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In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the 'explosion of complexity' problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

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This paper concerns the tracking control problem of a class of uncertain nonlinear systems subject to deferred time-varying state constraints and external disturbances. The states of the system are free in the initial phase and are restricted by some time-varying constraints after a particular time. A class of novel shifting functions are defined, which make any initial states that beyond the constraint region move to the desired position (such as zero). Thereafter, a new state transformation is implemented for the shifted state, which transforms the state constraint problem into the boundedness of a new variable. Compared with the existing BLF method, this approach avoids feasibility test for virtual control variables. Adaptive backstepping control and dynamic surface control are used in system controller design and stability analysis, and the ideal tracking performance is achieved. Finally, simulation example and comparative studies are carried out to illustrate the effectiveness and outstanding characteristics of the proposed approach. Simulation results show that the proposed control scheme broadens the scope of application, shortens running time and improves control efficiency compared with the existing control strategies.

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This article investigates a penalty-based distributed optimization algorithm of bipartite containment control for high-order nonlinear uncertain multi-agent systems with state constraints. The proposed method addresses the distributed optimization problem by designing a penalty function in the form of a quadratic function, which is the sum of the global objective function and the consensus constraint. Moreover, the observer is presented to address the unmeasurable state of each agent. Radial basis function neural networks (RBFNN) are employed to approximate the unknown nonlinear functions. Then, by integrating RBFNN and dynamic surface control (DSC) techniques, an adaptive backstepping controller based on the barrier Lyapunov function (BLF) is proposed. Finally, the effectiveness of the suggested control strategy is verified under the condition that the state constraints are not broken. Simulation results indicate that the output trajectories of all agents remain within the upper and lower boundaries, converging asymptotically to the global optimal signal.

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In this paper, sensorless robust speed control with nonlinear lumped mismatched disturbance observers for a permanent magnet type axial gap bearingless motor (AGBM) is designed. Multistage anti-windup-based dynamic surface control combined with integral backstepping control is proposed to control the motor's axial displacement and rotor speed. The approach is against parameter uncertainties and external disturbances, improving steady-state accuracy, eliminating the derivative explosion phenomenon, no chattering problem, and reducing the magnitude of the control system when current saturation occurs. In addition, a novel nonlinear lumped mismatched disturbance observer is proposed to improve the approach under unmodeled dynamics and external disturbances. To obtain high-accuracy tracking control, the control system includes the robust controller combined with the disturbance observers and anticipatory activation of anti-windup (AW) compensation, which means the controller is more complex. Then, to design a sensorless robust speed control for the motor, the rotor position and speed observer require higher accuracy. High-gain back-EMF observer combined with an improved phase-locked loop is proposed to estimate rotor angular position and speed even when the motor speed is reversed. Overall stability of closed-loop system control, including a sensorless speed control approach for motors using back-EMF estimation combined with saturation of the currents and lumped disturbance observers, is mathematically proven. Finally, the simulation results under measurement noise show that the proposed control system are obtained the effectiveness, feasibility, and robustness.

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The dual-motor driving servo system is continuously developed to satisfy strict safety and reliability requirements. However, several factors may degrade the system's performance, such as transmission backlash, parameter drift, and motor dynamic characteristic differences. To overcome these factors, this study proposes a finite-time tracking and synchronization control method for dual-motor servo systems that suffer from backlash and time-varying uncertainties. Our solution utilizes an adaptive dynamic surface and cross-coupling control scheme to deal with tracking and synchronization control issues and compensate for the unknown time-varying uncertainties. Through synchronizing the speed and acceleration states, the proposed controller guarantees high control performance and eliminates the force fighting caused by the motor's dynamic characteristic differences. In addition, finite-time control ensures the tracking error converges to an arbitrarily small neighborhood of zero in finite time. Moreover, the singularity problem in the derivative of the virtual control signal is avoided by introducing a new compensation term. Several simulations prove the proposed controller's stability and effectiveness.

