Parallel Distributed Compensation Scheme Research Articles

Improved results for T-S fuzzy systems with two additive time-varying delays via an extended binary quadratic function negative-determination lemma

This paper is concerned with the stability and stabilization problems for T-S fuzzy systems with two additive time-varying delays. Firstly, a novel Lyapounov-Krasovskii functional (LKF) is constructed by delay-product-type functional method together with the state vector augmentation. In order to handle time-delay square terms introduced into the derivative of LKF, an extended binary quadratic function negative-determination lemma is proposed. A less conservative delay-dependent stability condition is developed since not only some new bounding technologies are employed to deal with integral terms, but also the proposed lemma is employed to dispose nonlinear time-delay terms in derivative of constructed function. Then, the corresponding controller design method for closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, four numerical examples are given to illustrate the superiority and effectiveness of the proposed criteria.

Parallel distributed compensation scheme for chaotic masking system via Rivest cipher 4 stream cipher

AbstractThis study presents a design methodology for Takagi‐Sugeno (T‐S) fuzzy models‐based secure communications in multiple time‐delay chaotic (MTDC) systems with Rivest cipher 4 (RC4) algorithm. The main advantage of the RC4 algorithm is that the key length does not affect the encryption and decryption speeds. To block a hacker from stealing a message, this study proposes increasing the complexity of an encrypted message (ciphertext) using a method of double encryption using the RC4 algorithm and chaotic masking. As a result, this more secure communications system can effectively defend the encrypted message (ciphertext). First, the RC4 algorithm and a key are used to encrypt the initial message (plaintext). To enhance security, the encrypted message (ciphertext) is then converted into an encrypted signal, which is a double encryption using chaotic masking. Additionally, an improved genetic algorithm (IGA) is adopted in this study, it can seek better feedback gains of fuzzy controllers to speed up the synchronization. In accordance with the IGA, a model‐based fuzzy controller is synthesized to exponentially stabilize the error systems so that the trajectories of the slave systems can approach those of the master systems. Finally, a numerical example with simulations is provided to illustrate the effectiveness of the proposed method.

Robust stability and fuzzy controller synthesis for a class of hybrid re-entrant manufacturing systems

This paper addresses the problem of stability analysis and state feedback fuzzy control design for multi-line re-entrant manufacturing systems (RMSs) with impulse-type state jumps. Under the impulse effect, the RMS is modeled as a hyperbolic impulsive partial differential equation (IPDE) that possesses hybrid characteristics. Then, a matrix inequality condition depending on the discrete dynamic information is presented to deal with the jump behavior of the IPDE at impulse instants. Moreover, a robust fuzzy controller based on the parallel distributed compensation scheme is derived to render the RMS to a desired producing mode with steady feeding and output rates. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed robust fuzzy controller.

Delay-Variation-Dependent Criteria on Stability and Stabilization for Discrete-Time T–S Fuzzy Systems With Time-Varying Delays

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches.

Robust Multi-Objective H2/H∞ Load Frequency Control of Multi-Area Interconnected Power Systems Using TS Fuzzy Modeling by Considering Delay and Uncertainty

The main objective of this paper is to design a robust multi-objective H2/H∞ delayed feedback controller for load frequency control of a multi-area interconnected power system by taking into account all theoretical and practical constraints. To achieve more precise modelling and analysis, the limitation of valve position, governor, and transmission delay are considered to guarantee of LFC system’s stability in practical applications. The nonlinear delayed system is approximated by the Takagi–Sugeno fuzzy model. Then, a parallel distributed compensation scheme is utilized for designing the control system of the overall system. The proposed multi-objective and robust H2/H∞ controller simultaneously minimizes the H2 and H∞ control performance indexes. Finally, simulation results verify the robustness and effectiveness of the proposed scheme in dealing with the impact of load disturbances, model uncertainties, transmission time delays, and nonlinearities in the model.

