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This article investigates the problem of fuzzy adaptive consensus tracking control for nonlinear multiagent systems with unknown nonlinear control gain functions. In the control design, fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and a distributed state observer is constructed to estimate the unmeasured states. Under the case of directed graph, by constructing the logarithm Lyapunov functions, an adaptive fuzzy distributed control method is presented, which removes the restrictive assumptions about the unknown control gain functions must be constants in traditional adaptive intelligent output feedback control methods. The developed control scheme cannot only ensure that all signals of the controlled system are semiglobal uniformly ultimately bounded, but also make the outputs of all the followers keep consensus with the output trajectory of the leader. Finally, simulation results are given to illustrate the effectiveness of the developed consensus control scheme and theorem. [ABSTRACT FROM AUTHOR]

This article studies the fuzzy adaptive output feedback control design problem for nonstrict feedback multi-input–multi-output nonlinear systems with full-states prescribed performance in finite time. Fuzzy logic systems are introduced to solve the problem of unknown nonlinear dynamics. And on this basis, a fuzzy-based state observer is designed to observe the unmeasurable state. Further, by combining the adaptive back-stepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which not only solves the computational complexity explosion problem inherent in the back-stepping control algorithm, but also improves the control performance, in contrast to the traditional DSC methods with linear filters. Besides, to further improve the tracking performance under the structure of full-states prescribed performance, a new Lyapunov function is designed considering the transform error constraint. Based on the Lyapunov theory, the stability of the closed-loop system is analyzed to ensure that all signals of the closed-loop system are semiglobal practical finite-time stability. Finally, to elaborate on the feasibility and effectiveness of the proposed control method, a simulation example is provided. [ABSTRACT FROM AUTHOR]

This paper investigates the switching mechanism-based event-trig-gered fuzzy adaptive control issue of multi-input and multi-output (MIMO) nonlinear systems with prescribed performance (PP). Utilizing fuzzy logic systems (FLSs) to approximate unknown nonlinear functions. By using the switching threshold strategy, the system has more flexibility in strategy selection. The proposed control scheme can better solve the communication resource limitation. On account of the Lyapunov stability theory, the stability of the controlled system is proved. And all signals of the controlled system are bounded. Moreover, the tracking errors are controlled in a diminutive realm of the origin within the PP bounded. Simultaneously, the Zeno behavior is avoided. Finally, illustrate the effectiveness of the control scheme that has been proposed by demonstrating some simulation consequences. [ABSTRACT FROM AUTHOR]

In this article, a novel fuzzy adaptive tracking control scheme is concerned for a class of stochastic state-constrained switched nonlinear systems. The considered stochastic switched nonlinear system contains unknown nonlinearities and unstable inverse dynamics. In the design process, first, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear dynamics. Second, the stochastic barrier Lyapunov functions (BLFs) are constructed to deal with the state constraint problem. Then, an adaptive fuzzy state-feedback controller is designed by utilizing the Itô lemma and average dwell time (ADT) approach, which can guarantee both the control system and unstable inverse dynamics to be bounded in probability and all the states cannot violate their constrained sets. Two simulation examples are provided to show the effectiveness of the proposed control approach. [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]

This paper investigates an adaptive fuzzy output feedback control design problem for the switched multiple-input and multiple-output (MIMO) nontriangular structure nonlinear systems. The discussed system contains the unknown nonlinear dynamics, the unknown backlash hysteresis, the immeasurable states, and the unknown control directions under a class of switching signals. The fuzzy logic systems are utilized to learn the unknown nonlinear dynamics and construct an MIMO fuzzy switched nonlinear observer. By combining the property of the Nussbaum gain function with the Prandtl-Ishlinskii models, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the whole controlled system is proved via Lyapunov stability theory and the average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a novel fuzzy adaptive tracking control scheme is presented for a class of nonstrict-feedback uncertain switched nonlinear systems by taking into account constraint. The considered switched nonlinear system contains unknown nonlinearities. In the design process, firstly, the problem of state constraints is coped with by utilizing the asymmetric time-varying barrier Lyapunov functions (TABLFs), and the problem of "explosion of complexity" is solved by dynamic surface control (DSC) technology. Secondly, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear dynamics. Under the framework of adaptive control design, the switched adaptive state feedback controller is designed, which can guarantee all states cannot violate their constrained sets. Then, based on the Lyapunov function and average dwell time (ADT) approach, the theoretical analysis is provided for the closed-loop systems within constraint performance bounded. Finally, a numerical example is proposed to further 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]