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In the article, the adaptive composite dynamic surface neural controller design problem for nonlinear fractional-order systems (NFOSs) subject to delayed input is discussed. A fractional-order auxiliary system is first designed to solve the input-delay problem. By using the developed novel estimation models, the defined prediction errors and the states of error system can decide the weights of radial basis function neural networks (RBFNNs). During the dynamic surface controller design process, the developed fractional-order filters are designed to handle the complexity explosion problem when the classical backstepping control technique is utilized. It is shown that the designed adaptive composite neural controller ensures that all the system state variables are bounded and the tracking error of the considered system finally tends to a small neighborhood of zero. Finally, the results of the simulation explain the feasibility of the developed controller. In addition, the developed controller can also be applied to single input and single output(SISO) nonlinear systems subject to a unitary input function.

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This paper presents a distributed constant bearing guidance and model-free disturbance rejection control method for formation tracking of autonomous surface vehicles subject to fully unknown kinetic model. First, a distributed constant bearing guidance law is designed at the kinematic level to achieve a consensus task. Then, by using an adaptive extended state observer (AESO) to estimate the total uncertainties and unknown input coefficients, a simplified model-free kinetic controller is designed based on a dynamic surface control (DSC) design. It is proven that the closed-loop system is input-to-state stable The stability of the closed-loop system is established. A salient feature of the proposed method is that a cooperative behavior can be achieved without knowing any priori information. An application to formation control of autonomous surface vehicles is given to show the efficacy of the proposed integrated distributed constant bearing guidance and model-free disturbance rejection control.

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This paper suggests an adaptive funnel dynamic surface control method with a disturbance observer for the permanent magnet synchronous motor with time delays. An improved prescribed performance function is integrated with a modified funnel variable at the beginning of the controller design to coordinate the permanent magnet synchronous motor with the output constrained into an unconstrained one, which has a faster convergence rate than ordinary barrier Lyapunov functions. Then, the specific controller is devised by the dynamic surface control technique with first-order filters to the unconstrained system. Therein, a disturbance-observer and the radial basis function neural networks are introduced to estimate unmatched disturbances and multiple unknown nonlinearities, respectively. Several Lyapunov-Krasovskii functionals are constructed to make up for time delays, enhancing control performance. The first-order filters are implemented to overcome the "complexity explosion" caused by general backstepping methods. Additionally, the boundedness and binding ranges of all the signals are ensured through the detailed stability analysis. Ultimately, simulation results and comparison experiments confirm the superiority of the controller designed in this paper.

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This paper addresses a secure predictor-based neural dynamic surface control (SPNDSC) issue for a cyber-physical system in a nontriangular form suffering from both sensor and actuator deception attacks. To avoid the algebraic loop problem, only partial states are employed as input vectors of neural networks (NNs) for approximating unknown dynamics, and compensation terms are further developed to offset approximation errors from NNs. With introduction of nonlinear gain functions and attack compensators, adverse effects of an intelligent adversary are alleviated effectively. Furthermore, we present stability analysis and prove the ultimate boundedness of all signals in the closed-loop system. The effectiveness of the proposed control strategy is illustrated by two examples.

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The presented control scheme in this paper aims at stabilizing uncertain time-delayed systems requiring all states to change within the preset time-varying constraints. The controller design framework is based on the backstepping method, drastically simplified by the dynamic surface control technique. Meanwhile, the radius basis function neural networks are utilized to deal with the unknown items. To prevent all state variables from violating time-varying predefined regions, we employ the time-varying barrier Lyapunov functions during the backstepping procedure. Moreover, appropriate Lyapunov-Krasovskii functionals are used to cancel the influence of the time-delay terms on the system's stability. Under the presented control laws and Lyapunov analysis, it is proven that constraints on all state variables are not breached, good tracking performance of desired output is achieved, and all signals in the closed-loop systems are bounded. The effectiveness of our control scheme is confirmed by a simulation example.

