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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]

We propose, in this paper, a framework for time series and nonlinear system modeling, called the basis function matrix-based flexible coefficient autoregressive (BFM-FCAR) model. It has very flexible nonlinear structure. We show that many famous nonlinear time series models can be derived under this framework by choosing the proper basis function matrices. Some probabilistic properties (the conditions of geometrical ergodicity) of the BFM-FCAR model are investigated. Taking advantage of the model structure, we present an efficient parameter estimation algorithm for the proposed framework by using the variable projection method. Finally, we show how new models are generated from the proposed framework. [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]

Data-based spatio-temporal modeling has rapidly developed over the past ten years. However, traditional spatio-temporal modeling methods will encounter some uncertainty caused by model reduction. In addition, the established model is complicated and short of linguistic interpretability. In this study, a novel three-dimensional (3-D) fuzzy modeling framework without model reduction is proposed and a new 3-D fuzzy modeling method based on clustering and support vector regression is developed. This method is based on a 3-D fuzzy system that naturally fuses time/space separation and time/space synthesis into a unified framework. Utilizing the machine learning algorithms (clustering and support vector regression), a 3-D fuzzy system is constructed for modeling an unknown nonlinear distributed parameter system. The advantages of the proposed modeling method over the traditional spatio-temporal modeling method are linguistic interpretability and no reliance on model reduction. The proposed modeling method consists of three steps. First, the nearest neighborhood clustering algorithm is used to learn initial structure model of antecedent sets of 3-D fuzzy rules. Then, similarity measure is used to simplify the initial structure via combining similar fuzzy sets and similar fuzzy rules. Finally, a support vector regression algorithm is applied to calculate spatial functions in the consequent sets of 3-D fuzzy rules. The simulation results demonstrate the effectiveness of the proposed modeling method. [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]

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]

A sliding mode control strategy is developed for temperature control of a rapid thermal processing (RTP) system to enhance temperature accuracy and uniformity when heating in this work. Temperature dynamics of the RTP is nonlinear and infinite-dimensional while order of the controller should be finite due to implementation limitations. Developing a nonlinear low-order controller for the system is important if accurate and uniform control of the temperature is required. This work addresses this issue by developing a sliding mode controller based on the dominant modes of the system. The schemes are applied to a RTP system and excellent performances are achieved. [ABSTRACT FROM AUTHOR]

Many industrial processes belong to nonlinear distributed parameter systems (DPS) with significant spatio-temporal dynamics. They often work at multiple operating points due to different production and working conditions. To obtain a global model, the direct modeling and experiments in a large operating range are often very difficult. Motivated by the multi-modeling, a fuzzy-based spatio-temporal multi-modeling approach is proposed for nonlinear DPS. To obtain a reasonable operating space division, a priori information and the fuzzy clustering are used to decompose the operating space from coarse scale to fine scale gradually. To reduce the dimension in the local spatio-temporal modeling, the Karhunen–Loève method is used for the space/time separation. Both multi-modeling and space/time separation can reduce the modeling complexity. Finally, to get a smooth global model, a three-domain (3D) fuzzy integration method is proposed. Using the proposed method, the model accuracy will be improved and the experiments become easier. The effectiveness is verified by simulations. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both distributed measurement form and collocated boundary measurement form are considered. A Takagi–Sugeno (T–S) fuzzy PDE model is first applied to accurately represent the semilinear parabolic PDE system. Based on the T–S fuzzy PDE model, two types of fuzzy boundary controllers, which are easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and the vector-valued Wirtinger's inequality and presented in terms of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples. [ABSTRACT FROM PUBLISHER]

Abstract: A linear or second-order model is usually used to approximate a practical nonlinear system in probabilistic robust designs. This approximation often makes these designs less effective when the system has strong nonlinearity as well as large uncontrollable variation. In this paper, a novel probabilistic design approach is proposed to design a nonlinear system to be robust under circumstance of large random variation. First, a variable sensitivity approach is employed to place the nonlinear influence under the sensitivity matrix of the covariance model. On this basis, a robust design approach is proposed to minimize the influence of random variation in relation to the performance covariance. Since this proposed approach considers both nonlinear influence and probabilistic distribution in a large uncertain region, it can effectively ensure robustness of nonlinear systems even if large random variation exists. [Copyright &y& Elsevier]

