H∞ control of nonlinear continuous-time systems based on dynamical fuzzy models

This paper presents a solution of the H_∞ control problem for a class of continuous-time nonlinear systems. The method is based on a fuzzy dynamical model of the nonlinear system. A suitable piecewise differentiate quadratic (PDQ) Lyapunov function is used to establish asymptotic stability of the closed-loop system. Furthermore, a constructive algorithm is developed to obtain the stabilizing feedback control law. The controller design algorithm involves solving a set of suitable algebraic Riccati equations. An example is given to illustrate the application of the method     

Dissipative control for Markov jump non-linear stochastic systems based on T–S fuzzy model

The dissipative analysis and control problems for a class of Markov jump non-linear stochastic systems (MJNSSs) are investigated. A sufficient condition for the dissipativity of MJNSSs is given in terms of coupled non-linear Hamilton–Jacobi inequalities (HJIs). Generally, it is difficult to solve the coupled HJIs. In this paper, based on T–S fuzzy model, the dissipative analysis and controller design for MJNSSs is proposed via solving a set of linear matrix inequalities (LMIs) instead of HJIs. Finally, a numerical example is presented to show the effectiveness of the proposed method.     

Stability analysis of T–S fuzzy models for nonlinear multiple time-delay interconnected systems

In this paper, the Takagi–Sugeno (T–S) fuzzy model representation is extended to the stability analysis for nonlinear interconnected systems with multiple time-delays using linear matrix inequality (LMI) theory. In terms of Lyapunov’s direct method for multiple time-delay fuzzy interconnected systems, a novel LMI-based stability criterion which can be solved numerically is proposed. Then, the common P matrix of the criterion is obtained by LMI optimization algorithms to guarantee the asymptotic stability of nonlinear interconnect systems with multiple time-delay. Finally, the proposed stability conditions are demonstrated with simulations throughout this paper.     

Impulsive control for T–S fuzzy model-based chaotic systems

This paper provides an impulsive control scheme for chaotic systems based on their Takagi–Sugeno (T–S) fuzzy models. Firstly, we utilize a T–S fuzzy model to represent a chaotic system. Secondly, using comparison methods, a general asymptotical stability criteria is derived for chaotic systems with impulsive effects. Finally, as an illustrative example, Lorenz system is considered to verify the effectiveness of the control scheme.     

Evolving Takagi–Sugeno fuzzy model based on switching to neighboring models

In this paper, we propose a new online identification approach for evolving Takagi–Sugeno (TS) fuzzy models. Here, for a TS model, a certain number of models as neighboring models are defined and then the TS model switches to one of them at each stage of evolving. We define neighboring models for an in-progress (current) TS model as its fairly evolved versions, which are different with it just in two fuzzy rules. To generate neighboring models for the current model, we apply specially designed split and merge operations. By each split operation, a fuzzy rule is replaced with two rules; while by each merge operation, two fuzzy rules combine to one rule. Among neighboring models, the one with the minimum sum of squared errors – on certain time intervals – replaces the current model.To reduce the computational load of the proposed evolving TS model, straightforward relations between outputs of neighboring models and that of current model are established. Also, to reduce the number of rules, we define and use first-order TS fuzzy models whose generated local linear models can be localized in flexible fuzzy subspaces. To demonstrate the improved performance of the proposed identification approach, the efficiency of the evolving TS model is studied in prediction of monthly sunspot number and forecast of daily electrical power consumption. The prediction and modeling results are compared with that of some important existing evolving fuzzy systems.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Predictive functional control based on fuzzy T-S model for HVAC systems temperature control

In heating, ventilating and air-conditioning （HVAC） systems, there exist severe nonlinearity, time-varying nature, disturbances and uncertainties. A new predictive functional control based on Takagi-Sugeno （T-S） fuzzy model was proposed to control HVAC systems. The T-S fuzzy model of stabilized controlled process was obtained using the least squares method, then on the basis of global linear predictive model from T-S fuzzy model, the process was controlled by the predictive functional controller. Especially the feedback regulation part was developed to compensate uncertainties of fuzzy predictive model. Finally simulation test results in HVAC systems control applications showed that the proposed fuzzy model predictive functional control improves tracking effect and robustness. Compared with the conventional PID controller, this control strategy has the advantages of less overshoot and shorter setting time, etc.     

