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In this article, an adaptive tracking control approach is developed for a class of strict-feedback nonlinear systems with time-varying full state constraints. As a breakthrough in this system, the special function constraints (whose constraint boundary is relevant to both state variables and time) are considered, which are rarely studied by research work. And there is no doubt that this method increases the complexity of designing this scheme. Furthermore, the time-varying integral barrier Lyapunov functions combining with backstepping technique is introduced to break the limitation of traditional methods as well as achieve the full state constraints. Meanwhile, fuzzy logic systems are selected to approximate unknown nonlinear functions. It is verified that all closed-loop signals are bounded and all states are forced in the time-varying boundness. In addition, the proposed control strategy has a good performance. The effectiveness of the theoretical analysis results is proved via a simulation example. [ABSTRACT FROM AUTHOR]

This article focuses on the issue of addressing an adaptive neural network (NN) inverse optimal containment control for nonlinear multiagent systems (MASs), which are subject to immeasurable states and quantized input signals simultaneously. To tackle this problem, we utilize a NN to model unknown agents and design a NN observer to estimate the immeasurable states. Additionally, we decompose the hysteretic quantized input into two bounded nonlinear functions. By employing the adaptive backstepping approach and inverse optimal principle, we formulate an adaptive NN inverse optimal containment control method. The developed inverse optimal containment control scheme guarantees that the controlled system is input-to-state stabilizable (ISS). Finally, we validate the effectiveness of our proposed control scheme through simulation results. [ABSTRACT FROM AUTHOR]

The aim of this article is to study a fuzzy-based decentralized adaptive control strategy for the nonstrict-feedback fractional-order nonlinear large-scale systems with unknown control directions. In each step of the recursive processes, the fuzzy logic systems are employed to identify unknown nonlinear functions. To handle the difficulties caused by unknown control directions, a Nussbaum function technique is adopted. Furthermore, by introducing the dynamic surface control technique into the adaptive backstepping recursive design algorithm, a fuzzy-based decentralized adaptive control strategy is formulated. Both the stability of the controlled system and the convergence of the tracking errors are proved by constructing the fractional-order Lyapunov functions. Finally, the validity and effectiveness of the designed decentralized control scheme are confirmed via two simulation examples. [ABSTRACT FROM AUTHOR]

In the article, the issues of asymptotic adaptive tracking control for the uncertain nonlinear systems in the presence of actuator faults and unknown control directions are investigated. By using the properties of the Nussbaum function and backstepping technique, the problems resulting from the unknown signs of the nonlinear control functions are circumvented successfully. Moreover, a new adaptive asymptotic tracking control method is presented with the fault-tolerant control framework, which is capable of realising zero-tracking performance. The stability of the controlled system is ensured through fractional Lyapunov stability analysis. Finally, the validity of the raised scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, a new fuzzy adaptive resilient decentralized control method is presented for the nonlinear interconnected cyber-physical systems under false data injection (FDI) attacks. Fuzzy logic systems (FLS) are used to model unknown nonlinear dynamics and the FDI attacks are represented by the sum of the system states and unknown time-varying bounded functions. To deal with the problem of the system states are unavailable under FDI attacks, a new coordinate transformation is proposed for control design. By using the backstepping control design theory and Nussbaum function property, a fuzzy adaptive resilient decentralized control scheme is developed, where the Nussbaum functions are employed to deal with the unknown time-varying weight. Then, the stability of the controlled systems is proved by constructing a appropriate Lyapunov function. Finally, the effectiveness of the proposed fuzzy adaptive resilient decentralized control scheme is verified by the simulation and comparison results. • A new fuzzy adaptive resilient decentralized controller is designed for the nonlinear interconnected CPSs under FDI attacks. • The presented controller can ensure the controlled systems to be stable and compensate the impacts of FDI attacks. • the FLSs are utilized to approximate nonlinear functions and a new coordinate transformation under FDI attacks is given. [ABSTRACT FROM AUTHOR]

