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This article studies the adaptive fuzzy output-feedback decentralized control problem for the fractional-order nonlinear large-scale systems. Since the considered strict-feedback systems contain unknown nonlinear functions and unmeasurable states, the fuzzy-logic systems (FLSs) are used to model unknown fractional-order subsystems, and a fuzzy decentralized state observer is established to obtain the unavailable states. By introducing the dynamic surface control (DSC) design technique into the adaptive backstepping control algorithm and constructing the fractional-order Lyapunov functions, an adaptive fuzzy output-feedback decentralized control scheme is developed. It is proved that the decentralized controlled system is stable and that the tracking and observer errors are able to converge to a neighborhood of zero. A simulation example is given to confirm the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

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 studies the fuzzy adaptive finite-time consensus control problem for high-order nonlinear multiagent systems with unknown nonlinear dynamics. In control design,fuzzy logic systems (FLSs) are adopted to approximate the unknown nonlinear dynamics, and under the frameworks of adaptive backstepping recursive design and finite-time stability theory, an adaptive fuzzy finite-time consensus control method is developed. To save communication resources and reduce the numbers of controller execution times, a dynamic event-triggered mechanism with a relative threshold is established. Subsequently, an event-triggered-based finite-time fuzzy adaptive control scheme is formulated. Furthermore, by constructing novel integral-type Lyapunov functions and adding a power integrator technique, the finite-time stability of the closed-loop system and the convergence of consensus tracking errors are proved. Finally, a numerical simulation example is provided to verify the effectiveness of the proposed adaptive event-triggered consensus control method. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive neural-network (NN) tracking optimal control problem for stochastic nonlinear systems, which contain state constraints and uncertain dynamics. First, to avoid the violation of state constraints in achieving optimal control, the novel barrier optimal performance index functions for subsystems are developed. Second, under the framework of the identifier-actor-critic, the virtual and actual optimal controllers are presented based on the backstepping technique, in which the unknown nonlinear dynamics are learned by the NN approximators. Moreover, the quartic barrier Lyapunov functions are constructed instead of square ones to cope with the Hessian term to ensure the stability of the systems with stochastic disturbance. The proposed optimal control strategy can guarantee the boundedness of closed-loop signals, and the output can follow the given reference signal. Meanwhile, the system states are restricted within some preselected compact sets all the while. Finally, both numerical and practical systems are carried out to further illustrate the validity of the proposed optimal control approach. [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]

The adaptive fuzzy tracking control problems for a class of uncertain stochastic nonlinear systems are investigated in this article using the backstepping control approach. Different from the existing research, the crucial but highly restrictive hypothesis on the prior knowledge of unknown virtual control coefficients (UVCCs) is removed from this article. An asymptotic tracking control scheme is proposed by applying smooth functions and a bounded estimation method. By delicately constructing a specific composite Lyapunov function for the controlled system and several useful inequalities, the stability and asymptotic tracking performance with unknown nonlinear function and unknown UVCCs can be guaranteed almost surely. Finally, the method is illustrated with simulation examples. [ABSTRACT FROM AUTHOR]

This article is concerned with the adaptive event-triggered control (ETC) problem for uncertain nonlinear systems with full state constraints. By combining the asymmetric barrier Lyapunov functions with the backstepping technique, an adaptive ETC method is designed for the system under consideration. In addition, by introducing some well-defined smooth functions and the bounded estimation approach, the effects caused by the unknown virtual control coefficients and unknown nonlinear functions are counteracted. The asymptotic stability of the closed-loop system is ensured without violating the state constraints. Finally, the effectiveness of the control method is evaluated through simulations. [ABSTRACT FROM AUTHOR]

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method. [ABSTRACT FROM AUTHOR]

This paper studies the adaptive control problem for a class of uncertain fractional nonlinear systems with actuator faults, where the total number of failures is allowed to be infinite. A compensating term in a smooth function form of a conventional control law is introduced to compensate for the actuator faults. After the introduction of fractional-order adaptation laws, an adaptive controller is designed by using a modified backstepping technique. Fractional Lyapunov stability criterion is adopted to prove the convergence of the developed proposed controller even in the presence of actuator faults. Finally, a simulation example of fractional-order Chua–Hartley’s system is given to verify the effectiveness of the proposed fault-tolerant control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the finite time adaptive fuzzy decentralized control problem for interconnected large scale nonlinear systems in nonstrict feedback forms with output-constraint. The fuzzy logic systems are used to approximate the unknown nonlinear functions and a state observer is constructed to estimate the immeasurable states. In order to deal with the output constraint problem, the barrier Lyapunov function is introduced. By combining backstepping recursion design with a command filter, a finite time fuzzy adaptive decentralized control method is presented. The stability analysis can be obtained based on the finite time Lyapunov stability theory, which demonstrates that the closed-loop system are semi-global practical finite-time stability, the system outputs can track the given reference signals and keep in the given constraint bounds in a finite time. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control scheme. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural network (NN) controller is proposed for a class of nonlinear active suspension systems (ASSs) with hydraulic actuator. To eliminate the problem of “explosion of complexity” inherently in the traditional backstepping design for the hydraulic actuator, a dynamic surface control technique is developed to stabilize the attitude of the vehicle by introducing a first-order filter. Meanwhile, the presented scheme improves the ride comfort even when the uncertain parameter exists. Due to the existence of uncertain terms, the NNs are used to approximate unknown functions in the ASSs. Finally, a simulation for a servo system with hydraulic actuator is shown to verify the effectiveness and reliability of the proposed approach. [ABSTRACT FROM AUTHOR]

