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This study addresses adaptive fuzzy control for an axially moving slung-load cable system (AMSLCS) of a helicopter in the presence of an actuator fault, system uncertainty, and disturbances with the aid of a fuzzy logic system (FLS). The actuator fault considered is depicted by a more general faulty plant that includes an unknown actuator gain fault and a fault deviation vector. First, to compensate for system uncertainty and the fault deviation vector, a fuzzy control technique is adopted. Then, under the introduced FLS, a novel adaptive fuzzy control law is developed by employing a rigorous Lyapunov derivation. The closed-loop system of the AMSLCS is proved to be uniformly bounded even when considering the actuator fault, system uncertainty, and disturbances. Finally, a simulation is executed to expound the performance of the developed controller. [ABSTRACT FROM AUTHOR]

This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi–Sugeno (T–S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T–S fuzzy PDdE model and a Lyapunov–Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stabilization problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems via sampled-data fuzzy control approach. Initially, the nonlinear PDE system is accurately represented by the Takagi–Sugeno (T–S) fuzzy PDE model. Then, based on the T–S fuzzy PDE model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller under spatially point measurements such that the closed-loop fuzzy PDE system is exponentially stable with a given decay rate. The stabilization conditions are presented in terms of a set of linear matrix inequalities (LMIs). Finally, simulation results on the control of the diffusion equation and the FitzHugh–Nagumo (FHN) equation to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper presents a Lyapunov and partial differential equation (PDE)-based methodology to solve static collocated piecewise fuzzy control design of quasi-linear parabolic PDE systems subject to periodic boundary conditions. Two types of piecewise control, i.e., globally piecewise control and locally piecewise control are considered, respectively. A Takagi–Sugeno (T–S) fuzzy PDE model that is constructed via local sector nonlinearity method is first employed to accurately describe spatiotemporal dynamics of quasi-linear PDEs. Based on the T–S fuzzy PDE model, a static collocated piecewise fuzzy feedback controller is constructed to guarantee the locally exponential stability of the resulting closed-loop system. Sufficient conditions for the existence of such fuzzy controller are developed by applying vector-valued Poincaré–Wirtinger inequality and its variants and a linear matrix inequality (LMI) relaxation technique. These sufficient conditions are presented in terms of standard LMIs. Finally, the performance of the suggested fuzzy controller is illustrated by numerical simulation results of a nonlinear PDE system described by quasi-linear FitzHugh–Nagumo equation with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

This paper employs a Takagi–Sugeno (T-S) fuzzy partial differential equation (PDE) model to solve the problem of sampled-data exponential stabilization in the sense of spatial $L^\infty$ norm $\Vert \cdot \Vert _\infty$ for a class of nonlinear parabolic distributed parameter systems (DPSs), where only a few actuators and sensors are discretely distributed in space. Initially, a T-S fuzzy PDE model is assumed to be derived by the sector nonlinearity method to accurately describe complex spatiotemporal dynamics of the nonlinear DPSs. Subsequently, a static sampled-data fuzzy local state feedback controller is constructed based on the T-S fuzzy PDE model. By constructing an appropriate Lyapunov–Krasovskii functional candidate and employing vector-valued Wirtinger's inequalities, a variation of vector-valued Poincaré–Wirtinger inequality in one-dimensional spatial domain, as well as a vector-valued Agmon's inequality, it is shown that the suggested sampled-data fuzzy controller exponentially stabilizes the nonlinear DPSs in the sense of $\Vert \cdot \Vert _\infty$ , if sufficient conditions presented in term of standard linear matrix inequalities (LMIs) are fulfilled. Moreover, an LMI relaxation technique is utilized to enhance exponential stabilization ability of the suggested sampled-data fuzzy controller. Finally, the satisfactory and better performance of the suggested sampled-data fuzzy controller are demonstrated by numerical simulation results of two examples. [ABSTRACT FROM AUTHOR]

In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method. [ABSTRACT FROM PUBLISHER]

