Sampled-data Fuzzy Controller Research Articles

Tracking control design for interval type-2 fuzzy nonlinear unreliable networked control systems

This paper deals with the interval type-2 (IT2) fuzzy tracking control problem for nonlinear networked control systems with unreliable communication links. The plant is described by an IT2 fuzzy system, and the IT2 fuzzy sampled-data tracking controller is designed under the unreliable communication mechanism. By utilizing the Lyapunov theory, the stability demonstration is carried out under the mathematical expectation. The characteristics of membership functions are applied to enhance the stability of the IT2 fuzzy system. With the more sampling information used in the stability analysis, the less conservative sufficient condition is provided based on which a networked tracking controller is designed to ensure the anticipant tracking performance. Finally, the efficiency and the merits of this paper are shown by two simulation examples.

Exponential sampled‐data fuzzy stabilization of nonlinear systems and its application to basic buck converters

This study focuses on the exponential stability and stabilization of nonlinear systems via fuzzy sampled-data control technique. The stability and stabilization conditions are obtained through constructing suitable Lyapunov functional which contains the sampling information and the solvable linear matrix inequalities. Then, the dynamics of the nonlinear buck converter system and Lorenz system with the sampled-data controller is analyzed and designed. Finally, the proposed method is validated with a basic buck converter system model designed to reflect the characteristics of the power metal-oxide-semiconductor field-effect transistors in the numerical section. In addition, the superiority of the sufficient conditions obtained is shown by comparing with the existing methods of the Lorentz system.

Fuzzy Intermittent Extended Dissipative Control for Delayed Distributed Parameter Systems With Stochastic Disturbance: A Spatial Point Sampling Approach

In this article, the extended dissipative performance of distributed parameter systems (DPSs) with stochastic disturbances and multiple time-varying delays is studied by using a new fuzzy aperiodic intermittent sampled-data control strategy. Different from the previous fuzzy sampled-data control results, the state sampling of the proposed sampled-data controller occurs only in space and is intermittent rather than continuous in the time domain. By introducing a novel multitime-delay-dependent switched Lyapunov functional to explore the dynamic characteristics of the controlled system, and by means of the famous Jensen’s inequality with reciprocally convex approach, Wirtinger’s inequality, the criterion of the system’s mean square stabilization is established based on the LMI technique, which quantitatively reveals the relationship between the control period, the control length, and the upper bound of the control sampling interval. Especially, the optimal control gain is given by designing an optimized algorithm in the article, which greatly reduces the cost. Finally, two numerical examples are presented to demonstrate the effectiveness and superiority of the proposed approach.

Sampled-Data Adaptive Fuzzy Control of Switched Large-Scale Nonlinear Delay Systems

A decentralized adaptive fuzzy sampled-data control problem for switched large-scale nonlinear systems with time-varying delays is considered in this article. Fuzzy logic systems are applied to handle unknown nonlinear terms. A novel fuzzy adaptive law is proposed utilizing only the information of the system states at sampling instants. Moreover, a proper CLF and a new decentralized adaptive sampled-data control law are constructed to ensure that all states of the CLS are bounded. The developed strategy’s effectiveness is verified with two examples.

Decentralized sampled-data fuzzy controller design for a VTOL UAV

This study focuses on a sampled-data fuzzy decentralized tracking control problem for a quadrotor unmanned aerial vehicle (UAV) under the variable sampling rate condition. To this end, the overall dynamics of the quadrotor is expressed as a decentralized Takagi–Sugeno (T–S) fuzzy model interconnected with each other. Although the proposed decentralized control technique divides the overall UAV control system into attitude and position subsystems, the stability of the entire control system is guaranteed. Besides, in this paper, the model uncertainty, interconnection, and reference trajectory are considered as disturbances acting on the tracking error. To attenuate these disturbances, a novel sampled-data tracking control design technique is derived based on a linear reference model to be tracked and the time-dependent Lyapunov–Krasovskii functional (LKF). By doing so, both the stability of the tracking error dynamics and the minimization of tracking performance are guaranteed. Also, the proposed tracking control design method is derived as a linear matrix inequality (LMI)-based optimal problem. Finally, a simulation example is provided to demonstrate the effectiveness and feasibility of the proposed design methodology.