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This paper investigates the problem of output feedback neural network (NN) learning tracking control for nonlinear strict feedback systems subject to prescribed performance and input dead-zone constraints. First, an NN is utilized to approximate the unknown nonlinear functions, then a state observer is developed to estimate the unmeasurable states. Second, based on the command filter method, an output feedback NN learning backstepping control algorithm is established. Third, a prescribed performance function is employed to ensure the transient performance of the closed-loop systems and forces the tracking error to fall within the prescribed performance boundary. It is rigorously proved mathematically that all the signals in the closed-loop systems are semi-globally uniformly ultimately bounded and the tracking error can converge to an arbitrarily small neighborhood of the origin. Finally, a numerical example and an application example of the electromechanical system are given to show effectiveness of the acquired control algorithm.

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This paper studies an observer-based neural network position tracking control scheme for induction motors system operating under a field-oriented control scheme with the problem of stochastic disturbance. Firstly, the angular velocity is estimated by the constructed reduced-order observer. Then, the nonlinear functions are approximated by the neural networks and the stochastic Lyapunov functions are chosen to analyze the stability of the system. Besides, the "complexity of computation" existed in traditional backstepping control is solved by using the dynamic surface control technique. At last, the results of the comparison simulation experiments show that the proposed control scheme can reduce the influence of stochastic disturbance, and have faster tracking speed smaller tracking error. The designed observer can estimate the signals effectively.

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This paper studies the issue of adaptive fuzzy output-feedback event-triggered control (ETC) for a fractional-order nonlinear system (FONS). The considered fractional-order system is subject to unmeasurable states. Fuzzy-logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy state observer is founded to estimate the unmeasurable states. By constructing appropriate Lyapunov functions and utilizing the backstepping dynamic surface control (DSC) design technique, an adaptive fuzzy output-feedback ETC scheme is developed to reduce the usage of communication resources. It is proved that the controlled fractional-order system is stable, the tracking and observer errors are able to converge to a neighborhood of zero, and the Zeno phenomenon is excluded. A simulation example is given to verify the availability of the proposed ETC algorithm.

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For strict-feedback nonlinear systems (SFNSs) with unknown control direction, this paper synthesizes an asymptotic tracking controller by a combination of the dynamic surface control (DSC) technique, the Nussbaum gain technique (NGT) and fuzzy logic systems (FLSs). The SFNSs under study feature unknown nonlinear uncertainties and external disturbances. By utilizing the DSC technique with nonlinear filters, the issue of 'differential explosion' is obviated, in which the adaptive laws are constructed to conquer the effect of unknown functions. The FLSs are exploited to cope with uncertainties without any prior conditions of the ideal weight vectors and the approximation errors. In addition, by introducing the NGT, the unknown control direction problem is solved. Compared with the existing results, the proposed design procedure is able to simultaneously overcome the 'differential explosion' and the unknown control direction problems, and asymptotic tracking is accomplished. At the end, a second-order numerical system and a more realistic Norrbin nonlinear mathematical model are applied to confirm the feasibility of the design procedure.

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An adaptive finite-time approach to the feedback control of stochastic nonlinear systems is presented. The fuzzy logic system (FLS) and a state observer are used to estimate the uncertain function and unmeasured state of the controlled system, respectively. A dynamic surface control (DSC) scheme is employed to deal with the "computational explosion" problem, which is inherent in traditional backstepping methods since the repetitive calculation of the derivatives of virtual control signals is avoided. A new output feedback controller is developed to guarantee that all the signals of the controlled system are bounded within a finite time range and the tracking deviation can converge to an arbitrarily small residual set within finite time. Simulations confirm the analytical and theoretical results of the presented algorithm.

