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In this paper, the vibration control design of the Euler–Bernoulli beam with time-varying constraints is studied when the mass, bending stiffness and tension of the system parameters are known or unknown. For satisfying the time-varying constraints, the controller is designed and the system stability is analysed based on the tangent barrier Lyapunov function (TAN-BLF). Among them, the uncertainty of system parameters is dealt with by the adaptive method. In both cases, the vibration of the Euler–Bernoulli beam can be well restrained without violating the constraint conditions, and all signals in the system are bounded. Finally, the effectiveness of the proposed method is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel controller design method for stochastic nonlinear systems with unmodeled dynamics, uncertain parameters, and unknown covariance noise. In order to deal with these uncertainties, a new event‐based small gain controller is designed. The event‐triggered scheme can reduce the computational burden caused by disturbance and noise. By combining the technique of changing supply rate with small gain condition, a stochastic input‐to‐state practically stability Lyapunov function is obtained for the subsystem. Simultaneously, the changing supply function is used to treat with unmodeled dynamics. Based on backstepping process and adaptive control approach, the influence of unknown covariance noise is overcome. It is proved that the designed state‐feedback controller can ensure the overall system is stochastic input‐to‐state practically stability. [ABSTRACT FROM AUTHOR]

An adaptive neural network fault-tolerant control(FTC) scheme is proposed for nonlinear and nonstrict-feedback multi-agent systems (MASs) with directed fixed topology. Firstly, a disturbance observer is designed to estimate the unknown external disturbances in the systems, and realise the dynamic estimation of the disturbances. Secondly, the efficiency factor is estimated online, and then the FTC scheme is designed successfully under the backstepping framework. It is proved that all signals in the closed-loop systems are semi-globally uniformly bounded and the tracking error is controlled in a small range. Finally, an example is given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

An adaptive neural network (NN) distributed tracking control strategy is proposed for nonlinear strict‐feedback multi‐agent systems, which is affected by time‐varying full state constraints. The influence of asymmetric state constraints is also considered. The constraint bounds are related to both state vectors and time. Different from the usual constant boundary or function boundary, the constraint boundary adopted in this article not only considers the influence of state variables, but also takes time into consideration, which makes the constraint boundary more flexible and more difficult to solve. In addition, in order to solve the disturbance of the unknown function in the system, this article adopts the NN technology to realize the approximation effect of the unknown function, and designs a adaptive distributed controller based on the asymmetric obstacle Lyapunov function and backward step method, the closed‐loop signals are proved to be CSUUB. Finally, the effectiveness of the proposed method is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Summary: This article studies the fixed‐time time‐invariant formation control problem for a class of uncertain nonlinear heterogeneous multi‐agent systems (HMASs) with actuator faults and partial unknown control directions. Throughout the formation process, the possibility of actuator faults in systems and unknown control directions between individual agents are taken into account. Lipschitz conditions are introduced to identify the continuous uncertain nonlinear functions. To estimate the agents' local immeasurable states in HMASs, a distributed fixed‐time observer is proposed, which can ensure that the states of follower agents are observed in fixed time. In addition, a distributed formation fault‐tolerant control scheme will handle actuator faults. By designing a Nussbaum function, the problem of partial unknown control directions for HMASs can be solved in fixed time. Based on the fixed time stability theory, it is proved that the closed‐loop stability and the tracking performance can be guaranteed in fixed time, that is, the achieved time is independent of any initial states. In the end, a simulation example is given to testify the effectiveness of the proposed control method. [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]

In this paper, an event-triggered tracking optimization control method is proposed for nonlinear uncertain systems with H ∞ discounted cost. First, the linearization method using the infinite series expansion theorem is given. And the tracking control design problem is solved by appropriate state augment. Secondly, the zero sum differential game strategy is introduced to address the control design problem of uncertain systems with event-triggered inputs. The actor-critic-disturbance networks framework is used to approximate the optimization of event- triggered controller strategy, optimization costs, and the disturbance strategy, respectively. Due to the consideration of discrete time and continuous time dynamics, we put the impulsive system method to use and choose appropriate Lyapunov functions to prove stability and boundedness, at the same time, there will be no infinite triggering situation. Finally, the effectiveness of the proposed scheme is demonstrated by an example of a practical tractor system with n trailers through simulation compared with another typical design method. [ABSTRACT FROM AUTHOR]

