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Summary: This paper proposes a command filter‐based decentralized adaptive backstepping practical prescribed‐time (PPT) tracking control scheme for a class of non‐strict feedback interconnected systems with time varying parameters, unknown control coefficients, unmodeled dynamics, input deadzone and saturation. By the aid of the characteristics of Gaussian functions, the obstacles arising from the non‐strict feedback terms are successfully solved. By constructing a novel time‐varying scaling function and utilizing nonlinear mapping, the PPT tracking control is developed. The estimations of dynamical uncertainties resulting from unmodeled dynamics are accomplished by employing auxiliary signals, while the unknown continuous terms are characterized by the aid of radial basis function neural networks (RBFNNs). A superposition of two hyperbolic tangent functions is utilized to approximate input nonlinearity. Utilizing the compact set defined in the command filtered backstepping technique, the problem of unknown control direction is solved without using the Nussbaum gain technique. All the signals involved are proved to be semi‐global uniform ultimate bounded, and the tracking error can enter the pre‐specified convergence region within a pre‐specified time. Simulation results are used to demonstrate the effectiveness of the proposed control approach. [ABSTRACT FROM AUTHOR]

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a new dynamic event-triggered control solution is presented for state-constrained strict-feedback nonlinear systems. The current barrier Lyapunov function is required to assume or remove the feasibility conditions for virtual control signals. In this paper, a new scheme is proposed to guarantee the designed virtual control signals satisfy feasibility conditions. By introducing a dynamic variable into the event-triggered schedule, the dynamic event-triggered control scheme is established by using backstepping iterative design procedure. Moreover, the theoretical analysis illustrates that the proposed control solution can ensure the boundedness of all signals in SNS. Finally, simulation example is given to showcase the availability of the developed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of highly performance motion control of tank bidirectional stabilizer with dead zone nonlinearity and uncertain nonlinearity is addressed. First, the electromechanical coupling dynamics model of bidirectional stabilizer is developed finely. Second, the dead zone nonlinearity in bidirectional stabilizer is characterized as the combination of an uncertain time-varying gain and a bounded disturbance term. Meanwhile, an adaptive robust controller with dead zone compensation is proposed by organically combining adaptive technique and extended state observer (ESO) through backstepping method. The adaptive technique is employed to reduce the impact of unknown system parameter and dead zone parameter. Furthermore, the ESO is constructed to compensate the lumped uncertainties including unmodeled dynamics and dead zone residual, and integrated together via a feedforward cancellation technique. Moreover, the adaptive robust control law is derived to ensure final global stability. In stability analysis, the asymptotic tracking performance of the proposed controller can be guaranteed as the uncertainty nonlinearities in tank bidirectional stabilizer are constant. It is also guaranteed to achieve bounded tracking performance when time-varying uncertainties exist. Extensive co-simulation and experimental results verify the superiority of the proposed strategy. • A mechatronic dynamics model of the tank bidirectional stabilizer is developed, which is accurately modeled including couplings, nonlinearities and uncertainties. • The parametric adaptive function is constructed to update the unmeasurable dead zone parameters online, and the extended state observation technique is introduced to eliminate the dead zone nonlinearity and unmodeled dynamics. • The Lyapunov stability analysis demonstrates that the asymptotic tracking capability is guaranteed when the system uncertainty is constant, and the uniformly bounded tracking performance is guaranteed owing to the existence of time-varying uncertainties. • Comparative analysis of co-simulation and experiment confirms the effectiveness and feasibility of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this research, a new hybrid backstepping control strategy based on a neural network is proposed for tractor-trailer mobile manipulators in the presence of unknown wheel slippage and disturbances. To minimize the negative impacts of wheel slippage, the desired velocities of the tractor's wheels are computed with a proposed kinematic control model with an adaptive term. As the system's dynamical model contains unavoidable uncertainties, model-based backstepping control technique is unable to effectively manage these systems. Hence, the proposed controller blends a radial basis function neural network with the merits of a dynamical model-based backstepping approach. The neural networks are employed to approximate the non-linear unknown smooth function. To minimize the impact of external disturbances, and network reconstruction error an adaptive term is added to the control law. The Lyapunov theorem and Barbalat's lemma are employed to guarantee the stability of the control method. The tracking error is shown to be bounded and to rapidly converge to zero with the proposed method. To demonstrate the efficacy and validity of the control mechanism, comparison simulation results are presented. • A hybrid controller is proposed for tractor-trailer systems with wheel slippage. • By putting forward a kinematic control law, the desired velocities are calculated. • At the dynamical level, RBFNN is used to approximate the uncertainties of the system. • The stability of the system is analyzed with Lyapunov theory and Barbalat's Lemma. • The proposed control scheme is verified through simulation studies. [ABSTRACT FROM AUTHOR]

This article proposes a tracking control strategy based on fixed‐time for uncertain nonlinear systems with prescribed performance and actuator faults. Fuzzy logic systems are used to model unknown functions with uncertainties or fuzzy parameter features. The improvement of the conventional backstepping method through the introduction of command filtering technology has effectively addressed the challenge of a sharp increase in computational complexity during controller design. Additionally, a mechanism for error compensation has been established to mitigate the potential impact of errors that may arise during the filtering process on the system. Then, a new fixed‐time performance function is introduced into the adaptive backstepping method to ensure that the tracking signal with output error converges to an arbitrarily small neighborhood within a fixed time. Additionally, in order to enhance the tracking performance of the control method, the controller algorithm incorporates fault‐tolerant control based on the fixed‐time performance function. Finally, a numerical simulation of a power system with a static reactive power compensation device is presented, and demonstrate the effectiveness and feasibility of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This article focuses on a class of nonstrict feedback systems with input delay, state delays and time‐varying full‐state constraints by proposing an adaptive neural control scheme. To overcome the problems of all state variables effected by time‐varying constraints, the asymmetric time‐varying barrier Lyapunov functions are constructed. The influence of state delays and input delay is eliminated by employing suitable Lyapunov–Krasovskii functionals. Additionally, the process of controller design is based on backstepping method and the unknown functions can be approximated by radial basis function neural networks. Moreover, the problem of repeated differentiations for nonlinear components during controller design is hugely simplified by taking advantage of the dynamic surface control method. The boundness of all the closed‐loop signals can be ensured by the designed controller. Finally, two numerical simulations illustrate that the proposed adaptive neural control scheme is effective. [ABSTRACT FROM AUTHOR]