Design of Interval Type-2 Fuzzy Controllers for Active Magnetic Bearing Systems

This article proposes an active levitation control system composed of an active magnetic bearing (AMB) rotor and an interval type-2 (IT2) model-based fuzzy logic controller (FLC). The controller aims to achieve fast and stable levitation by compensating for system uncertainties via proper design of IT2 membership functions. In particular, the complex nonlinear dynamics of the AMB are modeled as a set of local linear systems around multiple operating points, which can be stabilized by a parallel distributed compensation scheme. Sufficient conditions are derived to guarantee the asymptotical stability of the closed-loop system based on the linear matrix inequality approach and the Lyapunov stability theory. Moreover, input constraints are applied in an enhanced version of the controller. Experiments on a real AMB platform were conducted to demonstrate the effectiveness and superiority of the proposed IT2 FLC.

Stability and stabilization for delayed fuzzy systems via reciprocally convex matrix inequality

This paper focuses on the problems of stability and stabilization for time-delayed fuzzy systems. By establishing a novel Lyapunov-Krasovskii functional (LKF) and using an extended reciprocally convex matrix inequality with auxiliary function integral inequality, an improved stability condition is proposed. To further improve the results, a delay-product-type term is introduced into the LKF. Then, a delay-dependent stabilization condition is developed based on parallel distributed compensation (PDC) scheme by some linearization techniques. Finally, the efficiency and benefits of the stability criterion and controller design method are illustrated by several classical numerical examples.

Finite-time Control for Takagi-Sugeno Fuzzy Systems with Time-varying Delay

This paper focuses on the problem of finite-time control for Takagi-Sugeno (T-S) fuzzy systems with time-varying delay and norm-bounded disturbance. By constructing a new augmented Lyapunov-Krasovskii functional, a delay-dependent finite-time boundedness criterion is derived for the T-S fuzzy time-delay system by aid of the auxiliary function-based integral inequalities and the reciprocally convex combination technique. Then, based on the parallel distributed compensation scheme, a state feedback controller is designed to ensure finite-time boundness of the closed-loop T-S fuzzy system, which can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.

Fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints

• The T-S fuzzy method is used to approximate the nonlinear uncertain dynamics. • A finite frequency control criterion is formulated based on the Lyapunov theory. • A parallel-distributed compensation strategy is used in the fuzzy SOF controller. This paper investigates the problem of fuzzy finite-frequency output feedback control for nonlinear active suspension systems with time delay and output constraints. Firstly, as the physical suspension systems always exist the phenomenon of sprung and un-sprung mass variation and time delay, the Takagi-Sugeno (T-S) fuzzy model is adopted to represent the nonlinear uncertain active suspension system with uncertainties and time delay. Secondly, since the human body is much more sensitive to vertical vibrations between 4 and 8 Hz, a finite-frequency control criterion is formulated for the controller deign with consideration of time delay and output constraints. Other mechanical constraints such as suspension travel, tire dynamic deflection and actuator saturation are also considered. Thirdly, on a practical point of view, not all the states are online measurable. Hence, a novel fuzzy static output feedback (SOF) controller is proposed by applying the parallel-distributed compensation (PDC) scheme. The sufficient conditions for deriving the fuzzy SOF controller are obtained in terms of linear matrix inequalities (LMIs). Finally, numerical simulations on a quarter-car suspension model are conducted to validate the effectiveness and applicability of the proposed fuzzy SOF controller.

Stability and Stabilization of T-S Fuzzy Systems With Time-Varying Delays via Delay-Product-Type Functional Method.

This paper is concerned with the stability and stabilization problems of T-S fuzzy systems with time-varying delays. The purpose is to develop a new state-feedback controller design method with less conservatism. First, a novel Lyapunov-Krasovskii functional is constructed by combining delay-product-type functional method together with the state vector augmentation. By utilizing Wirtinger-based integral inequality and an extended reciprocally convex matrix inequality, a less conservative delay-dependent stability condition is developed. Then, the corresponding controller design method for the closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, two classic numerical examples are given to show the effectiveness and merits of the proposed approaches.

Design of robust <i>H</i><SUB align="right">∞ fuzzy output feedback controller for affine nonlinear systems: fuzzy Lyapunov function approach

In this paper, we propose a new systematic approach based on non-quadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.