In this paper, by adopting sliding mode control, an adaptive memoryless control scheme has been developed for uncertain Rössler chaotic systems with unknown time delays. Firstly, the proposed adaptive control can force the trajectories of controlled Rössler time-delayed chaotic systems into the specified sliding manifold. Then, the Riemann sum is introduced to analyze the stability of the equivalent dynamics in the sliding manifold. The control performance can be predicted even if the controlled systems have unmatched uncertainties and unknown time delays, which have not been well addressed in the literature. Numerical simulations are included to demonstrate the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

The leader‐following consensus problem of a class of non‐strict feedback multi‐agent systems with unknown disturbances, this paper develops a novel adaptive event‐triggered control strategy ground on the consideration of the full state constraints. Combining the dynamic surface control and event triggering mechanism, the unknown external disturbances are estimated by designing a disturbance observer. In order to deal with unknown functions, this paper employs the neural networks. On purpose of keeping the output variable within a constraint boundary, the barrier Lyapunov function is chosen during the design course. Then, through the backstepping method and the Lyapunov stability theorem, it is proved that all signals in the closed‐loop systems are bounded, and the control performance of the closed‐loop system is ensured by selecting design parameters reasonably. Eventually, the availability of the control strategy is guaranteed through experimental example. [ABSTRACT FROM AUTHOR]

Summary: In this article, based on partial differential equations (PDEs), the flexible manipulator system with both dead‐zone input and state constraints is studied. The dynamic model of the flexible manipulator system is described by PDEs. The parameters of the dead‐zone input are unknown, and the state constraint problem is also considered. An adaptive approach is proposed to offset the effects caused by dead‐zone input. Thus, to guarantee that all states remain within their respective constraint regions, the boundary control law based on the barrier Lyapunov function is given, and an adaptive controller is designed. According to the Lyapunov analysis method, the control method is given to ensure that all signals of the closed‐loop system are bounded and all states satisfy the constraint conditions. Finally, simulation results show the effectiveness of the proposed control method in this article. [ABSTRACT FROM AUTHOR]

A robust adaptive tracker is newly proposed for a class of nonlinear systems with input nonlinearities and uncertainties. Because the upper bounds of input nonlinearities and uncertainties are difficult to be acquired, the adaptive control integrated with sliding mode control (SMC) and radial basis function neural network (RBFNN) are utilized to cope with these undesired problems and effectively complete the robust tracker design. The main contributions are concluded as follows: (1) new sufficient conditions are obtained such that the proposed adaptive control laws can avoid overestimation; (2) A smooth tanh function is introduced to eliminate the undesired chattering phenomenon in the traditional SMC systems; (3) A robust tracker is proposed such that the controlled system outputs can robustly track the pre-specified trajectories directly, even when subjected to unknown input nonlinearities and uncertainties. Finally, the numerical simulation results are illustrated to verify the proposed approach. [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]

In this paper, a reinforcement learning-based adaptive control algorithm is proposed to solve the tracking problem of a discrete-time (DT) nonlinear state and input time delayed system of the wheeled mobile robot (WMR). With the typical model of the WMR transformed into an affine nonlinear DT system, a delay matrix function and appropriate Lyapunov–Krasovskii functionals are introduced to overcome the problems caused by the state and input time delays, respectively. Furthermore, with the approximation of the radial basis function neural networks (NNs), the adaptive controller, the critic NN, and action NN adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the WMR system, and the tracking errors convergence to a small compact set to zero. Two examples of simulation are given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the global robust output regulation problem of a class of uncertain nonlinear systems is investigated by the event-triggered adaptive control law for the case of unknown control direction. The Nussbaum-type function-based technique is proposed to tackle the presence of unknown control direction. Then, by applying the adaptive control technique and the internal model principle, a new event-triggered adaptive control method is proposed. With the proposed corresponding event-triggered mechanism, the output regulation of the nonlinear systems can be realized regardless of the unknown control direction, meanwhile the Zeno behavior can be excluded. Finally, a numerical example is presented to verify the effectiveness of the proposed control law. [ABSTRACT FROM AUTHOR]