Extended dissipative analysis for T–S fuzzy semi-Markov jump systems with sampled-data input and actuator fault

This paper is concerned with reliable robust sampled-data control for T–S fuzzy semi-Markov jump systems (SMJSs) with time-varying delay. The asynchronous model is established, which makes the fuzzy sampled-data controller share the premise variable of the fuzzy plant with the fuzzy system. By adjusting the free weight matrix in the concept of extended dissipative, H∞, L2−L∞, passive and Q,S,R-dissipative performance are solved in a unified framework. A novel mode-dependent Lyapunov–Krasovskii functional (LKF) is constructed, which fully utilizes the characteristics of the real sampled period. Based on Lyapunov stability theory, Newton–Leibniz condition and new integral inequality techniques, some less conservative sufficient conditions are obtained to guarantee the close-loop system is stochastically stable and extended dissipative. Based on sampled-data approach, a robust reliable controller can be developed by solving the linear matrix inequalities (LMIs). The advantage and effectiveness of the proposed design method can be illustrated by the numerical example.

Switched Fuzzy Sampled-Data Control of Chaotic Systems With Input Constraints

This paper designs a sampled-data controller to exponentially stabilize a kind of chaotic systems (CSs) which are represented by T-S fuzzy model with nonuniform sampling. By employing a switched technology and Lyapunov functional dependent on fuzzy membership-functions (FMFs), a new control criterion for chaotic systems was established. Compared with the existing methods, less conservatism and a large sampling period can be obtained by above approaches. Consequently, the amount of transmitted information is greatly reduced and the efficiency of bandwidth is much improved. Finally, the proposed T-S fuzzy sampled-data (TSFSD) controller is applied to Lorenz system to prove the effectiveness of those methods.

Fuzzy quantized sampled-data control for extended dissipative analysis of T–S fuzzy system and its application to WPGSs

This paper investigates the issues of extended dissipativity performance and stabilization for T–S fuzzy model (TSFM) based wind power generation systems (WPGSs). Firstly, the stochastic coupled leakage time-varying delays (CLTVDs) and randomly occurring uncertainty parameters (ROUPs) are firstly introduced for constructing more general TSFM. Second, on basis of the time-delay-product function (TDPF) and looped function strategy, a relaxed Lyapunov–Krasovskii functional (LKF) with the negative definite term and the time-varying matrix is developed, which can get the utmost out of the information of various communication delays. Third, by utilizing the tighter integral inequalities and reciprocally convex combination technique (RCCT), new stabilization criteria are established in terms of the linear matrix inequalities (LMIs). Simultaneously, the desired fuzzy sampled-data control (FSDC) is designed under the state quantization mechanism. Finally, a simulation example is presented to validate the efficiency of the proposed result.

Takagi–Sugeno fuzzy sampled‐data model‐based less conservative stability criterion for a Francis hydropower unit's governing system

In this study, the stability analysis and controller design of a hydropower unit's governing system (HUGS) were studied based on a Takagi–Sugeno (T–S) fuzzy model and constant sampled-data control. First, according to the T–S fuzzy theory, the non-linear Francis hydro-turbine governing system under rigid water hammer is linearised and then the approximate linear system was obtained. Second, a fuzzy sampled-data controller was designed in the case of periodic sampling, and the closed-loop sampling system was discretised. After constructing the Lyapunov function and using the forward difference method, the stabilisation condition was given with less conservatism in a symmetrical linear matrix inequality form. Finally, the numerical simulation results showed that under four different sampling periods, the HUGS can quickly achieve stability and that it has different stability performance. In addition, the superiority of the controller was verified in comparison with traditional proportional–integral–derivative control and fuzzy control techniques.

T–S Fuzzy Sampled-Data Control for Nonlinear Systems With Actuator Faults and Its Application to Wind Energy System

This article concerns the problem of stability analysis of nonlinear systems under the sampled-data control (SDC) with actuator faults. The addressed nonlinear systems can be expressed by a number of linear arrangements, based on the Takagi–Sugeno (T–S) fuzzy technique. The time-dependent SDC with actuator faults of the addressed nonlinear systems delineates based on the input model of Markovian variability. The time-scheduled Lyapunov functional and the looped-functional are taken together in the production of a Lyapunov functional candidate. Based on a free matrix-based integral inequality and the Lyapunov functional, some sufficient linear matrix inequality conditions are delivered to guarantee the mean-square asymptotic stability under <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> performance of the considered sampled-data T–S fuzzy systems with actuator faults. Finally, we demonstrate the feasibility and strength of our proposed method through some examples.