Design of robust H_ fuzzy output feedback controller for affine nonlinear systems: Fuzzy Lyapunov function approach

In this paper, we propose a new systematic approach based on non-quadratic Lyapunov function and technique of introducing slack matrices, for a class of affine nonlinear systems with disturbance. To achieve the goal, first, the affine nonlinear system is represented via Takagi-Sugeno (T-S) fuzzy bilinear model. Subsequently, the robust H∞ controller is designed based on parallel distributed compensation (PDC) scheme. Then, the stability conditions are derived in terms of linear matrix inequalities (LMIs) by utilising Lyapunov function. Moreover, some slack matrices are proposed to reduce the conservativeness of the LMI stability conditions. Finally, for illustrating the merits and verifying the effectiveness of the proposed approach, the application of an isothermal continuous stirred tank reactor (CSTR) for Van de Vusse reactor is discussed in details.

Optimal fuzzy tracking control with obstacles avoidance for a mobile robot based on Takagi-Sugeno fuzzy model

This paper presents a trajectory tracking control approach for a mobile robot in the presence of static obstacles on the reference trajectory. The tracking control is developed based on the fuzzy parallel distributed compensation scheme where the linear quadratic regulator is used as a state feedback controller for each subsystem. The obstacle avoidance task is accomplished by applying a linear quadratic regulator on the overall open loop Takagi-Sugeno (T-S) fuzzy system, in which the weighting matrices are adjusted dynamically using a fuzzy controller. A fuzzy fusion controller is designed to combine the tracking and the obstacle avoidance velocities in order to perform both tasks simultaneously. Simulation results illustrate the effectiveness of the proposed control strategy.

Synchronization of IT2 stochastic fuzzy complex dynamical networks with time-varying delay via fuzzy pinning control

In this paper, the problem of synchronization on interval type-2 (IT2) stochastic fuzzy complex dynamical networks (CDNs) with time-varying delay via fuzzy pinning control is fully studied. Firstly, a more general complex network model is considered, which involves the time-varying delay, IT2 fuzzy and stochastic effects. More specifically, IT2 fuzzy model, as a meaningful fuzzy scheme, is investigated for the first time in CDNs. Then, with the aid of Lyapunov stability theory and stochastic analysis technique, some new sufficient criteria are established to ensure synchronization of the addressed systems. Moreover, on basis of the parallel-distributed compensation (PDC) scheme, two effective fuzzy pinning control protocols are proposed to achieve the synchronization. Finally, a numerical example is performed to illustrate the effectiveness and superiority of the derived theoretical results.

Exponential stability analysis and [formula omitted]-gain control synthesis for positive switched T–S fuzzy systems

In this paper, the problems of exponential stability analysis and weighted L2-gain control synthesis for positive switched T–S fuzzy systems are addressed. Firstly, by proposing a piecewise quadratic copositive Lyapunov function, a less conservative stability condition for positive switched T–S fuzzy systems is derived for the first time. Then, sufficient conditions for the positive switched T–S fuzzy system to be exponentially stable with a weighted L2-gain performance are obtained. Based on the obtained results, a state-feedback controller by the parallel distributed compensation scheme is designed to stabilize the positive switched T–S fuzzy system, while guaranteeing the prescribed weighted L2-gain performance and positivity in closed-loop. Finally, two numerical examples are presented to demonstrate the effectiveness of the obtained theoretical results.

H∞stabilization for sampling fuzzy systems with asynchronous constraints on membership functions

This paper investigates the problem of $H_\infty $ stabilization for nonuniform sampling fuzzy systems. To achieve better performance, a parallel distributed compensation scheme is proposed to design a nonlinear controller. By taking the deviation bounds of asynchronous normalized membership functions into account, the $H_\infty $ stability criterion is first obtained, which is dependent on the deviation bounds of asynchronous normalized membership functions. To reduce the computational complexity, a method for eliminating slack variables and a structured vertex separator for reducing the number of linear matrix inequalities are provided, and then an $H_\infty $ stabilization criterion with less complexity and less conservatism is obtained. Finally, an illustrative example is given to show the effectiveness of the proposed method and the significant improvement on the existing results.