In this article, we study the control problem of the vehicle active suspension systems (ASSs) subject to actuator failure. An adaptive control scheme is presented to stabilize the vertical displacement of the car-body. Meanwhile, the ride comfort, road holding, and suspension space limitation can be guaranteed. In order to overcome the uncertainty, the neural network is developed to approximate the continuous function with the unknown car-body mass. Furthermore, to improve the transient regulation performance of ASSs when the actuator failure occurs, we propose a novel control scheme with the prescribed performance function to characterize the tracking error convergence rate and maximum overshoot in ASSs. Then, the stability of the proposed control algorithm can be proven based on the Lyapunov theorem. Finally, the comparative simulation results of two actuator failure types (i.e., the float fault and the loss of effectiveness fault) are given to demonstrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

In this paper, a novel adaptive fuzzy tracking control strategy is developed for nonlinear time-varying delayed systems with full state constraints. State constraints and time delays are normally found in various real-life plants, which are two important factors for degrading system performance significantly. In the framework of adaptive control, the effects of state constraints and time-varying delays are removed simultaneously. The integral Barrier Lyapunov functionals (IBLFs) are applied to achieve full-state-constraint satisfactions and remove the need of the transformed error constraints in previous BLFs. The unknown time-varying delays are completely compensated by introducing the separation technique and Lyapunov–Krasovskii functionals (LKFs). The unknown functions existing in systems are approximated by employing fuzzy logic systems (FLSs). With the help of less-adjustable parameters, only one parameter is needed to be adjusted online in each step of control design. The novel strategy can guarantee that a satisfactory tracking performance is achieved and the signals existing in the closed-loop system are bounded. Finally, by presenting simulation results, the efficiency of the proposed approach is revealed. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive neural network (NN) control scheme is proposed for a quarter-car model, which is the active suspension system (ASS) with the time-varying vertical displacement and speed constraints and unknown mass of car body. The NNs are used to approximate the unknown mass of car body. It is commonly known that the stability and security of the ASSs will be weakened when the constraints are violated. Thus, the control problem of the time-varying vertical displacement and speed constraints for the quarter-car ASSs is a very important task because of the demand of the handing safety. The time-varying barrier Lyapunov functions are used to guarantee the constraints of the vertical displacement not violated, and it can prove the stability of the closed-loop system. Finally, a simulation example for the ASSs is employed to show the feasibility and rationality of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an adaptive fuzzy control approach of multiple‐input–multiple‐output (MIMO) switched uncertain systems, which involve time‐varying full state constraints (TFSCs) and unknown disturbances. In the design procedure, the fuzzy logic systems are adopted to approximate the unknown functions in the systems. The adaptive fuzzy controller is set up by backstepping technique. According to the tangent barrier Lyapunov function (BLF‐Tan), a novel adaptive MIMO switched nonlinear control algorithm is designed. Under the rule of arbitrary switchings and the proposed control laws, it is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero with TFSCs. Furthermore, the simulation example validates the effectiveness of presented control strategy. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with adaptive tracking control for switched uncertain nonlinear systems, which contain the time‐varying output constraint (TVOC) and input asymmetric saturation characteristic. In response to the unknown functions, the fuzzy logic systems are adopted. The controller is constructed by the backstepping technique. Based on the Tangent Barrier Lyapunov Function (BLF‐Tan), an adaptive switched control scheme is designed. It is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded with TVOC under arbitrary switchings. Furthermore, the effectiveness of presented control method is validated via the simulation example. [ABSTRACT FROM AUTHOR]