Robust H ∞ control for T–S fuzzy systems with time-varying delay

This article focuses on the problem of robust H _∞ control for uncertain T–S fuzzy systems with time-varying delay. By employing a novel technique, new delay-dependent stabilisation conditions for the existence of a robust H _∞ controller are obtained based on the parallel distributed compensation method. The result obtained is an important contribution as it establishes a new way that can reduce the conservatism without imposing any restrictions and computational efforts at the same time. In this article, all the conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using LMI optimisation techniques. Two numerical examples are given to demonstrate the merits of the approach proposed in this article. Finally, application to control a truck-trailer is also given to demonstrate the effectiveness of the proposed design method.     

Observer-based reliable passive control for uncertain T–S fuzzy systems with time-delay

This paper is concerned with the problem of observer-based reliable passive control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-delay and actuator faults. By employing Lyapunov stability theory, fault treatment method and linear matrix inequalities (LMIs), a sufficient condition on the existence of an observer-based reliable passive controller is given. Further, the LMI conditions are proposed for the observer-based reliable passive controller design. The gain of reliable controller and observer can be obtained by solving the proposed LMIs. Using the reliable passive controller, the closed-loop system is not only internally stable but also strictly passive even though some actuator components fail and system state fails to be measured completely. Finally, a truck-trailer system example is given to verify the effectiveness and advantages of the designed approach.     

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

ABSTRACT

This 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.     

Intelligent control using multiple models based on on-line learning

In this paper we deal with the problem of plants with large parameter variations under different operating modes. A novel intelligent control algorithm based on multiple models is proposed to improve the dynamical response performance. At the same time adaptive model bank is applied to establish models without prior system information. Multiple models and corresponding controllers are automatically established on-line by a conventionally adaptive model and a re-initialized one. A best controller is chosen by the performance function at every instant. The closed-loop system’s stability and asymptotical convergence of tracking error can be guaranteed. Simulation results have confirmed the validity of the proposed method.     

Delay-dependent T–S fuzzy control for nonlinear interconnected systems: Using dithers as auxiliaries

In this study, a novel approach via the composite of fuzzy controllers and dithers is presented. According to this approach, we can synthesize a set of fuzzy controllers and find appropriate dithers to stabilize nonlinear multiple time-delay (NMTD) interconnected systems. A robustness design of model-based fuzzy control is first proposed to overcome the effect of modeling errors between the NMTD interconnected subsystems and Takagi–Sugeno (T–S) fuzzy models. In terms of Lyapunov's direct method, a delay-dependent stability criterion is then derived to guarantee the asymptotic stability of NMTD interconnected systems. Based on this criterion and the decentralized control scheme, a set of model-based fuzzy controllers is synthesized via the technique of parallel distributed compensation (PDC) to stabilize the NMTD interconnected system. When the designed fuzzy controllers cannot stabilize the NMTD interconnected systems, a batch of high-frequency signals (commonly referred to as dithers) is simultaneously introduced to stabilize it. If the frequencies of dithers are high enough, the outputs of the dithered interconnected system and those of its corresponding mathematical model–the relaxed interconnected system can be made as close as desired. This makes it possible to obtain a rigorous prediction of the stability of the dithered interconnected system based on the one of the relaxed interconnected system. Finally, a numerical example is given to illustrate the feasibility of our approach.     