Summary: This article studies the adaptive fuzzy finite‐time quantized control problem of stochastic nonlinear nonstrict‐feedback systems with full state constraints. During the control design process, fuzzy logic systems are used to identify the unknown nonlinear functions, integral barrier Lyapunov functions are employed to solve the state constrained problem. In the frame of backstepping design, an adaptive fuzzy finite‐time quantized control scheme is developed. Based on the stochastic finite‐time Lyapunov stability theory, it can be guaranteed that the closed‐loop system is semiglobal finite‐time stable in probability, and the tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to testify the effectiveness of the developed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a novel fuzzy adaptive output-feedback control design scheme is concerned for a class of non-strict feedback switched nonlinear systems. The considered nonlinear system contains arbitrary switching, unmodeled dynamics, unmeasured states, and unknown nonlinearities. In the design process, fuzzy logic systems (FLSs) are utilised to identify the unknown nonlinear functions. A state observer without depending on the switching signal is constructed to deal with the unmeasured states. By combining adaptive backstepping with dynamic surface control (DSC) technique, a fuzzy adaptive control scheme is presented to overcomes the 'explosion of complexity' problem. It is proved that all the signals of the closed-loop system can be bounded by the common Lyapunov function theory. Finally, a simulation example is provided to elaborate the feasibility and effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

In this work, the fuzzy adaptive output feedback control is investigated for single-input single-output (SISO) uncertain nonlinear systems in strict-feedback form. The controlled systems under consideration of this work contain the immeasurable states and unknown control gain functions. The immeasurable states are estimated by constructing a fuzzy state observer, and the uncertain nonlinear functions are approximated by fuzzy logic systems. In order to settle the issue of 'explosion of complexity' inherent in the conventional backstepping design process, the 'dynamic surface control' (DSC) method is introduced. An observer-based fuzzy adaptive control algorithm is proposed by employing the adaptive backstepping control design technique and constructing the Logarithm Lyapunov functions. The designed fuzzy adaptive control scheme can settle the complexity problem of control scheme and insure that the closed-loop system is semi-globally uniformly ultimately boundedness (SGUUB), a simulation example is considered to illustrate the availability of the designed controller. [ABSTRACT FROM AUTHOR]