This paper presents a distributed adaptive formation control method for uncertain multiple quadrotor systems under a directed graph that characterizes the interaction among the leader and followers. The proposed approach is based on an adaptive dynamic surface control, consensus algorithm and graph theory, where the system uncertainties are approximately modelled by interval type-2 fuzzy neural networks. The adaptive laws of interval type-2 fuzzy neural network parameters are derived from the stability analysis. In this study, the robust stability of the closed-loop system is guaranteed by the Lyapunov theorem, and the leader-follower formation goal can be asymptotically achieved. The developed control scheme is applied to the followers of quadrotor systems for performance evaluations. Simulation results are also provided to compare with the existing methods and reveal the superiority of the proposed adaptive formation controller. [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]

The adaptive event-triggered control problem is studied for the flexible beam system modeled by partial differential equations (PDEs) with uncertain system parameters and state constraint. In the design process of the controller, the event-triggered mechanism of relative threshold strategy is added to reduce the communication pressure. It further makes the communication process more flexible and improves the system working ability. The tangent barrier Lyapunov function (TAN-BLF) is selected to ensure that the system states satisfy their corresponding time-varying constraint bounds. The adaptive technique is chosen to solve the uncertain parameter problem. The system stability is verified on account of Lyapunov stability analysis method, and the boundedness of all system signals is proved. Furthermore, the Zeno behavior is successfully avoided. Finally, simulation results show the effectiveness and rationality of the proposed control strategy. [ABSTRACT FROM AUTHOR]

An adaptive control approach based on the fuzzy systems for a class of uncertain nonlinear multi-input multi-output (MIMO) systems is presented in this paper. This class of systems is in the nested multiple coupling structure and their states are constrained in the corresponding compact sets. The properties of the system structure are inevitable to bring about a complicated design and a difficult task. The fuzzy logic systems are employed to approximate the unknown functions of systems, and the decoupling backstepping way is proposed to design the stability controller and adaptation laws. Barrier Lyapunov functions (BLFs) are constructed in the backstepping design to guarantee that the constraint bounds are not violated. Based on Lyapunov analysis in barrier form, we can prove the stability of the closed-loop system. Two simulation examples are viewed to verify the feasibility of the approach. [ABSTRACT FROM AUTHOR]

An adaptive control scheme is developed in the paper for nonlinear stochastic systems with unknown parameters. All the states in the systems are required to be constrained in a bounded compact set, i.e., the full state constraints are considered in the systems. It is for the first time to control nonlinear stochastic systems with the full state constraints. In contrast to deterministic systems, the stochastic systems with the full state constraints are more difficult to be stabilized and the design procedures are more complicated. By constructing Barrier Lyapunov Functions (BLF) in symmetric and asymmetric forms, it can be ensured that all the states of the stochastic systems are not to transgress their constraint bounds. Thus, the proposed scheme not only solves the stability problem of stochastic systems, but also overcomes the effect of the full state constraints on the control performance. Finally, it is proved that all the signals in the closed-loop system are semi-global uniformly ultimately bounded (SGUUB) in probability, the system output is driven to follow the reference signals, and all the states are ensured to remain in the predefined compact sets. The validity of the proposed scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

A novel adaptive multi-context cooperatively coevolving particle swarm optimization (AM-CCPSO) algorithm is proposed in an attempt to improve the performance on solving large-scale optimization problems (LSOP). Due to the curse of dimensionality, most optimization algorithms show their weaknesses on LSOP, and the cooperative co-evolution (CC) is often utilized to overcome such weaknesses. The basic CC framework employs one context vector for cooperatively, but greedily coevolving different subcomponents, which sometimes fails to find global optimum, especially on some complex non-separable LSOP. In the AM-CCPSO, more than one context vectors are employed to provide robust and effective co-evolution. These vectors are selected with respect to each particle of each subcomponent according to their own adaptive probabilities. In the AM-CCPSO, a new PSO updating rule is also proposed to exploit 'four best positions' via Gaussian sampling. On a comprehensive set of benchmarks (up to 1000 real-valued variables), as well as on a real world application, the performance of AM-CCPSO can rival several state-of-the-art evolutionary algorithms. Experimental results indicate that the novel adaptive multi-context CC framework is effective to improve the performance of PSO on solving LSOP and can be generally extended in other evolutionary algorithms. [ABSTRACT FROM AUTHOR]