In the paper, the adaptive observer and controller designs based fuzzy approximation are studied for a class of uncertain nonlinear systems in strict feedback. The main properties of the considered systems are that all the state variables are not available for measurement and at the same time, they are required to limit in each constraint set. Due to the properties of systems, it will be a difficult task for designing the controller and the stability analysis. Based on the structure of the considered systems, a fuzzy state observer is framed to estimate the unmeasured states. To ensure that all the states do not violate their constraint bounds, the Barrier type of functions will be employed in the controller and the adaptation laws. In the stability analysis, the effect caused by the constraints for all the states can be overcome by using the Barrier Lyapunov functions. Based on the proposed control approach, it is proved that the system output is driven to track the reference signal to a bounded compact set, all the signals in the closed-loop system are guaranteed to be bounded, and all the states do not transgress their constrained sets. The effectiveness of the proposed control approach can be verified by setting a simulation example. [ABSTRACT FROM AUTHOR]

Summary: This paper develops a novel fuzzy adaptive backstepping dynamic surface control scheme for a class of strict‐feedback nonlinear systems with unknown time delay based on adaptive dynamic programming. The whole control scheme is composed of 2 parts, ie, feedforward control and feedback optimal control. Fuzzy logic systems are used to identify nonlinear systems. The control design method, which combined the backstepping design technique and the dynamic surface control approach, is applied to convert triangular structure systems to affine nonlinear systems; it not only can solve the problem of “explosion of complexity” but also can avoid the appearance of unknown terms. The closed‐loop system is guaranteed to be uniformly ultimately bounded based on the Lyapunov and optimal control theory, and the system output can track the desired reference signal in an optimal manner. The simulation results of numerical examples are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates an adaptive fuzzy output feedback control design problem for switched nonlinear system in non-triangular structure form. The discussed system contains unknown nonlinear dynamics, unmeasured states and unknown time-varying delays under a batch of switching signals. Fuzzy logic systems are utilised to learn unknown nonlinear dynamics and construct a fuzzy switched nonlinear observer. By combining the property of fuzzy basis function with Lyapunov–Krasovskii functional and the command filter, a novel observer-based fuzzy adaptive backstepping schematic design algorithm is presented. Furthermore, the stability of the closed-loop control system is proved via Lyapunov stability theory and average dwell time method. The simulation results are presented to verify the validity of the proposed control scheme. [ABSTRACT FROM PUBLISHER]

This paper deals with the problem of adaptive fuzzy tracking control for a single-link robotic manipulator coupled to a brushed direct current motor with actuator saturation. Fuzzy logic systems are used to approximate the unknown nonlinear systems. The filtered signals are introduced to eliminate the interference of high-frequency signals. The virtual/actual control inputs are derived from the solutions of a series of dynamical equations. Under the framework of the backstepping control design, an observer-based output feedback control design scheme is proposed. It is proved that the control approach can guarantee that all the signals in the closed-loop system are bounded. [ABSTRACT FROM AUTHOR]

The problem of adaptive fuzzy output-constrained tracking fault-tolerant control (FTC) is investigated for the large-scale stochastic nonlinear systems of pure-feedback form. The nonlinear systems considered in this paper possess the unstructured uncertainties, unknown interconnected terms and unknown nonaffine nonlinear faults. The fuzzy logic systems are employed to identify the unknown lumped nonlinear functions so that the problems of structured uncertainties can be solved. An adaptive fuzzy state observer is designed to solve the nonmeasurable state problem. By combining the barrier Lyapunov function theory, adaptive decentralized and stochastic control principles, a novel fuzzy adaptive output-constrained FTC approach is constructed. All the signals in the closed-loop system are proved to be bounded in probability and the system outputs are constrained in a given compact set. Finally, the applicability of the proposed controller is well carried out by a simulation example. [ABSTRACT FROM PUBLISHER]