This paper gives a membership-function-dependent approach to solve the design problem of fuzzy pointwise state feedback controller for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs), where only a few actuators are discretely distributed in space. In the proposed design method, a Takagi–Sugeno (T–S) fuzzy PDE model obtained by using the sector nonlinearity method is first utilized to accurately describe the nonlinear spatiotemporal dynamics of the PDE system. As only the state information at some known specified points in the spatial domain (i.e., the pointwise state information) is available for the controller design, the favorable property offered by sharing all the same premises in the fuzzy PDE plant model and fuzzy controller cannot be employed to develop the fuzzy control design method. To overcome this drawback, a linear matrix inequality (LMI) relaxation technique is developed to enhance the stabilization ability of the fuzzy controller. Based on the T–S fuzzy PDE model, a membership-function-dependent fuzzy pointwise state feedback control design is then proposed by employing the Lyapunov technique, integration by parts, the vector-valued Wirtinger’s inequality and the LMI relaxation technique, and presented in term of standard LMIs. Finally, the satisfactory and better performance of the proposed design method are demonstrated by the extensive numerical simulation results of two numerical examples. [ABSTRACT FROM AUTHOR]

A fuzzy guaranteed cost sampled-data control problem is addressed in this paper for a class of nonlinear coupled systems of an n -dimensional lumped parameter system modeled by ordinary differential equation (ODE) with a scalar reaction–diffusion process represented by parabolic partial differential equation (PDE). A Takagi–Sugeno (T–S) fuzzy coupled ODE–PDE model is initially proposed to accurately represent the nonlinear coupled ODE–PDE system. Based on the T–S fuzzy coupled ODE–PDE model, a fuzzy sampled-data controller is subsequently developed via the Lyapunov's direct method to not only locally exponentially stabilize the nonlinear coupled system, but also provide an upper bound of the given cost function. Moreover, a suboptimal fuzzy sampled-data control design is also addressed in the sense of minimizing the upper bound of the cost function. The main contribution of this study lies in that a new parameterized linear matrix inequality (LMI) technique is proposed to reduce the conservativeness of the method, and an LMI-based fuzzy suboptimal sampled-data control design is developed for the nonlinear coupled ODE–PDE system based on this parameterized LMI technique. Simulation results on the sampled-data control of hypersonic rocket car are provided to illustrate the effectiveness and merit of the design method. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fuzzy control design for a class of nonlinear distributed parameter systems represented by a cascaded model consisting of a Takagi–Sugeno (T–S) fuzzy ordinary differential equation and a linear first-order hyperbolic partial differential equation (PDE), where the control input affects the entire system through a boundary condition of the PDE. This characteristic makes the PDE subject to an inhomogeneous boundary condition. A state transformation is introduced to make the inhomogeneous boundary condition homogeneous, and a composite Lyapunov function that involves a fuzzy Lyapunov function and an entropy-like Lyapunov function is constructed for the transformed system. Based on this composite Lyapunov function, a sufficient condition for the closed-loop exponential stability of the cascaded system is presented in terms of a set of algebraic linear matrix inequalities in space. Using the sector bound approach and the finite spatial domain, a linear matrix inequality-based fuzzy control design procedure is developed from the obtained stability analysis result. Finally, simulation results on two numerical examples are provided to illustrate the effectiveness and merit of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper considers the problem of multiobjective fuzzy control design for a class of nonlinear spatially distributed processes (SDPs) described by parabolic partial differential equations (PDEs), which arise naturally in the modeling of diffusion-convection-reaction processes in finite spatial domains. Initially, the modal decomposition technique is applied to the SDP to formulate it as an infinite-dimensional singular perturbation model of ordinary differential equations (ODEs). An approximate nonlinear ODE system that captures the slow dynamics of the SDP is thus derived by singular perturbations. Subsequently, the Takagi–Sugeno fuzzy model is employed to represent the finite-dimensional slow system, which is used as the basis for the control design. A linear matrix inequality (LMI) approach is then developed for the design of multiobjective fuzzy controllers such that the closed-loop SDP is exponentially stable, and an L2 performance bound is provided under a prescribed H\infty constraint of disturbance attenuation for the slow system. Furthermore, using the existing LMI optimization technique, a suboptimal fuzzy controller can be obtained in the sense of minimizing the L2 performance bound. Finally, the proposed method is applied to the control of the temperature profile of a catalytic rod. [ABSTRACT FROM PUBLISHER]