In this article, a new n-step fuzzy adaptive output tracking prescribed performance control problem is investigated for a class of nontriangular structure nonlinear systems. In the control design process, the mean value theorem is used to separate the virtual state variables needed for the control design, and the implicit function theorem is exploited to assert the existence of the desired continuous control. The fuzzy logic systems are used to identify the unknown nonlinear functions and ideal controller, respectively. By constructing a novel iterative Lyapunov function, a new n-step adaptive backstepping control design algorithm is established. The prominent characteristics of the proposed adaptive fuzzy backstepping control design algorithm are as follows: one is that it can ensure the closed-loop control system is the semiglobally uniformly ultimately bounded and the tracking error can converge within the prescribed performance bounds. The other is that it solves the controller design problem for the nontriangular nonlinear systems that the previous adaptive backstepping design techniques cannot deal with. Two examples are provided to show the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the problem of fuzzy adaptive finite-time output feedback control for a class of multi-input and multi-output (MIMO) nonlinear systems with errors constraint and unknown dead zone. In control design, the fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear functions and a state observer is constructed to estimate the unmeasurable states. The simplified barrier Lyapunov function (SBLF) and performance function are considered to solve the problem of errors-constraint. Combining backstepping design with prescribed performance technique, an observer-based finite-time adaptive fuzzy control scheme is presented. The presented control scheme not only guarantees that all signals of the closed-loop system are bounded, but also ensures that tracking errors converge to a small neighborhood of the zero within the prescribed performance bounded. Finally, a numerical example is provided to elaborate the effectiveness of the presented control scheme. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on consensus quantized control design problem for uncertain nonlinear multiagent systems with unmeasured states. Every follower can be denoted through a system with unmeasurable states, hysteretic quantized input, and unknown nonlinearities. Fuzzy state observer and Fuzzy logic systems are employed to estimate unmeasured states and approximate unknown nonlinear functions, respectively. The hysteretic quantized input can be split into two bounded nonlinear functions to avoid chattering problem. By combining adaptive backstepping and first‐order filter signals, an observer‐based fuzzy adaptive quantized control scheme is designed for each follower. All signals exist in closed‐loop systems are semiglobally uniformly ultimately bounded, and all followers can accomplish a desired consensus results. Finally, a numerical example is employed to elaborate the effectiveness of proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time adaptive fuzzy control problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems. During the control design process, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and fuzzy state observer is constructed to estimate the unmeasured states. By combining adaptive backstepping with the dynamic surface control (DSC) technique, a finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem. The stability of the close-loop systems can be proved based on the finite-time Lyapunov stability theory. The presented control scheme demonstrates that the closed-loop systems are semiglobal practical finite-time stability, and tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to show the effectiveness of the presented control method. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the adaptive fuzzy prescribed performance output‐feedback decentralized control problem for a class of stochastic interconnected nonlinear large‐scale systems. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a state observer is designed to estimate the unmeasured states. By combining the backstepping recursive design principle with prescribed performance theory, an adaptive fuzzy decentralized control method is presented. In order to overcome the problem of "explosion of complexity" in the adaptive backstepping control design, the first‐order filter signals are introduced into adaptive fuzzy decentralized control design algorithm and form a new simplized. The stability is proven based on the Lyapunov stability theory, which demonstrated that all the signals of the closed‐loop system are semiglobally uniformly ultimately bounded in probability and the tracking errors remain a small neighborhood of the origin within the prescribed performance bounds. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This study investigates the problem of adaptive fuzzy output feedback control for a class of switched uncertain non‐linear systems with input quantisation. The considered system contains unknown non‐linearities, the switching signals, hysteretic quantised input and immeasurable states. Fuzzy logic systems are used to approximate the unknown non‐linearities and a fuzzy switched state observer is designed to estimate the unmeasured states. The hysteretic quantised input is divided into two bounded non‐linear functions in the control design to avoid chattering problem. By incorporating command filter into the backstepping design procedure, a fuzzy adaptive control scheme is developed, which solves the 'explosion of complexity' problem in conventional backstepping control schemes. Finally, the stability of the closed loop and convergence of the tracking error are proved via average dwell time and multiple Lyapunov functions methods. The effectiveness of the proposed approach is verified by a numerical simulation example. [ABSTRACT FROM AUTHOR]

In this paper, an output feedback control method with prescribed performance is proposed for single-input and single-output (SISO) switched non-strict-feedback nonlinear systems. It is assumed that nonlinear functions of the concerned systems are unknown, switching signals are unknown and arbitrary, and the states are unmeasured. A linear state observer is designed to estimate the unmeasured states, and an observer-based output feedback control scheme is developed. The key advantages of the proposed control strategy are that virtual control gains of the concerned non-strict-feedback nonlinear systems are not required to be known, and only one tuning parameter is needed. Based on Lyapunov stability theory, it is shown that all the signals in the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by a numerical example. [ABSTRACT FROM AUTHOR]