Exponential stabilisation for nonlinear PDE systems via sampled-data static output feedback control

ABSTRACT This paper focuses on the problem of exponential stabilisation for nonlinear partial differential equation (PDE) systems by designing sampled-data static output feedback controller. First, the nonlinear PDE systems are reconstructed by Takagi-Sugeno (T-S) fuzzy model. Subsequently, the closed-loop systems are obtained by introducing sampled-data static output feedback fuzzy controller. Then, stability conditions of the closed-loop system are obtained based on Lyapunov function approach, which can guarantee that the considered systems are exponential stabilisation and satisfy dissipative performance. Finally, the effectiveness of the developed method is demonstrated by a simulation study.

Sampled-Data Fuzzy Control for Nonlinear Delayed Distributed Parameter Systems

Under spatially local averaged measurements (SLAMs), this article introduces a sampled-data fuzzy control (SDFC) for nonlinear delayed distributed parameter systems (DDPSs). First, we use a Takagi–Sugeno (T–S) fuzzy parabolic partial differential-difference equation (PDDE) to accurately describe the nonlinear DDPS. Then, on basis of the T–S fuzzy PDDE model, an SDFC design under SLAMs via space-dependent linear matrix inequalities (SDLMIs) is subsequently developed to ensure the exponential stability of the closed-loop nonlinear DDPSs by using inequality techniques and Lyapunov functional, where slow-varying and fast-varying delays are respected. Furthermore, to solve SDLMIs, the SDFC design problem for nonlinear DDPS under SLAMs is formulated as a linear matrix inequality feasibility problem. Finally, numerical simulations of two examples are presented to support the given SDFC strategy.

Non-fragile sampled-date dissipative analysis for uncertain T–S fuzzy time delay system with actuator saturation

In this paper, non-fragile fuzzy sampled-data control is used to analyze the dissipation of uncertain time-varying delay T–S fuzzy system under actuator saturation. First, this paper builds a novel augmented Lyapunov–Krasovskii functional that is more flexible. It involves complete information about the relevant sampled-data patterns. Second, the use of Wirtinger-based integral inequality and Newton–Leibniz formulas yields less conservative results. Next, we discuss the sufficient conditions of the dissipative performance for T–S model, then use the linear matrix inequality (LMI) to give the non-fragile fuzzy sampled-data controller with actuator saturation. Finally, the routine examples show that the advanced approach is effective and feasible and has certain advantages.

Estimator-Based $H_\infty$ Sampled-Data Fuzzy Control for Nonlinear Parabolic PDE Systems

This paper considers the estimator-based $H_{\infty }$ sampled-data fuzzy control (SDFC) problem of nonlinear parabolic partial differential equation (PDE) systems. First, a Takagi–Sugeno (T–S) fuzzy parabolic PDE model is proposed to represent the nonlinear PDE system. Second, with the aid of the T–S fuzzy PDE model, an estimator-based SDFC design ensuring the exponential stability of the closed-loop fuzzy PDE system with an $H_{\infty }$ performance is developed via a Lyapunov functional. The outcome of the estimator-based $H_{\infty }$ SDFC problem is formulated as a bilinear matrix inequality optimization problem, which is solved by an iterative algorithm on the basis of the linear matrix inequalities. Finally, for demonstrating the effectiveness of the proposed method, simulation results are provided to control the diffusion equation and the FitzHugh–Nagumo equation.

Fuzzy Sampled-Data Control for Synchronization of T-S Fuzzy Reaction-Diffusion Neural Networks With Additive Time-Varying Delays.

This article focuses on the exponential synchronization problem of T-S fuzzy reaction-diffusion neural networks (RDNNs) with additive time-varying delays (ATVDs). Two control strategies, namely, fuzzy time sampled-data control and fuzzy time-space sampled-data control are newly proposed. Compared with some existing control schemes, the two fuzzy sampled-data control schemes cannot only tolerate some uncertainties but also save the limited communication resources for the considered systems. A new fuzzy-dependent adjustable matrix inequality technique is proposed. According to different fuzzy plant and controller rules, different adjustable matrices are introduced. In comparison with some traditional estimation techniques with a determined constant matrix, the fuzzy-dependent adjustable matrix approach is more flexible. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the fuzzy-dependent adjustable matrix approach, new exponential synchronization criteria are derived for T-S fuzzy RDNNs with ATVDs. Meanwhile, the desired fuzzy time and time-space sampled-data control gains are obtained by solving a set of linear matrix inequalities (LMIs). In the end, some simulations are presented to verify the effectiveness and superiority of the obtained theoretical results.