This paper considers the adaptive fuzzy output feedback control design problem for a class of switched nonlinear systems. The considered switched nonlinear systems contain unknown nonlinearities, the switching signals with average dwell time, and without requiring that state variables are available for measurement. Fuzzy logic systems are used to approximate the unknown nonlinearities, and a fuzzy switched state observer is designed to estimate the immeasurable states. In the framework of observer-based output feedback control design technique, and by introducing a command filter into the backstepping design algorithm, a command filter-based adaptive fuzzy backstepping output feedback control scheme is developed. The stability of the closed-loop system and the convergence of the tracking error are proved via average dwell time and multiple Lyapunov function. A numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates fuzzy adaptive output feedback optimal control problem for a class of strict-feedback nonlinear systems. With the help of fuzzy logic systems approximating the unknown nonlinear functions and cost function, the unmeasured states are estimated by designing fuzzy adaptive state observer. Combining state observer with backstepping design technique, a feedforward controller is designed. Based on the designed feedforward control strategy, the controlled nonlinear system can be converted to an equivalence nonlinear system in affine-form. Finally, a fuzzy adaptive optimal controller with parameters adaptive laws is developed. The whole control scheme consists of a feedforward controller and a feedback optimal controller. It is shown that the proposed output feedback optimal control approach can guarantee that all signals in the closed-loop system are bounded, and the system output can track the reference signal. In addition, the proposed control approach can guarantee cost function is the smallest. Simulation results are given to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper studies adaptive fuzzy output feedback tracking control problem for nonstrict-feedback switched nonlinear systems. The switched systems under consideration contain unknown nonlinearities, unmeasured states, and unknown deadzones. Fuzzy logic systems are utilized to approximate the unknown nonlinearities, and a switched fuzzy state observer is designed, and thus, the immeasurable states are estimated via it. In the framework of observer-based output feedback control, and by using the certainty equivalence deadzone inverse, a novel adaptive fuzzy output feedback control design method with the parameters adaptation laws is developed. The stability of the closed-loop system and the convergence of the tracking error are proved based on Lyapunov function and the average dwell-time methods. Two simulation examples are provided to check the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper investigates the problem of fault-tolerant control (FTC) for a class of switched nonlinear systems. These systems are under arbitrary switchings and are subject to both lock-in-place and loss-of-effectiveness actuator faults. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. Under the framework of the backstepping control design, FTC, fuzzy adaptive control and common Lyapunov function stability theory, an adaptive fuzzy 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 semi-globally uniformly ultimately bounded (SGUUB) and the tracking error remains an adjustable neighbourhood of the origin. Two simulation examples are provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy controller is constructed for a class of nonlinear discrete-time systems with unknown functions and bounded disturbances. The main characteristics of the systems are that they take into account the effect of discrete-time dead zone and the system states are not required to be measurable. The stability problem of this class of systems is for the first time to be addressed in this paper. Due to the unavailability of the states and the presence of the discrete-time dead zone, the controller design becomes more difficult. To stabilize the uncertain nonlinear discrete-time systems, the fuzzy logic systems are used to approximate the unknown functions, a fuzzy state observer is designed to estimate the immeasurable states, and the effect caused by discrete-time dead zone can be solved via establishing an adaptation auxiliary signal. Based on the Lyapunov approach, it is proved that all the signals of the closed-loop system are the semiglobal uniformly ultimately bounded, and the tracking error is made within a small neighborhood around zero. The feasibility of the developed control scheme is verified via two simulation examples. [ABSTRACT FROM PUBLISHER]

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, the problem of adaptive fuzzy output-feedback control is investigated for a class of uncertain switched nonlinear systems in strict-feedback form. The considered switched systems contain unknown nonlinearities, dead-zone, and immeasurable states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, a switched fuzzy state observer is designed and thus the immeasurable states are obtained by it. By applying the adaptive backstepping design principle and the 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 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 PUBLISHER]

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]

In this paper, the adaptive fuzzy output feedback control problem is investigated for a class of single-input and single-output (SISO) stochastic nonlinear systems unknown dead-zones and unknown control direction. In the design, by using a linear state transformation, the unknown control coefficient and the unknown slope characteristic of the dead-zone are lumped together, and the original system is transformed to a new system. Fuzzy logic systems are employed to identified the uncertain nonlinear systems, a nonlinear fuzzy state observer is constructed to solve the problem of unmeasured states, and a special Nussbaum function is introduced into the control design to solve the unknown control direction problem, respectively. To address the problem of “explosion of complexity”, the dynamic surface control (DSC) technique is employed, a stable adaptive fuzzy output-feedback tracking control scheme is developed. The stability is proven based on Lyapnov theory, and it can guarantee that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of prescribed performance adaptive fuzzy output feedback control is investigated for a class of single-input and single-output nonlinear stochastic systems with input saturation and unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, the input saturation is approximated by a smooth function, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. The simulation example and the comparative results are provided to show the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy output tracking control approach is proposed for a class of single input and single output (SISO) uncertain pure-feedback switched nonlinear systems under arbitrary switchings. Fuzzy logic systems are used to identify the unknown nonlinear system. Under the framework of the backstepping control design and fuzzy adaptive control, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) 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]