This article investigates an adaptive reinforcement learning (RL) optimal control design problem for a class of nonstrict-feedback discrete-time systems. Based on the neural network (NN) approximating ability and RL control design technique, an adaptive backstepping RL optimal controller and a minimal learning parameter (MLP) adaptive RL optimal controller are developed by establishing a novel strategic utility function and introducing external function terms. It is proved that the proposed adaptive RL optimal controllers can guarantee that all signals in the closed-loop systems are semiglobal uniformly ultimately bounded (SGUUB). The main feature is that the proposed schemes can solve the optimal control problem that the previous literature cannot deal with. Furthermore, the proposed MPL adaptive optimal control scheme can reduce the number of adaptive laws, and thus the computational complexity is decreased. Finally, the simulation results illustrate the validity of the proposed optimal control schemes. [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]

This article first investigates the adaptive fuzzy inverse optimal control design problem for a class of uncertain strict-feedback nonlinear systems. Fuzzy logic systems are utilized to identify the unknown nonlinear dynamics, and then, an equivalent system and an auxiliary system are established. Based on the auxiliary system and using backstepping recursive design algorithm, an adaptive fuzzy inverse optimal scheme, associating with a meaningful objective functional, is developed. It is proved that the presented adaptive fuzzy inverse optimal control scheme can guarantee that the considered system is input-to-state stabilizable and also achieves the goal of inverse optimality with respect to the cost functional. Finally, the simulation studies and comparisons via two examples are provided to confirm the validity of the developed control strategy. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fuzzy output-feedback backstepping control design problem for uncertain strict-feedback nonlinear systems in the presence of unknown virtual and actual control gain functions and unmeasurable states. A fuzzy state observer is designed via fuzzy-logic systems, thus the unmeasurable states are estimated based on the designed fuzzy state observer. By constructing the logarithm Lyapunov functions and incorporating the property of the fuzzy basis functions and bounded control design technique into the adaptive backstepping recursive design, a novel observer-based adaptive fuzzy output-feedback control method is developed. The proposed fuzzy adaptive output-feedback backstepping control scheme can remove the restrictive assumptions in the previous literature that the virtual control gains and actual control gain functions must be constants. Furthermore, it can make the control system be semiglobally uniformly ultimately boundedness (SGUUB) and keep the observer and tracking errors to remain in a small neighborhood of the origin. The numerical simulation example is presented to validate the effectiveness of the proposed control scheme and theory. [ABSTRACT FROM AUTHOR]

This paper addresses the decentralized output feedback problem of an interconnected nonlinear system subject to uncertain interactions. A decentralized event-triggered control scheme is presented so that the decentralized output feedback problem is solved with only event-sampling states. With the proposed triggering mechanism, each subsystem only uses local signals to construct the decentralized controller at its own triggering times or the switching times. It is proved that both the tracking performance and the closed-loop stability can be preserved via the presented approach. Moreover, a uniform positive lower bound for the interevent time is guaranteed. Simulation results are presented to illustrate the effectiveness of the proposed control design. [ABSTRACT FROM AUTHOR]

Summary: Traditional adaptive event‐triggered design methods compensated for the event‐triggered error are not direct, and the stability analysis of resulting close‐loop systems is rather complicated. To alleviate the above restrictions, we propose a direct and simple event‐triggered co‐design method to solve the tracking control problem for parameter strict‐feedback systems with actuator faults and uncertain disturbances. By introducing a compensating terms in a smooth function form of a conventional control law and certain positive integrable functions, the effects of actuator faults and event‐triggered error can be compensated completely. Such a direct design method has the following features: (i) a direct compensation of the event‐triggered error is achieved without introducing any extra design parameters; (ii) it is not necessary to know any bound information on the parameters of event‐triggered threshold, and global asymptotic tracking control of the overall closed‐loop system is achieved; and (iii) the resulting stability criteria of the proposed event‐triggered control design are much simpler and easier to fulfill by virtue of the introduced co‐design method. Simulations are then carried out to validate the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of adaptive tracking control for a class of strict-feedback nonlinear state constrained systems with input delay. To alleviate the major challenges caused by the appearances of full state constraints and input delay, an appropriate barrier Lyapunov function and an opportune backstepping design are used to avoid the constraint violation, and the Pade approximation and an intermediate variable are employed to eliminate the effect of the input delay. Neural networks are employed to estimate unknown functions in the design procedure. It is proven that the closed-loop signals are semiglobal uniformly ultimately bounded, and the tracking error converges to a compact set of the origin, as well as the states remain within a bounded interval. The simulation studies are given to illustrate the effectiveness of the proposed control strategy in this paper. [ABSTRACT FROM AUTHOR]