In this study, the fault‐tolerant control problem is investigated for a class of non‐affine output‐constrained multi‐input multiple‐output non‐linear systems with actuator faults. The controlled systems contain unknown non‐linear functions, unknown external disturbance and immeasurable states. The fuzzy logic systems and a robust compensation function are employed to deal with the unknown non‐linear functions and non‐affine non‐linear actuator fault problems. Then, the state observer and the non‐linear disturbance observer are developed for estimating the immeasurable states and unknown compounded disturbance, respectively. By using the barrier Lyapunov function method and in the unified framework of adaptive backstepping output feedback control design, a novel adaptive fuzzy fault‐tolerant controller design scheme is developed. It is shown that all the variables of the closed‐loop system are semi‐globally uniformly bounded. Moreover, the system outputs cannot violate their predefined bounds in the presence of the non‐affine non‐linear faults. A simulation is given to validate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive fuzzy quantized output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict feedback form. The considered switched systems contain unknown nonlinearities, hysteretic quantized input and without requiring the system states being available for measurement. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a switched fuzzy state observer is designed to estimate the unmeasured states. The hysteretic quantized input is implemented to avoid the oscillation caused by logarithmic quantizer and decomposed into two bounded nonlinear functions. Based on the estimated states and using the backstepping design principle, an adaptive fuzzy quantized output feedback control scheme is developed. It is proved that whole adaptive fuzzy quantized control scheme can guarantee that all the variables in the closed-loop system are bounded under a class of switching signals with average dwell time, and also that the system output can track a given reference signal as closely as possible. The simulation results are given to check the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy output feedback control approach is proposed for a class of multi-input and multi-output (MIMO) uncertain nonlinear systems with unmeasured states and unknown control directions. In the control design, by using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed for state estimation as well as system identification, and a Nussbaum gain function is introduced into the control design to solve the unknown control direction problem. By applying the backstepping design techniques, a fuzzy adaptive output feedback control is constructed recursively. To address the problems of output constraint and “explosion of complexity”, the barrier Lyapunov function method and dynamic surface control technique are employed, respectively. It is proved that the proposed control approach can guarantee the semi-globally uniform ultimate boundedness for all the signals and the tracking errors to a small neighborhood of the origin. Simulation studies illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy output tracking control approach is proposed for a class of uncertain nonlinear switched systems with unmeasured states, unknown nonlinear functions, unmodeled dynamics, and dynamical disturbances. In the control design, fuzzy logic systems are used to approximate the unknown switched nonlinear functions and a switched fuzzy state observer is designed for estimating the unmeasured states. The problem of unmodeled dynamics and dynamic disturbance are solved by introduce a modified dynamical signals and nonlinear damping terms into the backsteping design procedure. Under the framework of backstepping control design, fuzzy adaptive control and average dwell time method, an adaptive fuzzy output-feedback tracking control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop switched system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the problem of adaptive fuzzy output-feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states. To address output constraint and input constraint, a barrier Lyapunov function and an auxiliary design system are employed, respectively. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the fuzzy state observer, and combining the adaptive backstepping technique with adaptive fuzzy control design, an observer-based adaptive fuzzy output-feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the input and output constraints are circumvented simultaneously. A numerical example is provided to illustrate the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this paper, an adaptive fuzzy decentralized control approach is proposed for a class of uncertain large-scale stochastic nonlinear systems with unknown functions, unknown dead-zone and unmodeled dynamics. In the controller design, fuzzy logic systems are used to approximate the unknown nonlinear functions, and by combining the backstepping recursive design with the dynamical signal technique, a robust adaptive fuzzy decentralized control approach is developed. It is proved that the proposed control approach can guarantee that the closed-loop system is input-state-practically stability (ISpS) in probability, and the output of the system converges to a small neighborhood of the origin in the presence of unknown dead-zone and unmodeled dynamics. A simulation example is provided to show the effectiveness of the proposed control approach. [Copyright &y& Elsevier]

