncertainties, which can be captured with the lower and upper membership functions. The IT2 fuzzy model and IT2 fuzzy controller are not required to share the same lower and upper membership functions. In order to design the state-feedback fuzzy model predictive controller, an optimization problem which minimizes the upper bound of a quadratic objective function subject to input constraints and packets dropout is formulated and solved at every sampling instant in the finite time horizon. By introducing some slack matrices, less conservative conditions are developed for system stability analysis. Two examples are given to demonstrate the effectiveness and merits of the proposed new design techniques.

A Learning-Based Fault Tolerant Tracking Control of an Unmanned Quadrotor Helicopter

This paper presents a novel learning-based fault tolerant tracking control approach by using an extended Kalman filter (EKF) to optimize a Mamdani fuzzy state-feedback tracking controller. First, a robust state-feedback tracking controller is designed as the baseline controller to guarantee the expected system performance in the fault-free condition. Then, the EKF is employed to regulate the shape of membership functions and rules of fuzzy controller to adapt with the working conditions automatically after the occurrence of actuator faults. Next, based on the modified fuzzy membership functions and rules, the baseline controller is readjusted to properly compensate the adverse effects of actuator faults and asymptotically stabilize the closed-loop system. Finally, in order to verify the effectiveness of the proposed method, several groups of numerical simulations are carried out by comparing the performance of a tracking control scheme and the presented technique. Simulation results demonstrate that the proposed method is effective for optimizing the fuzzy tracking controller on-line and counteracting the side effects of actuator faults, and the control performance is significantly improved as well.

A Unified Anti-Windup Technique for Fuzzy and Sliding Mode Controllers

This paper proposes the unified treatment of an anti-windup technique for fuzzy and sliding mode controllers. A back-calculation and tracking anti-windup scheme is proposed in order to prevent the zero error integrator wind-up in the structures of state feedback fuzzy controllers and sliding mode controllers. The state feedback sliding mode controllers are based on the state feedback-based computation of the switching variable. An example that copes with the position control of an electro-hydraulic servo-system is presented. The conclusions are pointed out on the basis of digital simulation results for the state feedback fuzzy controller.

Resilient finite‐time stabilization of fuzzy stochastic systems with randomly occurring uncertainties and randomly occurring gain fluctuations

This paper addresses the problem of resilient finite-time boundedness of a class of Takagi–Sugeno (T–S) fuzzy stochastic systems, in which there may happen the phenomena of randomly occurring uncertainties and randomly occurring gain fluctuations simultaneously. Two independent Bernoulli distributions are introduced to describe these random phenomena. And then, a resilient H∞ state feedback fuzzy controller is designed such that the closed-loop fuzzy system is finite-time stochastic bounded with a prescribed H∞ performance. Moreover, the sufficient conditions on the existence of the finite-time H∞ controller are derived. A numerical example is exploited to illustrate the effectiveness and potentials of the proposed approach.

<inline-formula><tex-math>$H_\infty$</tex-math></inline-formula> Fuzzy Control for a Class of Nonlinear Coupled ODE-PDE Systems With Input Constraint

This paper deals with the problem of $H_\infty$ fuzzy control design with an input constraint for a class of coupled systems, which consist of an $n$ -dimensional nonlinear subsystem of ordinary differential equations (ODEs) and a scalar linear parabolic subsystem of partial differential equation (PDE) connected in feedback. Initially, the nonlinear coupled system is represented by a Takagi–Sugeno (T–S) fuzzy-coupled ODE-PDE model. Then, based on the fuzzy model and parallel distributed compensation scheme, a fuzzy state feedback control design is developed via Lyapunov's direct method, such that the resulting closed-loop fuzzy-coupled system is exponentially stable, and a prescribed $H_\infty$ performance of disturbance attenuation is satisfied. The existing condition of the proposed $H_\infty$ fuzzy controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude, a suboptimal $H_\infty$ -constrained fuzzy control problem is also addressed, which is formulated as an LMI optimization problem. Finally, the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness.

A T–S Fuzzy Approach to the Local Stabilization of Nonlinear Discrete-Time Systems Subject to Energy-Bounded Disturbances

This paper addresses the local stabilization problem of nonlinear discrete-time systems subject to energy-bounded disturbances by means of T–S fuzzy models. A fuzzy state feedback controller is designed such that the input-to-state stability in the \(\ell _2\) sense of the original nonlinear system is guaranteed in a bounded region of the state space. Such a region is related to the exactness of the T–S model and describes the domain around the origin where the convexity property remains valid. In addition, an estimate of the closed-loop reachable set is provided for a given class of \(\ell _2\) disturbances. Three (convex) optimization problems are proposed to either minimize the estimate of the reachable set, improve the disturbance tolerance or minimize the \(\ell _2\)-gain from the disturbance input to the regulated output. Numerical examples are considered to illustrate the approach demonstrating the effectiveness of the proposed technique for the control synthesis of nonlinear discrete-time systems.

Robust stabilization for uncertain Markovian jump fuzzy systems based on free weighting matrix method

This paper presents a new methodology of robust state feedback fuzzy controller based on free weighting matrix method for a class of uncertain Markovian jump nonlinear systems. The class of systems under consideration is represented by the T–S fuzzy model with partly known transition probability matrix. The free weighting matrix method is proposed to obtain a less conservative stochastic stability criterion of the uncertain Markovian jump fuzzy systems (MJFSs) in terms of linear matrix inequalities (LMIs). Furthermore, a sufficient condition for the mode-dependent state feedback fuzzy controller is derived for the MJFSs for all admissible parameter uncertainties. Finally, a simulation example is provided to illustrate the effectiveness of the proposed methodology.