Robust fuzzy sampled-data attitude control of spacecraft with actuator saturation and persistent disturbance

This paper is concerned with robust fuzzy attitude control of spacecraft with aperiodically sampled measurements, actuator saturation, and persistent disturbance. Takagi-Sugeno (T-S) fuzzy model is employed to describe the kinematics and dynamics of spacecraft. Under the constraint of actuator saturation, a digital fuzzy controller consisting of discrete-time states and an exponentially decaying term is newly proposed to carry out exponential attitude stabilization of the considered spacecraft. Moreover, compared with H∞ performance most often encountered when considering robust attitude control of spacecraft, L∞-gain performance is designed to deal with persistent bounded disturbance in this study. Based on time-dependent Lyapunov functional and invariant set, the stability of closed-loop system is strictly proved. With the aid of convex optimization techniques, the desired sampled-data controller can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, illustrative simulation results are presented to validate the effectiveness of the theoretical developments shown in this paper.

Fuzzy optimal control for nonlinear systems with time-varying delay via sampled-data controller

This work is devoted to a fuzzy sampled-data optimal control problem for nonlinear systems with time-varying delay in Takagi–Sugeno fuzzy form. Based on the Lyapunov–Krasovskii functional theory, some novel stability criteria are established. A fuzzy sampled-data controller is developed to ensure that the fuzzy closed-loop sampled-data control system is asymptotically stable and the guaranteed cost performance is also minimized. It is shown that the obtained results are less conservative in the stability analysis. Two examples of the computer-simulated truck-trailer system and the continuous stirred tank reactor system are provided to show the effectiveness and the merits of the proposed design.

자율주행로봇을 위한 강인 H∞ 샘플치 퍼지제어기 설계

본 논문은 수중청소로봇의 핵싱기능을 표현하는 자율주행로봇의 강인 H<SUB>∞</SUB> 샘플치제어기 설계를 논한다. 비선형 자율주행로봇의 기구학으로부터 타카기-수게노(Takagi-Sugeno) 퍼지모델을 구성한다. 샘플치제어기 설계조건은 이산시간 모델을 사용하지 않으며, 연속시간 리아푸노프(Lyapunov) 안정도이론을 기반으로 유도되며, 선형행렬부등식로 표현된다. 수치적 모의실험을 보여 제안한 기법의 적절성을 예시한다.

Reliable Fuzzy Tracking Control of Near-Space Hypersonic Vehicle Using Aperiodic Measurement Information

This paper is concerned with reliable fuzzy tracking control for a near-space hypersonic vehicle (NSHV) subject to aperiodic measurement information and stochastic actuator failures. The NSHV dynamics is approximated by the Takagi–Sugeno fuzzy models and the stochastic failures are characterized by a Markov chain. Different with the existing tracking results on NSHV, only the aperiodic sampling measurements are available during system operation. To realize the tracking objective, a reliable fuzzy sampled-data tracking control strategy is presented. An appropriate time-dependent Lyapunov function is constructed to fully capture the real sampling pattern. The sampling-interval-dependent mean square exponential stability criterion with disturbance attenuation is then established. The solution of the tracking controller gains can be obtained by solving an optimization problem. Finally, the simulation studies on NSHV dynamics in the entry phase are performed to verify the validity of the developed fuzzy tracking control strategy.

Exponential sampled-data control for T–S fuzzy systems: application to Chua's circuit

ABSTRACTThis study deals with the chaotic phenomenon of nonlinear Chua's circuit for power generator systems. Takagi–Sugeno (T–S) fuzzy model of a nonlinear system is established. By constructing a suitable Lyapunov functional, exponential stability conditions are obtained for fuzzy systems. Based on the sampled-data control theory, extreme sensitivity is visualised in the state trajectory depending on the initial conditions and sampled-data fuzzy controllers are designed in the form of linear matrix inequality (LMI). Finally, some numerical simulation results are shown that the sampled-data fuzzy control system adopts a well-designed methodology.