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Unmodeled dynamics and output constraint are very often experienced in many physical applications, while few studies on them simultaneously are constructed. This study concentrates on the problem of adaptive multi-dimensional Taylor network dynamic surface control (MTN-DSC) for a class of strict-feedback uncertain nonlinear systems subjected to unmodeled dynamics and output constraint. The purpose is to make this study more practical, and design a controller with simple structure to improve the system performance. A barrier Lyapunov function is used to restrict the system output to within the prescribed constraint. At each step during the backstepping design process, an MTN is applied to approach the generated unknown composite function stemming from the unknown functions and uncertain disturbances, rather than individually; this simplifies the structure and reduces the complexity of the controllers. Meanwhile, the computational burden is further reduced, as only one parameter is adjusted online, which has the minimum number of parameters to be adjusted. Additionally, DSC technique is introduced to eliminate the inherent "explosion of complexity" problem in traditional backstepping design procedure. Furthermore, it is proved that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and that the output constraint is never violated. The validity of the proposed control scheme is illustrated through the numerical and applied simulation examples.

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In this paper, an output-feedback fuzzy adaptive dynamic surface controller (FADSC) based on fuzzy adaptive extended state observer (FAESO) is proposed for autonomous underwater vehicle (AUV) systems in the presence of external disturbances, parameter uncertainties, measurement noises and actuator faults. The fuzzy logic system is incorporated into both the observers and controllers to improve the adaptability of the entire system. The dynamics of the AUV system is established first, considering the external disturbances and parameter uncertainties. Based on the dynamic models, the ESO, combined with a fuzzy logic system tuning the observer bandwidth, is developed to not only adaptively estimate both system states and the lumped disturbances for the controller, but also reduce the impact of measurement noises. Then, the DSC, together with fuzzy logic system tuning the time constant of the low-pass filter, is designed using estimations from the FAESO for the AUV system. The asymptotic stability of the entire system is analyzed through Lyapunov's direct method in the time domain. Comparative simulations are implemented to verify the effectiveness and advantages of the proposed method compared with other observers and controllers considering external disturbances, parameter uncertainties and measurement noises and even the actuator faults that are not considered in the design process. The results show that the proposed method outperforms others in terms of tracking accuracy, robustness and energy consumption.

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This paper presents an adaptive neural network output feedback control method for stochastic nonlinear systems with full state constraints. The barrier Lyapunov functions are used to conquer the effect of state constraints to system performance. The neural network state observer is established to estimate the unmeasured states. By using dynamic surface control technique, the "explosion of complexity" issue existing in the backstepping design is overcome. The proposed control scheme can guarantee that all signals of the system are bounded and the system output can follow the desired signal. Finally, two examples are given to verify the effectiveness of our control method.

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This study is concerned with the attitude control problem of variable-structure near-space vehicles (VSNSVs) with time-varying state constraints based on switched nonlinear system. The full states of vehicles are constrained in the bounded sets with asymmetric time-varying boundaries. Firstly, considering modeling uncertainties and external disturbances, an extended state observer (ESO), including two distinct linear regions, is proposed with the advantage of avoiding the peaking value problem. The disturbance observer is utilized to estimate the total disturbances of the attitude angle and angular rate subsystems, which are described in switched nonlinear systems. Then, based on the estimation values, the asymmetric time-varying barrier Lyapunov function (BLF) is employed to construct the active disturbance rejection controller, which can ensure the full state constraints are not violated. Furthermore, to resolve the 'explosion of complexity' problem in backstepping control, a modified dynamic surface control is proposed. Rigorous stability analysis is given to prove that all signals of the closed-loop system are bounded. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

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This paper presents a novel integral terminal sliding mode control (ITSMC) algorithm compounded with Barrier Lyapunov's Function (BLF) for high precision output tracking objective of uncertain N-dimensional strict feedback class of non-linear systems subjected to non-infringement of system output constraint. Besides, the proposed algorithm also employs uncertainty and disturbance estimator (UDE) technique for abating the existence of unknown mismatched and matched uncertainties. Most of the preliminary SMC schemes encompass the UDE technique to cope with unknown matched uncertainties only. However, the presented method embodies the dynamic surface control (DSC) architecture to get rid of the matching architectural constraint in UDE approach as well as 'complexity explosion' concern in backstepping approach. Additionally, the introduced method also applies the notion of symmetric BLF to enforce strict bounds on output tracking deviation from its reference value. To emphasize on the strengths of devised methodology, two examples are simulated by comparing the derived outcomes with already existing techniques in literature.