The problem of adaptive fuzzy decentralized fault-tolerant optimal control is investigated for nonlinear large-scale systems with actuator faults in this paper. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions and learn cost functions. Filtered signals are adopted to circumvent the problems of an algebraic loop on designing the decentralized controllers. Based on the backstepping technique and fault-tolerant control technique, a decentralized feedforward control strategy is designed. Based on the adaptive critic technique, a decentralized feedback optimal control strategy is designed. By combining the feedforward control strategy with the feedback optimal control strategy, a novel adaptive fuzzy decentralized fault-tolerant optimal control scheme is established. The stability of the closed-loop system is proved by using the Lyapunov stability theory. The effectiveness of the proposed decentralized control approach is confirmed via a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of an adaptive fuzzy event-triggered control (ETC) for uncertain multi-input and multi-output nonlinear systems. To reduce the communication burden of the network control systems, a novel state-dependent event-triggering condition is designed to decide when to update the controllers. By combining the backstepping and event-trigged techniques, the adaptive fuzzy ETC strategies are developed and the resulting closed-loop system is semi-global bounded. Finally, the analytical results are substantiated using simulation studies. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fuzzy control method with prescribed performance is proposed for multi-input and multioutput block-triangular-structured nonlinear systems with immeasurable states. Fuzzy logic systems are adopted to identify the unknown nonlinear system functions. Adaptive fuzzy state observers are designed to solve the problem of unmeasured states, and a new observer-based output-feedback control scheme is developed based on adaptive fuzzy control principle and bacsktepping design technique. The proposed control method not only overcomes the problem of “explosion of complexity” existing in the backstepping design, but also removes the restrictive assumption that unknown nonlinear functions must satisfy global Lipschitz condition. The proposed scheme can ensure that all variables of the control systems are semiglobally uniformly ultimately bounded and the tracking errors converge to a small residual set with the prescribed performance bound. Simulation results of chemical process control system are presented to further demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper considers the optimal decentralized fuzzy adaptive control design problem for a class of interconnected large-scale nonlinear systems in strict feedback form and with unknown nonlinear functions. The fuzzy logic systems are introduced to learn the unknown dynamics and cost functions, respectively, and a state estimator is developed. By applying the state estimator and the backstepping recursive design algorithm, a decentralized feedforward controller is established. By using the backstepping decentralized feedforward control scheme, the considered interconnected large-scale nonlinear system in strict feedback form is changed into an equivalent affine large-scale nonlinear system. Subsequently, an optimal decentralized fuzzy adaptive control scheme is constructed. The whole optimal decentralized fuzzy adaptive controller is composed of a decentralized feedforward control and an optimal decentralized control. It is proved that the developed optimal decentralized controller can ensure that all the variables of the control system are uniformly ultimately bounded, and the cost functions are the smallest. Two simulation examples are provided to illustrate the validity of the developed optimal decentralized fuzzy adaptive control scheme. [ABSTRACT FROM PUBLISHER]

In this paper, the problem of adaptive fuzzy decentralized optimal control is investigated for a class of nonlinear large-scale systems in strict-feedback form. The considered nonlinear large-scale systems contain the unknown nonlinear functions and unmeasured states. By utilizing the fuzzy logic systems to approximate the unknown nonlinear functions and cost functions, a fuzzy state observer is established to estimate the unmeasured states. The control design is divided into two phases. First, by using the state observer and the backstepping design technique, a feedforward decentralized controller with parameters adaptive laws is designed, by which the original controlled strict-feedback nonlinear large-scale system is transformed into an equivalent affine nonlinear large-scale system. Second, by using adaptive dynamic programming theory, a feedback decentralized optimal controller is developed for the equivalent affine nonlinear system. The whole adaptive fuzzy decentralized optimal control scheme consists of a feedforward decentralized controller and a feedback decentralized optimal controller. It is shown that the proposed adaptive fuzzy decentralized optimal control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking errors converge to a small neighborhood of zero. In addition, the proposed control approach can guarantee that the cost functions are minimized. Simulation results are given to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM PUBLISHER]

