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An adaptive neural network fault‐tolerant control method is proposed for the non‐affine multi‐agent systems with actuator failure and input saturation. Through the transformation of the original multi‐agent systems, an equivalent model is proposed. Considering that the signal input of multi‐agent systems is limited, this article will solve the input saturation problem. But in a real system, the actuator would probably fail. Therefore, a fault tolerant control algorithm is proposed to solve the fault problem in the systems. In this article, an adaptive distributed controller is designed to eliminate the uncertainty of the systems. At the same time, the integral barrier Lyapunov function is selected to verify the stability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method. [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]

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, 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, 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]

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 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]

In this paper, based on an adaptive nonbackstepping design algorithm, we proposed a novel variable universe of discourse fuzzy control (VUDFC) approach for a class of single-input-single-output strict-feedback nonlinear systems with unknown dead-zone inputs. Firstly, we convert the form of system into a normal form on the basis of some new state variables and coordinate transformation; at the same time, state-feedback control is changed to output-feedback control. Secondly, we design observers to estimate the new unmeasurable states. Then, different from considering the traditional backstepping-based fuzzy control scheme, we introduce a direct VUDFC scheme, which is mainly based on changing of contraction-expansion factors to modify the universe of discourse online, and fuzzy rules can automatically reproduce to develop the control performance; thus, the size of initial rule base is greatly reduced. This new algorithm can alleviate tracking error, improve the accuracy of the system, and strengthen robustness. Lastly, according to Lyapunov theorem analysis, we prove that all the signals in the closed-loop system can be guaranteed to be stable, and the output can track the reference signal very well. Simulation results illustrated the effectiveness of the proposed VUDFC approach. [ABSTRACT FROM AUTHOR]

An adaptive control-based neural network for a n -link robot is studied and the considered robot can be transformed as a class of multi-input–multioutput systems. The position of the robot or the output of the transformed systems is constrained in a time-varying compact set. It is commonly known that the constant constraint belongs to a special case of the time-varying constraint, and thus, it can be more general for handling practical problem as compared with the existing methods for robot. The neural approximation is used to estimate the unknown functions of systems and the time-varying barrier Lyapunov function is used to overcome the violation of constraints. It can prove the stability of the closed-loop systems by using Lyapunov analysis. The feasibility of the approach is demonstrated by performing a simulation example. [ABSTRACT FROM PUBLISHER]

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]

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]

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]

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]

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]

In this paper, an anti-disturbance output tracking control strategy is proposed for turbofan systems with multiple disturbances. The considered turbofan models are described by switched systems. For the unmeasured disturbances, a disturbance observer is designed. Then, the observer-based controller is proposed such that the system output tracks the desired signal and multiple disturbances are successfully suppressed. Applying the multiple Lyapunov functions method, the stability of the closed-loop system with H ∞ control performance is analyzed and proved. Finally, a simulation example of turbofan system is presented to illustrate the effectiveness of the proposed method. • Studied the output tracking control problem under multiple disturbances. • The design of the controller directly utilizes the tracking signal as part of the feedback. • The proposed H ∞ output tracking anti-disturbance control scheme can improve the performance of the turbofan switched systems. [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]

This brief studies an adaptive neural output feedback tracking control of uncertain nonlinear multi-input–multi-output (MIMO) systems in the discrete-time form. The considered MIMO systems are composed of n subsystems with the couplings of inputs and states among subsystems. In order to solve the noncausal problem and decouple the couplings, it needs to transform the systems into a predictor form. The higher order neural networks are utilized to approximate the desired controllers. By using Lyapunov analysis, it is proven that all the signals in the closed-loop system is the semi-globally uniformly ultimately bounded and the output errors converge to a compact set. In contrast to the existing results, the advantage of the scheme is that the number of the adjustable parameters is highly reduced. The effectiveness of the scheme is verified by a simulation example. [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]

This article puts forward an adaptive neural network fault‐tolerant control scheme under the state constraints for the flexible manipulator system with uncertain terms. The dynamic model of the system is described by partial differential equations. The tangent barrier Lyapunov functions are chosen in the design process for the sake of ensuring that all states in the system satisfy the constrained conditions. The uncertainties resulted from load mass, hub inertia, and bending stiffness in the system are approximated by using the universal approximation property of neural networks. The adaptive method is used to counteract the influence of joint motor actuator failure. At the same time, combining with the backstepping design framework to design effective controllers to assure that all signals in the closed‐loop system are bounded. Lyapunov stability analysis method is used to prove the stability of the system. Finally, the simulation results prove the availability of the raised control method. [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]

In this paper, we design an adaptive neural network (NN) controller of uncertain ${n}$ -joint robotic systems with time-varying state constraints. By proposing a nonlinear mapping, the robotic systems are transformed into the multiple-input, multiple-output systems. Compared with constant constraints, the time-varying state constraints are more general in the real systems. To overcome the design challenge, the time-varying barrier Lyapunov function is introduced to ensure that the states of the robotic systems are bounded within the predetermined time-varying range. The NN approximations are employed to approximate the uncertain parametric and unknown functions in the robotic systems. Based on the Lyapunov analysis, it can be proved that all signals of robotic systems are bounded; the tracking errors of system output converge on a small neighborhood of zero and the time-varying state constraints are never violated. Finally, a simulation example is performed to demonstrate the feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, for the flexible marine riser system with the top tension constraint, the output feedback controller is developed to suppress the vibration of the riser. The dynamic behavior of the flexible riser is expressed by the partial differential equation (PDE). Firstly, a high-gain observer is designed to estimate unmeasurable system states. Secondly, the top tension of the riser is constrained with the aid of the logarithmic barrier Lyapunov function, and the output feedback boundary controller is developed using the direct Lyapunov method. Through rigorous mathematical analysis, the consistently bounded stability of the closed-loop system is achieved. Finally, the simulation is carried out to show that the developed control can stabilize the system with good performance under proper selection of design parameters. [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]

In this paper, an effective adaptive tracking control approach is constructed for the sixth-order induction motor model which is in discrete-time form. The fuzzy logic systems (FLSs) are applied to estimate a control law and used to a block strict feedback form (BSFF) which is in existence of bounded disturbances. Then, a desired optimal control can be achieved. Depend on the Lyapunov analysis approach, for the considered system, the stability is guaranteed, the tracking error can be ensured to a small neighborhood around zero, and the weight estimates can be insured to semi-global uniformly ultimately bounded (SGUUB). An advantage for the controlled system is that the proposed algorithm needs only less parameters which is different from the existing results, therefore, it can reduce the calculation amount. The practicality of the scheme is verified via a simulation. [ABSTRACT FROM AUTHOR]