Many industrial processes are nonlinear distributed parametersystems(DPSs). Data-based spatiotemporal modeling is required for analysisand control when the first-principles model is unknown. Because aDPS is infinite-dimensional and time–space coupled, a low-ordermodel is necessary for prediction and control in practice. For low-ordermodeling, traditional principal component analysis (PCA) is oftenused for dimension reduction and time–space separation. However,it is a linear method and leads to only one set of fixed spatial basisfunctions. Therefore, it might not be always effective for nonlinearsystems. In this study, a spatiotemporal multimodeling approach isproposed for unknown nonlinear DPSs. First, multimodel decompositionis performed, where probabilistic PCA (PPCA) is used to obtain multiplesets of spatial basis functions from the experimental data by maximizinga likelihood function. Using these multiple sets of PCA spatial basesfor time–space separation, the high-dimensionality spatiotemporaldata can be reduced to multiple sets of low-dimensionality temporalseries. Then, multiple low-order neural models can be easily establishedto model these local dynamics. Finally, the original spatiotemporaldynamics can be reconstructed by multimodel synthesis. Because theproposed spatiotemporal modeling approach involves a multimodelingmechanism, it can achieve better performance than the traditionalPCA-based single-modeling for nonlinear DPSs, which is demonstratedby numerical simulations. [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]

Most self-tuning control algorithms for nonlinear systems become invalid when the controlled systems have nonminimum phase property. In this article, a direct neural network-based self-tuning control strategy is developed to deal with this problem under the certainty equivalence principle. Based on an equivalent linearized model from the local linearization, the controller structure is designed using a modified Clarke index with the guaranteed closed-loop stability and without the traditional requirement of the globally boundedness. For the system with unknown parameters, the controller is self-tuned by an on line RBF neural network identifier. Satisfactory simulations illustrate the effectiveness and adaptability of the proposed strategy even under system parameter variations. [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 discrete time adaptive control approach using dynamic neural networks (DNNs) is developed in this paper for the trajectory tracking of a robotic manipulator with unknown nonlinear dynamics. By using dynamic inversion constructed by a DNN, the assumption under which the system state should be on a compact set can be removed. This assumption is usually required in neuro-adaptive control. The NN-based variable structure control is designed to guarantee the stability and improve the dynamic performance of the closed-loop system. The proposed control scheme ensures the global stability and desired tracking as well. [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]

Model uncertainty often results from incomplete system knowledge or simplification made at the design stage. In this paper, a hybrid model/data-based probabilistic design approach is proposed to design a nonlinear system to be robust under the circumstances of parameter variation and model uncertainty. First, the system is formulated under a linear structure which will serve as a nominal model of the system. All model uncertainties and nonlinearities will be placed under a sensitivity matrix with its bound estimated from process data. On this basis, a model-based robust design method is developed to minimize the influence of parameter variation in relation to performance covariance. Since this proposed design approach possesses both merits from the model-based robust design as well as from the data-based uncertainty compensation, it can effectively achieve robustness for partially unknown nonlinear systems. Finally, two practical examples demonstrate and confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: An internal model-based neural network control is proposed for unknown non-affine discrete-time multi-input multi-output (MIMO) processes in nonlinear state space form under model mismatch and disturbances. Based on the neural state-space model built for an unknown nonlinear MIMO state space process, an approximate internal model and approximate decoupling controllers are derived simultaneously. Thus, the learning of the inverse process dynamics is not required. A neural network model-based extended Kalman observer is used to estimate the states of a nonlinear process as not all states are accessible. The proposed neural internal model control can work for open-loop unstable processes with its closed-loop stability derived analytically. The application to a distributed thermal process shows the effectiveness of the proposed approach for suppressing nonlinear coupling and external disturbances and its feasibility for the control of unknown non-affine nonlinear discrete-time MIMO state space processes. [Copyright &y& Elsevier]