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]

The angular response (AR) effect which reduces multibeam backscatter image quality significantly cannot be removed by the traditional AR correction methods effectively. Therefore, the paper puts forward two self-adaptive AR correction methods, namely the AR modeling method and the AR clustering method. The former uses the AR parameters of the average AR curve for modeling and correction, while the latter uses the AR curve of each seabed sediment for AR correction. Both methods overcome the defects of the traditional methods, and improve the image quality obviously. The validities of the methods have been verified by the experiments. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive controller design is studied for single-input–single-output (SISO) nonlinear systems with parameter uncertainties and the systems are enforced to subject to the full state constraints. A remarkable feature of the constrained systems is that the so-called control direction is unknown, or in other words, the signs of control gains are unknown. In the existing results, we discover that all the state constraint control results are required to determine a priori knowledge of control direction. It will be inevitable to bring about a different design procedure and a difficult task when no a priori knowledge of control direction is known. To stabilize this class of systems, two parameter adaptive controllers with Nussbaum gain technique are constructively framed to overcome the unknown control direction problem, and the novel symmetric and asymmetric Barrier Lyapunov Functions (BLFs) are adopted to guarantee that the states are not to violate their constraints. Then, the proposed BLF strategy can be to conquer the conservatism of the traditional BLF-based controls for the full state constraints. Finally, two theorems are provided to show that all the signals in the closed-loop system are bounded, the outputs are driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets. The effectiveness of the proposed scheme is performed via a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive tracking control approach is framed for a class of switched discrete-time nonlinear systems with unknown parameters. Allowable switching law is constructed and the controller is chosen by switched Lyapunov function schema. Adaptive updating control algorithm for discrete-time nonlinear switched systems are first derived. Moreover, we can prove that the closed-loop switched system is uniformly stable and the output tacking error is guaranteed to converge to a small neighborhood of zero. Lastly, an illustrative example is given to demonstrate the effectiveness of proposed approach. [ABSTRACT FROM AUTHOR]

The external disturbance, model uncertainty and actuator faults can affect performance even the safety of flight. To tackle such problems, an adaptive fault-tolerant control method is presented integrated with fast terminal sliding mode control (FTSMC) technology and neural network (NN) for the attitude system of a quadrotor unmanned aerial vehicle, where the NN is employed to approximate the uncertain terms in the system. First, for the loss of effectiveness, an adaptive law is developed to estimate the unknown fault coefficient. Then considering the unknown upper bound of the total disturbance, an adaptive law is designed to predict the unknown upper bound. Furthermore, considering the transient response, a FTSMC scheme is developed for the attitude system, which has better convergence rate than conventional terminal sliding mode control. Finally, the contrast test is performed to verify the effectiveness and superiority of the proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, we aim to solve the optimal tracking control problem for the Henon Mapping chaotic system using the direct heuristic dynamic programming (DHDP) setting with filtered tracking error. The fuzzy logic system is used to approximate the long-term utility function. Compared with the results for chaotic discrete-time system, the cost of the controller is reduced. The Lyapunov analysis approach is utilized to prove the stability of the chaotic system. It is shown that the tracking error, the adaptation law and the control input retain the property of uniformly ultimate boundedness. A simulation example is given to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this study, an adaptive control technique is developed for a class of uncertain nonlinear parametric systems. The considered systems can be viewed as a class of nonlinear pure-feedback systems and the full state constraints are strictly required in the systems. One remarkable advantage is that only less adjustable parameters are used in the design. This advantage is first to take into account the pure-feedback systems with the full state constraints. The characteristics of the considered systems will lead to a difficult task for designing a stable controller. To this end, the mean value theorem is employed to transform the pure-feedback systems to a strict-feedback structure but non-affine terms still exist. For the transformed systems, a novel recursive design procedure is constructed to remove the difficulties for avoiding non-affine terms and guarantee that the full state constraints are not violated by introducing Barrier Lyapunov Function (BLF) with the error variables. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded and the tracking error is remained in a bounded compact set. Two simulation studies are worked out to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This article focuses on the adaptive control problem for Arneodo chaotic systems. It is considered a phenomenon of single state constraint for the systems. In the proposed scheme, the barrier Lyapunov function approach was successfully used to prevent the single state from violating constraint conditions. In the current circumstances, a great many of the results for chaotic systems neglect the situation of constraint. Finally, it is proved that all the signals in the Arneodo chaotic system are bounded. A representative example is proposed in numerical simulations compared with existing results. The performance of the proposed control scheme was validated by using a simulated example. [ABSTRACT FROM PUBLISHER]