In this paper, the adaptive fuzzy backstepping output feedback tracking control problem is considered for a class of uncertain stochastic multi-input and multi-output (MIMO) nonlinear systems in pure-feedback form. The stochastic MIMO nonlinear systems under study have unknown nonlinear functions, input saturation and immeasurable states. By using fuzzy logic systems to identify the uncertain nonlinear system, and a smooth function to approximate the input saturation, a fuzzy state observer is designed and the estimations of the immeasurable states are obtained. Based on the backstepping recursive design technique, an adaptive fuzzy output feedback tracking control approach is developed. It is shown that the proposed control approach guarantees that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean-square in the sense of probability, and the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy robust output feedback control problem is considered for a class of single-input and single-output nonlinear systems in a strict-feedback form. The considered systems possess the unstructured uncertainties, unknown dead zone, and the dynamics uncertainties, and they do not assume the states being available for the controller design. In the controller design, fuzzy logic systems are first used to approximate the unstructured uncertainties, and by utilizing the information of the bounds of the dead-zone slopes and treating the time-varying inputs coefficients as a system uncertainty, a fuzzy state observer is designed to estimate the unmeasured states. By combining a backstepping technique with a nonlinear small-gain approach, a new adaptive fuzzy robust output feedback control has been developed. It is proved that the proposed fuzzy adaptive control approach can guarantee the semiglobal uniform ultimate boundedness for all the solutions of the closed-loop systems. Simulation studies and comparisons with previous methods are included to illustrate 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, two adaptive fuzzy output feedback control approaches are proposed for a class of uncertain stochastic nonlinear strict-feedback 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 fuzzy adaptive control design, an adaptive fuzzy output feedback control approach is developed. To overcome the problem of “explosion of complexity” inherent in the proposed control method, the dynamic surface control (DSC) technique is incorporated into the first adaptive fuzzy control scheme, and a simplified adaptive fuzzy output feedback DSC approach is developed. It is proved that these two control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) in mean square, and the observer errors and the output of the system converge to a small neighborhood of the origin. A simulation example is provided to show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper addresses a class of uncertain non-strict feedback nonlinear systems and proposes an event-triggered fuzzy adaptive prescribed performance control (PPC) strategy. Fuzzy logic systems (FLSs) are employed to approximate unknown smooth functions. In the control design, an event-triggered mechanism (ETM) from sensor-to-controller is introduced to economize on unnecessary transmission and communication resources. Additionally, a novel performance function is constructed to bound tracking errors, and a series of error transformations are devised to convert the "constrained" system into an equivalent "unconstrained" system. The proposed control strategy ensures that all signals in the closed-loop system have semi-globally uniformly bounded stability. Moreover, prescribed performance bounds ensure output tracking with minimal (or even zero) overshoot. Finally, the effectiveness and practicality of the proposed control method are validated through comparative simulations. [ABSTRACT FROM AUTHOR]

In this paper, the optimal fault-tolerant control (FTC) design problem is investigated for strict-feedback nonlinear systems. The considered nonlinear systems contain actuator faults, which are bias fault and gain fault. The problem of actuator faults is solved by utilizing the adaptive compensation technique. Applying the backstepping design technique, a main fault-tolerant controller is established. Via the designed main fault-tolerant control strategy, the controlled nonlinear system can be converted to an equivalent nonlinear system in affine form. Subsequently, a fuzzy logic system (FLS) is introduced to approximate the unknown cost function, and an adaptive fuzzy feedback optimal controller is developed. The whole adaptive fuzzy fault-tolerant optimal control scheme consists of a main controller and a feedback optimal controller. Based on the Lyapunov theory, it is proved that all the signals in the closed-loop system are bounded, the system output can track a bounded reference signal. In addition, the proposed control method can guarantee the cost function is the smallest. Simulation results are provided to illustrate the effectiveness of the proposed fault-tolerant optimal control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive fuzzy output feedback control is investigated for a class of uncertain stochastic nonlinear systems. The stochastic nonlinear systems under study have unknown nonlinear uncertainties, unmodeled dynamics, input saturation and without the direct measurement of state variables. Fuzzy logic systems and a smooth function are first utilized to approximate the unknown nonlinear functions and the input saturation, respectively, and then a fuzzy state observer is designed to estimate the unmeasured states. By combining the adaptive backstepping design technique with the dynamic surface control (DSC) design technique and using the concept of the dynamical signal, a new adaptive fuzzy output feedback tracking control approach is developed. It is proved that all the variables involved in the closed-loop system are semi-globally uniformly ultimately bounded (SUUB) in probability, and also that both observer errors and tracking errors converge to a small neighborhood of the origin by appropriate selecting the design parameters. The proposed adaptive fuzzy control approach is finally applied to the two-stage chemical reactor with recycle streams, and achieves the satisfactory control performance. [ABSTRACT FROM AUTHOR]