Output consensus for heterogeneous nonlinear multi-agent systems based on T-S fuzzy model

In this paper, the output consensus problem of general heterogeneous nonlinear multi-agent systems subject to different disturbances is considered. A kind of Takagi-Sukeno fuzzy modeling method is used to describe the nonlinear agents’ dynamics. Based on the model, a distributed fuzzy observer and controller are designed based on parallel distributed compensation scheme and internal reference models such that the heterogeneous nonlinear multi-agent systems can achieve output consensus. Then a necessary and sufficient condition is presented for the output consensus problem. And it is shown that the consensus trajectory of the global fuzzy model is determined by the network topology and the initial states of the internal reference models. Finally, some simulations are given to illustrate and verify the effectiveness of the proposed scheme.

Reliable fuzzy H∞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping

A fault-tolerant fuzzy H∞ control design approach for active suspension of in-wheel motor driven electric vehicles in the presence of sprung mass variation, actuator faults and control input constraints is proposed. The controller is designed based on the quarter-car active suspension model with a dynamic-damping-in-wheel-motor-driven-system, in which the suspended motor is operated as a dynamic absorber. The Takagi-Sugeno (T-S) fuzzy model is used to model this suspension with possible sprung mass variation. The parallel-distributed compensation (PDC) scheme is deployed to derive a fault-tolerant fuzzy controller for the T-S fuzzy suspension model. In order to reduce the motor wear caused by the dynamic force transmitted to the in-wheel motor, the dynamic force is taken as an additional controlled output besides the traditional optimization objectives such as sprung mass acceleration, suspension deflection and actuator saturation. The H∞ performance of the proposed controller is derived as linear matrix inequalities (LMIs) comprising three equality constraints which are solved efficiently by means of MATLAB LMI Toolbox. The proposed controller is applied to an electric vehicle suspension and its effectiveness is demonstrated through computer simulation.

Fault Detection and Isolation for Affine Fuzzy Systems With Sensor Faults

This paper investigates the fault detection and isolation (FDI) problem for a class of nonlinear systems with sensor outage faults. The considered nonlinear systems are described as affine fuzzy models, and the system outputs are chosen as the premise variables of fuzzy models. Different from the existing results, the influence of sensor faults on premise variables is considered. As a result, the well-known parallel distributed compensation scheme cannot be used for FDI filters design. By using the structural information encoded in the fuzzy rules, the affine fuzzy system is represented by multiple operating-regime-based models in fault-free case and faulty cases. In the multiple-model scheme, a bank of piecewise FDI filters are constructed, each of them is based on the affine fuzzy model that describes the system in the presence of a specified fault. The fault-dependent residual signals generated from the filters are used for detecting and isolating the specified fault. The FDI filter design conditions are obtained in the formulation of linear matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness and merits of the proposed method.

Fuzzy-Model-Based Robust $H_{\infty}$ Design of Nonlinear Packetized Networked Control Systems

This paper is concerned with the fuzzy-model-based robust $H_{\infty}$ design of a nonlinear packetized networked control system with time-varying transmission delays and transmission intervals based on a delay-distribution approach combined with an improved Lyapunov–Krasovskii method. By the delay-distribution approach, the real-time distribution of input delays is described as a dependent and nonidentically distributed process, and the nonlinear packetized networked control system is modeled as a novel randomly switched Takagi–Sugeno fuzzy system with multiple uncertain input-delay subsystems. The improved Lyapunov–Krasovskii method is proposed to more rationally exploit the real-time distribution of input delays and the synchronous membership functions of the Takagi–Sugeno fuzzy models of the plant and the packetized parallel distributed compensation scheme. New de- lay-distribution-dependent sufficient conditions are derived for the deterministic robust exponential stability and $H_{\infty}$ performance of the overall system. The resulting controller design method of the packetized parallel distributed compensation scheme is equivalent to an iterative linear optimization algorithm with linear matrix inequality constraints. Detailed numerical examples are presented to substantiate the effectiveness and advantage of our theoretical results.