The paper presents an improved adaptive sliding mode control method based on fuzzy neural networks for a class of nonlinear systems subjected to input nonlinearity with unknown model dynamics. The control scheme consists of the modified adaptive and the compensation controllers. The modified adaptive controller online approximates the unknown model dynamics and input nonlinearity and then constructs the sliding mode control law, while the compensation controller takes into account the approximation errors and keeps the system robust. Based on Lyapunov stability theorem, the proposed method can guarantee the asymptotic convergence to zero of the tracking error and provide the robust stability for the closed-loop system. In addition, due to the modification in controller design, the singularity problem that usually appears in indirect adaptive control techniques based on fuzzy/neural approximations is completely eliminated. Finally, the simulation results performed on an inverted pendulum system demonstrate the advanced functions and feasibility of the proposed adaptive control approach. [ABSTRACT FROM AUTHOR]

In this study, we investigate an adaptive fuzzy controller design for a class of nonlinear multi-input multi-output (MIMO) systems in interconnected form. The systems considered comprise n subsystems and an unknown interconnection term is included in every equation for each subsystem. The interconnection term is a function of all the states from the first to the ( n − 1 ) th subsystems. Moreover, the effects of dead-zone models are considered in each subsystem of the systems. These properties of the systems cause the difficulties and add further complexity to the design. In order to overcome these difficulties, we use the following methods: (1) the fuzzy logic systems are employed to approximate the appropriate unknown functions of the systems, (2) a novel backstepping design procedure is constructively designed, and (3) compensative adaptation laws are provided to compensate for the effects of the dead-zone inputs. We show that all the signals in the closed-loop system are bounded and that the outputs converge to a compact set by using the Lyapunov analysis theorem. Simulated examples are presented that validate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

In this paper, a stable reinforcement learning control approach using neural networks (NNs) is developed for the trajectory tracking of an n-link rigid robot manipulator. The considered systems are in discrete time form. The proposed controller design consists of two NNs. One is the critic network that is used to approximate the long-term cost function, whereas other is that the action NN is employed to generate the system input. Then, an optimal control input can be obtained compared with other robot manipulator systems. Using the Lyapunov approach, the tracking error and weight estimates are proven to be semi-global uniformly ultimately bounded. A simulation example is employed to illustrate the effectiveness of the proposed controller. [ABSTRACT FROM PUBLISHER]