In this paper, a distributed fuzzy control design based on Proportional–spatial Derivative (P–sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi–Sugeno (T–S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T–S fuzzy PDE model, a novel distributed fuzzy P–sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz–Hugh–Nagumo equation. [ABSTRACT FROM AUTHOR]

This paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations (PDEs), for which a finite number of actuators are used. A fuzzy control design methodology is developed for these systems by combining the PDE theory and the Takagi–Sugeno (T–S) fuzzy-model-based control technique. Initially, a T–S fuzzy parabolic PDE model is proposed to accurately represent a semilinear parabolic PDE system. Then, based on the T–S fuzzy model, a Lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed-loop PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities (SDLMIs). Furthermore, a recursive algorithm is presented to solve the SDLMIs via the existing linear matrix inequality optimization techniques. Finally, numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, a PSO-based intelligent integration of design and control is proposed for one kind of nonlinear curing process. This method combines the merits of both fuzzy modeling/control and PSO method, where fuzzy modeling/control is proposed to approximate/control the nonlinear process in a large operating region and the PSO-based intelligent optimization method is developed to solve non-convex and non-differential integration problem with design and control optimized simultaneously. Finally, the proposed method is compared with the traditional sequential method on controlling the temperature profile of a nonlinear curing process. [ABSTRACT FROM AUTHOR]

Many industrial processes are spatiotemporal dynamic systems. A three-dimensional fuzzy-logic controller (3-D FLC) has been recently developed to process the inherent capability of spatiotemporal dynamic systems. Sensor placement, which is always crucial to the control of spatiotemporal dynamic systems, is also critical to the design of the 3-D FLC. In this paper, a new sensor-placement strategy is developed. Its main feature is to position the sensor by utilizing the main characteristics of spatial distribution. The key technique is to use a spatial-constrained fuzzy c-means algorithm to extract the characteristics of spatial distribution. For an easy implementation, a systematic sensor-placement design scheme in four steps (i.e., data collection, dimension reduction, data clustering, and sensor locating) is developed. Finally, control of a catalytic packed-bed reactor is taken as an application to demonstrate the effectiveness of the proposed sensor-placement scheme. [ABSTRACT FROM PUBLISHER]

An interval-valued fuzzy logic controller (I-V FLC) is presented to control a class of nonlinear distributed parameter systems. The proposed FLC is inspired by human operators' knowledge or expert experience to control a distributed parameter process from the point of view of overall space domain. Based on spatial fuzzy set, the I-V FLC employs a centralized rule base over the space domain. Using spatial membership degree fusion operation, the I-V FLC can compress spatial input information into interval-valued fuzzy sets and then execute an interval-valued rule inference mechanism; thereby the I-V FLC has the capability to process spatial information over the space domain. Compared with traditional FLCs, the I-V FLC can improve its control performance due to its increased ability to express and process spatial information. The I-V FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLCs. The results demonstrate its effectiveness to control the unknown nonlinear distributed parameter process. [ABSTRACT FROM AUTHOR]

The observer-based indirect and direct adaptive fuzzy controllers are developed for a class of SISO uncertain nonlinear systems. The proposed approaches do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations. Thus, a new hybrid adaptive fuzzy control method is proposed by combining the above adaptive fuzzy system with the H∞ control technique. Based on Lyapunov stability theorem, the proposed adaptive fuzzy control system can guarantee the stability of the whole closed-loop systems and obtain good tracking performance as well. The proposed methods are applied to an inverted pendulum system and a chaotic system and achieve satisfactory simulation results. [Copyright &y& Elsevier]

A stable direct adaptive fuzzy output tracking control scheme is developed for the single-input–single-output (SISO) unknown nonlinear systems. Using a high-gain observer, the proposed adaptive fuzzy algorithm does not require the state variables to be measurable. First, a direct adaptive fuzzy state controller is constructed with the aid of its H∞ control technique to achieve the H∞ tracking performance. Afterwards, a high-gain observer is used to estimate the system states, by which the above adaptive fuzzy state controller becomes an adaptive fuzzy output feedback control. The proposed control scheme can guarantee the stability of the closed-loop system and the good tracking performance as well. [Copyright &y& Elsevier]