In this study, a robust adaptive fuzzy decentralised backstepping output feedback control approach is proposed for a class of uncertain non‐linear stochastic large‐scale systems in pure‐feedback form. The non‐linear large‐scale systems under study have unknown non‐linear functions, unknown dead‐zone and immeasurable states. Fuzzy logic systems are used to approximate the unknown non‐linear functions, and a K‐filters state observer is designed for estimating the unmeasured states. Based on the information of the bounds of the dead‐zone slopes as well as treating the time‐varying inputs coefficients as a system uncertainty, a robust adaptive fuzzy decentralised output feedback control approach is constructed via the backstepping recursive design technique. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system can be regulated to a small neighbourhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive fuzzy decentralized fault-tolerant control (FTC) problem for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear system contains the unknown nonlinear functions, i.e., unmeasured states and actuator faults, which are modeled as both loss of effectiveness and lock-in-place. With the help of fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive observer is designed to estimate the unmeasured states. By combining the backstepping technique with the nonlinear FTC theory, a novel adaptive fuzzy decentralized FTC scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded, and the tracking errors between the system outputs and the reference signals converge to a small neighborhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy output feedback fault-tolerant control scheme is developed for a class of nonlinear systems with actuator faults, unmodeled dynamics and without assuming the states being available for control design. Fuzzy logic systems are employed to approximate unknown nonlinear functions, and a fuzzy state observer is established to estimate the unmeasured states. By combining adaptive backstepping technique with changing supplying function technique and the nonlinear fault-tolerant control theory, a novel adaptive fuzzy fault-tolerant output feedback control approach is developed. It is proved that proposed control approach guarantees that all the variables of the closed-loop system are bounded. The simulation results are provided to illustrate the effectiveness of the proposed control approach. Compared with the existing results, the main contributions of this paper are as follows: (1) the proposed control method removes the restrictive assumption that all the states of the controlled system be measured directly; and (2) the proposed control method cannot only compensate for the actuator faults, but also solve the problem of the unmodeled dynamics. [ABSTRACT FROM AUTHOR]

SUMMARY In this paper, an adaptive fuzzy backstepping dynamic surface control approach is considered for a class of uncertain pure-feedback nonlinear systems with immeasurable states. Fuzzy logic systems are first employed to approximate the unknown nonlinear functions, and then an adaptive fuzzy state observer is designed to estimate the immeasurable states. By the combination of the adaptive backstepping design with a dynamic surface control technique, an adaptive fuzzy output feedback backstepping control approach is developed. It is proven that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the observer and tracking errors converge to a small neighborhood of the origin by choosing the design parameters appropriately. Simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of adaptive fuzzy tracking control for a class of multi-input and multi-output (MIMO) strict-feedback nonlinear systems with both unknown nonsymmetric dead-zone inputs and immeasurable states. In this research, fuzzy logic systems are utilized to evaluate the unknown nonlinear functions, and a fuzzy adaptive state observer is established to estimate the unmeasured states. Based on the information of the bounds of the dead-zone slopes as well as treating the time-varying inputs coefficients as a system uncertainty, a new adaptive fuzzy output feedback control approach is developed via the backstepping recursive design technique. It is shown that the proposed control approach can assure that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded. It is also shown that the observer and tracking errors converge to a small neighborhood of the origin by selecting appropriate design parameters. Simulation examples are also provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses the tracking control problem for a class of permanent magnet synchronous motors (PMSM) systems with asymmetric full-state constraints. To overcome the difficulty of controller design caused by the state constraint problems of system, a nonlinear transformation function i introduced to transform the state constraint problems into a non-constraint problems. Then, radial basis function neural networks (NN) is employed to approximate the uncertainties in the system. In addition, by combining the techniques of command filter and finite-time control, a novel virtual control signal and modified error compensation signals are proposed to construct the actual control law, which solves the problems of "explosion of complexity" and "singularity". It is shown that all signals of the closed-loop system are bounded and the tracking error remains in a small neighborhood of the origin in finite time. Finally, the simulations show the performance and feasibility of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, we present an event-triggered scheme for fractional order nonlinear systems under full-state constraints. The neural networks are employed to approximate the continuous nonlinear unknown functions in the system. Moreover, a new adaptive event-triggered strategy is designed under the unified framework of backstepping control method, which can largely reduce the amount of communications. Since the state constraints are frequently emerged in the control procedure, the barrier Lyapunov functions is used to avoid the violation of state constraints. The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis. Finally, the effectiveness of the proposed scheme is verified by simulation examples. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large-scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the fuzzy state observer, and by combining the adaptive backstepping technique with decentralized control design, an adaptive fuzzy decentralized output feedback control approach is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approach. [Copyright &y& Elsevier]