In this paper, an adaptive critic neural network controller is designed for a class of discrete-time chaotic system. The critic neural network is used to approximate the long-term function. In contrast with the existing results for discrete-time chaotic systems, in this paper, a near optimal control input can be generated when the long-term function is minimized. It is proven that the tracking error, the adaptation laws and the control input are uniformly bounded. A simulation example is employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper designs a fuzzy adaptive control approach for the Continuous Stirred Tank Reactors (CSTRs) with full state constraints and actuator faults. Using the backstepping design technique and Integral barrier Lyapunov function (IBLF), the full state constraints are handled in the design process of the adaptive controller. Besides, there exist unknown internal dynamics in the CSTRs system, which are identified by the fuzzy logic system. It is shown that the constraints are not overstepped and the CSTRs operate reliably is ensured, despite the presence of system nonlinearities, stuck faults and loss of control effectiveness. Based on the Lyapunov stability theory, the proposed approach can ensure that all the signals of the CSTRs system are globally bounded. Finally, the simulation results on CSTRs are showed to reveal the availability of the developed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive control algorithm is proposed for a class of robot manipulator systems with unknown functions and dead-zone input by using a reinforcement learning scheme. The parameters of the dead zone are supposed to be unknown but bounded. The unknown functions can be approximated based on the neural networks, which is one part of the reinforcement learning scheme, namely an action network. The other part is called critic network which is used to approximate the reinforcement signal. Then, the prominent advantage of the proposed approach is that an optimal control input can be obtained by using two networks compared with the results of robot manipulator with dead zone: an additional term is given to compensate for the effect of the dead zone, and a special design procedure to solve the difficulties in constructing the controllers and adaptation laws. Based on the Lyapunov analysis theory, all the signals of the closed-loop system are proved to be bounded and the system output can track the reference signal to a bounded compact set. Finally, a simulation example is given to illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper studies an adaptive output-feedback control for a class of nonlinear single-input and single-output (SISO) systems with the full-state constraints. A state observer is designed to estimate those unmeasured states. At present, all the results in the output-feedback area ignore the effects of the full-state constraints. The presence of these constraints results in a complicated procedure and the major difficulties in the design. The barrier Lyapunov function (BLF) and a novel design procedure are given to overcome these difficulties. The adaptation law and the controllers are obtained based on the backstepping design procedure. In addition, only one adjustable parameter needs to be updated, and thus, the online computation burden is alleviated. The stability of the closed-loop system is proven by using the Lyapunov theorem. A simulation example is given to verify the effectiveness of the approach. [ABSTRACT FROM PUBLISHER]

In this article, a direct adaptive neural networks control algorithm is presented for a class of SISO discrete-time systems with non-symmetric dead-zone. The property of the dead-zone is discretized. Mean value theorem is used to transform the systems into a special form. The unknown functions in the input–output model are approximated using the radial basis function neural networks. Compared with the results for the discrete non-symmetric dead-zone, this article presents a new algorithm to reduce the computational burden. Lyapunov analysis method is utilized to prove that all the signals in the closed-loop systems are semi-global uniformly ultimately bounded. The tracking error is proved to converge to a small set around the zero. A simulation example provided to illustrate the effectiveness of the control schemes. [ABSTRACT FROM AUTHOR]

A robust adaptive NN output feedback control is proposed to control a class of uncertain discrete-time nonlinear multi-input-multi-output (MIMO) systems. The high-order neural networks are utilized to approximate the unknown nonlinear functions in the systems. Compared with the previous research for discrete-time MIMO systems, robustness of the proposed adaptive algorithm is obvious improved. Using Lyapunov stability theorem, the results show all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood of zero by choosing the design parameters appropriately. [ABSTRACT FROM AUTHOR]

In this paper, a direct adaptive neural network control algorithm based on the backstepping technique is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. The neural networks are utilized to approximate unknown functions, and a stable adaptive neural network controller is synthesized. The fact that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded is proven and the tracking error can converge to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the previous research for discrete-time systems, the proposed algorithm improves the robustness of the systems. A simulation example is employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