Research on vacuum gripper based on fuzzy control for micromanipulators

This paper presents a vacuum gripper （as an actuator of an intelligent micromanipulator） for micro objects （with a diameter of 100 - 300μm） assembly tasks. The gripper is composed of a vacuum unit and a control unit. The vacuum unit with a proportional valve and a pressure sensor, and the control unit with a PC ＋ MCU two-layered control architecture are designed. The mechanical structure, workflow and major programs of the micro-gripper are presented. This paper discusses the major components of the adhesion force acting on micro objects. Some equations of the operation conditions m three phases of pick, hold and place are derived by mechanics analysis. The pneumatic system＇s pressure loss is inevitable. There are some formulas for calculating the amount of the pressure loss, but parameters in formulas are diffficult to be quantified and evaluated. To control the working pressure accurately, a pressure controller based on fuzzy logic is designed. With MATLAB＇s fuzzy logic toolbox, simulation experiments are performed to validate the performance of the fuzzy PD controller. The gripper is characterized by a steady and reliable performance and a simple structure, and it is suitable for handling micro objects with a sub-millimeter size.     

Observer-based H ∞-control for discrete-time T–S fuzzy systems

This article further studies the observer-based H _∞-control problem for discrete-time Takagi–Sugeno (T–S) fuzzy systems. By using fuzzy Lyapunov functions and introducing slack variables, a sufficient condition, which can guarantee observer-based H _∞-control performance for T–S fuzzy systems, is proposed in terms of a set of bilinear matrix inequalities. Moreover, in the so-called two-step procedure, results of the first step are allowed to select in order to reduce the conservatism of previous approaches. In comparison with the existing literature, the proposed approach not only provides more relaxed H _∞-control conditions but also ensures better H _∞-control performance. Finally, the validity and applicability of the proposed approach are successfully demonstrated through two numerical examples.     

Passivity control for uncertain singular discrete T–S fuzzy time-delay systems subject to actuator saturation

This paper deals with passivity control for uncertain singular discrete T–S (Takagi-Sugeno) fuzzy time-delay systems subject to actuator saturation. Primarily, a sufficient condition is derived which guarantees that the uncertain singular discrete T–S (Linear matrix inequality) constraints is formulated to estimate the domain of attraction for the discrete T–S closed-loop system. At last, we show the applicability and superiority of obtained theoretical results through three simulations.     

Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems

A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minify the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.     

Dynamic modeling of SOFC based on a T–S fuzzy model

The operating temperature and voltage are the key parameters affecting the performance of Solid Oxide Fuel Cell (SOFC). In this article a Takagi–Sugeno (T–S) fuzzy model is proposed to describe the nonlinear temperature and voltage dynamic properties of the SOFC system. During the process of modeling, a Fuzzy Clustering Means (FCM) method is used to determine the nonlinear antecedent parameters, and the linear consequent parameters are identified by a recursive least squares algorithm. The validity and accuracy of modeling are tested by simulations. The simulation results show that it is feasible to establish the dynamic model of SOFC by using the T–S fuzzy identification method.     

Effective position–posture control strategy based on switching control for planar three-link underactuated mechanical system

A planar three-link passive–active–active (PAA) underactuated mechanical system is a kind of nonlinear system with a passive first joint. The position–posture control objective for the planar PAA system is to move the end effector from an initial position to a target position with a specified posture. This paper presents a switch control strategy to solve the position–posture control problem. First, a Lyapunov function is constructed based on the system control objective. Then, a set of main controllers based on this Lyapunov function are designed. However, the main controllers may make the system stabilise at one of equilibrium points, which is not the system target position. To avoid the above phenomenon, when the system is about to stabilise at one non-target position, the main controllers are switched to a set of sub-controllers, which are designed according to another Lyapunov function constructed based on the control objective of the active links. When the sub-controllers are running, their design parameters are adjusted to try to keep the derivative of the first Lyapunov function being a non-positive function. Therefore, the switch control between the main controllers and the sub-controllers realises the position–posture control objective of the system. Finally, the simulation results demonstrate the effectiveness of the switch control strategy.