In this paper, an adaptive fuzzy output constrained control design approach is addressed for multi-input multioutput uncertain stochastic nonlinear systems in nonstrict-feedback form. The nonlinear systems addressed in this paper possess unstructured uncertainties, unknown gain functions and unknown stochastic disturbances. Fuzzy logic systems are utilized to tackle the problem of unknown nonlinear uncertainties. The barrier Lyapunov function technique is employed to solve the output constrained problem. In the framework of backstepping design, an adaptive fuzzy control design scheme 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]

A neural network (NN) adaptive control design problem is addressed for a class of uncertain multi-input-multi-output (MIMO) nonlinear systems in block-triangular form. The considered systems contain uncertainty dynamics and their states are enforced to subject to bounded constraints as well as the couplings among various inputs and outputs are inserted in each subsystem. To stabilize this class of systems, a novel adaptive control strategy is constructively framed by using the backstepping design technique and NNs. The novel integral barrier Lyapunov functionals (BLFs) are employed to overcome the violation of the full state constraints. The proposed strategy can not only guarantee the boundedness of the closed-loop system and the outputs are driven to follow the reference signals, but also can ensure all the states to remain in the predefined compact sets. Moreover, the transformed constraints on the errors are used in the previous BLF, and accordingly it is required to determine clearly the bounds of the virtual controllers. Thus, it can relax the conservative limitations in the traditional BLF-based controls for the full state constraints. This conservatism can be solved in this paper and it is for the first time to control this class of MIMO systems with the full state constraints. The performance of the proposed control strategy can be verified through a simulation example. [ABSTRACT FROM PUBLISHER]

In this paper, we address an adaptive control problem for a class of nonlinear strict-feedback systems with uncertain parameter. The full states of the systems are constrained in the bounded sets and the boundaries of sets are compelled in the asymmetric time-varying regions, i.e., the full state time-varying constraints are considered here. This is for the first time to control such a class of systems. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions (TABLFs) are employed in each step of the backsstepping design and we also establish a novel control TABLF scheme to ensure the asymptotic output tracking performance. The performances of the adaptive TABLF-based control are verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of adaptive fuzzy output feedback control for a class of stochastic nonlinear switched systems. The controlled system in this paper possesses unmeasured states, completely unknown nonlinear system functions, unmodeled dynamics, and arbitrary switchings. A state observer which does not depend on the switching signal is constructed to tackle the unmeasured states. Fuzzy logic systems are employed to identify the completely unknown nonlinear system functions. Based on the common Lyapunov stability theory and stochastic small-gain theorem, a new robust adaptive fuzzy backstepping stabilization control strategy is developed. The stability of the closed-loop system on input-state-practically stable in probability is proved. The simulation results are given to verify the efficiency of the proposed fuzzy adaptive control scheme. [ABSTRACT FROM PUBLISHER]

This paper investigates a robust adaptive fuzzy control stabilization problem for a class of uncertain nonlinear systems with arbitrary switching signals that use an observer-based output feedback scheme. The considered switched nonlinear systems possess the unstructured uncertainties, unmodeled dynamics, and without requiring the states being available for measurement. A state observer which is independent of switching signals is designed to solve the problem of unmeasured states. Fuzzy logic systems are used to identify unknown lumped nonlinear functions so that the problem of unstructured uncertainties can be solved. By combining adaptive backstepping design principle and small-gain approach, a novel robust adaptive fuzzy output feedback stabilization control approach is developed. The stability of the closed-loop system is proved via the common Lyapunov function theory and small-gain theorem. Finally, the simulation results are given to demonstrate the validity and performance of the proposed control strategy. [ABSTRACT FROM PUBLISHER]

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 discusses the adaptive fuzzy partial tracking errors constrained control problem for a class of uncertain stochastic nonlinear systems. The concerned systems contain the unknown nonlinear functions, unmeasured state variables, and the switching signal with average dwell time. The fuzzy logic systems are first used to approximate the unknown nonlinear functions, and a switched fuzzy state observer is developed for estimating the unmeasured states. By introducing the performance function and error transformation into the backstepping dynamic surface control design, a new observer-based adaptive fuzzy control design approach is developed. By employing the multiple Lyapunov function and the average dwell time methods, it is proved that all the signals of the resulting closed-loop system are bounded, and the partial tracking errors are confined all times within the prescribed bounds. A simulation example is provided to show the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

This paper investigates an adaptive fuzzy tracking control design problem for single-input and single-output uncertain nonstrict feedback nonlinear systems. For the cases of the states measurable and the states immeasurable, fuzzy logic systems are separately adopted to approximate the unknown nonlinear functions or model the uncertain nonlinear systems. In the unified framework of adaptive backstepping control design, both adaptive fuzzy state feedback and observer-based output feedback control design schemes are proposed. The stability of the closed-loop systems is proved by using Lyapunov function theory. The simulation examples are provided to confirm the effectiveness of the proposed control methods. [ABSTRACT FROM PUBLISHER]

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]