An adaptive output feedback control is studied for uncertain nonlinear single-input–single-output systems with partial unmeasured states. In the scheme, a reduced-order observer (ROO) is designed to estimate those unmeasured states. By employing radial basis function neural networks and incorporating the ROO into a new backstepping design, an adaptive output feedback controller is constructively developed. A prominent advantage is its ability to balance the control action between the state feedback and the output feedback. In addition, the scheme can be still implemented when all the states are not available. The stability of the closed-loop system is guaranteed in the sense that all the signals are semiglobal uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to validate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problems of stability and control for a class of uncertain nonlinear systems with unknown state time-delay are studied by using the fuzzy logic systems. Because the dynamic surface control technique is introduced to deal with the uncertain time-delay systems, the designed adaptive fuzzy controller can avoid the issue of "explosion of complexity", which comes from the traditional backstepping design procedure. Compared with the existing results in the literature, the robustness to the fuzzy approximation errors is improved by adjusting the estimations of the unknown bounds for the approximation errors. It is shown that the resulting closed-loop system is stable in the sense that all the signals are bounded and the system output track the reference signal in a small neighborhood of the origin by choosing design parameters appropriately. Three simulation examples are given to demonstrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the adaptive fuzzy tracking control problem for a class of uncertain nonlinear MIMO systems with the external disturbances. The adaptive fuzzy controllers are designed under the constraint that only system output is available for measurement. Then, it is needed to design a state observer to estimate the unmeasured states. In the observer design procedure, two prominent advantages are that it does not require the sign of the control gain coefficient to be known and only two parameters need to be adjusted on-line for each subsystem. By using Lyapunov analysis method, it is proven that all the signals in the closed-loop system are guaranteed to be bounded and the system outputs track the reference signals to a bounded compact set. The feasibility of the proposed approach is validated by using two simulation examples. [ABSTRACT FROM AUTHOR]

Abstract: Based on the universal approximation property of the fuzzy-neural networks, an adaptive fuzzy-neural observer design algorithm is studied for a class of nonlinear SISO systems with both a completely unknown function and an unknown dead-zone input. The fuzzy-neural networks are used to approximate the unknown nonlinear function. Because it is assumed that the system states are unmeasured, an observer needs to be designed to estimate those unmeasured states. In the previous works with the observer design based on the universal approximator, when the dead-zone input appears it is ignored and the stability of the closed-loop system will be affected. In this paper, the proposed algorithm overcomes the affections of dead-zone input for the stability of the systems. Moreover, the dead-zone parameters are assumed to be unknown and will be adjusted adaptively as well as the sign function being introduced to compensate the dead-zone. With the aid of the Lyapunov analysis method, the stability of the closed-loop system is proven. A simulation example is provided to illustrate the feasibility of the control algorithm presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract: Based on the backstepping technique, a direct adaptive neural network control algorithm is proposed for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. Neural networks are utilized to approximate unknown functions, and a stable adaptive neural backstepping controller is synthesized. It is proven that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero by choosing the design parameters appropriately. Compared with the existing results for discrete-time systems, the proposed algorithm needs only less parameters to be adjusted online, therefore, it can reduce online computation burden. A simulation example is employed to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This article extends the application of the adaptive neural network control to a new class of uncertain MIMO non-linear systems, which are composed of interconnected subsystems where each interconnected subsystem is in the non-affine pure-feedback form. Because both the variables which are used as virtual controllers and the actual controllers appear non-linearly in unknown functions of the MIMO systems, thus, this class of systems is difficult to control. The radial basis function neural networks are utilised to approximate the desired virtual controllers and the desired actual controllers which are obtained by using implicit function theorem. The salient property of the proposed approach is that the number of the adjustable parameters is less than the numerous alternative approaches existing in the literature. It is proven that, under appropriate assumptions, all the signals in the closed-loop system are uniformly bounded and the tracking errors converge to a small neighbourhood of the origin by appropriately choosing design parameters. The feasibility of the developed approach is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

Abstract: The universal approximation theorem of the fuzzy logic systems (FLS) is utilized to develop an adaptive control scheme for a class of nonlinear MIMO systems by the backstepping technique. The MIMO systems consist of some subsystems and each subsystem is able to be reputed as non-affine pure-feedback structure. The external disturbances appear in each equation of each subsystem and the disturbance coefficients are assumed to be unknown functions rather than constant one. The two main advantages of the developed scheme are that (1) it does not require a priori knowledge of the signs of the control gains and (2) only one parameter is needed to be adjusted online in controller design procedure for each subsystem. It is proven that, under the appropriate assumptions, the developed scheme can achieve that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. Effectiveness of the developed scheme is illustrated by the simulation example. [Copyright &y& Elsevier]