In this paper, a novel decentralized adaptive state‐feedback design method is proposed for large‐scale stochastic nonlinear systems. Different from the existing results, we consider more practical and more general systems, that is, systems with both unknown covariance and time‐varying powers. When dealing with the unknown time‐varying covariance, we do not need to know its bound, but use the estimator to design an adaptive law function. Then, a new adaptive controller is constructed with the backstepping method to ensure that the closed‐loop system is globally stable in probability, and that the states are regulated to the origin almost surely. Finally, a simulation example is given to illustrate the effectiveness of the design scheme. [ABSTRACT FROM AUTHOR]

In this paper, a quick convergence adaptive structure is proposed for trajectory tracking of an articulated type robotic manipulator using the Hardware in the Loop (HIL) simulation technique. A novel Nonlinear Quick Convergence Adaptive Sliding Backstepping Control (QCASBC) algorithm is implemented on a C2000 real-time controller board. The performance of the proposed control algorithm is inspected concerning the sliding mode PID (SM-PID) control technique to estimate its correlation with the proposed algorithm. The experimental part of the HIL simulation tests has been carried out on a simulated model of a three-link serial robot manipulator. A dynamic model of the robotic manipulator has been developed using Matlab Simulink software and its performance is analyzed using the HIL technique via a C2000 real-time controller for tracking the desired trajectory. Results show that the speed of convergence while tracking the desired trajectory of the manipulator is better in the proposed algorithm. It is also estimated that the positional error of the QCASBC algorithm is superior to the SM-PID control algorithm. The observed average angle error is improved by 14% and the average response time error is improved by 11% by using the proposed QCASBC algorithm compared to the SM-PID approach. [ABSTRACT FROM AUTHOR]

This paper investigates a finite-time adaptive fuzzy prescribed performance fault-tolerant control (FTC) issue for the steer-by-wire vehicle (SBWV) systems with intermittent actuator faults. Different from the steer-by-wire (SBW) system studied by the previous literatures, the SBWV system involved in this study consists of a vehicle dynamics model and an SBW system, including unmeasurable states and unknown nonlinear dynamics. Fuzzy logic systems (FLSs) are first used to identify the unknown model dynamics, and a fuzzy state observer is constructed to estimate the unmeasured states. Then, to compensate for the influence of intermittent actuator faults, a novel finite-time output-feedback prescribed performance adaptive FTC scheme is developed by using the adaptive backstepping control methodology and co-designing the last virtual controller. The presented control scheme not only guarantees that all signals of the closed-loop system are bounded in the presence of actuator faults, but also ensures that the tracking error converges to a small neighborhood of the zero within the prescribed performance bounded. The computer simulation and comparison results demonstrate the effectiveness of the proposed fuzzy control algorithm. [ABSTRACT FROM AUTHOR]

This article presents an adaptive control algorithm for stochastic nonholonomic systems subject to state constraints and input saturation simultaneously. We give a state‐input scaling transformation and a novel auxiliary variable to transform the stochastic nonholonomic system into a new one to make it easier to design the controller, and adopt a switching strategy to eliminate the phenomenon of uncontrollability. By introducing a barrier Lyapunov function and defining a suitable adaptive parameter, we construct a novel adaptive neural network controller with only one adaptive law, which can alleviate computation burden. The presented controller not only overcomes the effects of both full‐state constraints and full‐input saturation on system performance, but also ensures that all states of the closed‐loop are semi‐globally uniformly ultimately bounded in probability. Additionally, all state variables are restricted to the predefined compact sets. Finally, an example is used to validate the efficacy of the established controller. [ABSTRACT FROM AUTHOR]

This article investigates the command‐filter‐based improved predefined‐time tracking control problem for a class of switched nonlinear systems with the quantized input signal. Essentially different from most tracking control works of switched nonlinear systems under input quantization, the nonlinear decomposition method is employed to tackle the obstacles from the predefined‐time controller design. Subsequently, to achieve more faster convergence times, an improved predefined‐time lemma is designed, and for subsequent simulation work, the designed lemma is coupled with a quantizer. Furthermore, to tackle the problem of complexity explosion encountered during the iterative process of backstepping, the command filter is adopted. Finally, two examples are employed to demonstrate the effectiveness of the established results. [ABSTRACT FROM AUTHOR]

In this paper, a disturbance observer‐based adaptive neural backstepping integral sliding mode control (BISMC) is developed for a flexible joint robot (FJR) with the integration of an adjustable stiffness rotary actuator (ASRA). This system suffers from unknown system dynamics, external disturbance, and the influence of variable stiffness, which is a challenge for achieving precision tracking performance. Considering the lumped disturbances in FJR generated by the hydraulic system and the stiffness modulation of the ASRA, we investigate the structural dynamics nonlinear model of the FJR system, including hydraulic actuator dynamics. While other linear control strategies are applied for the FJR, the proposed controller uses BISMC, neural networks (NN), and nonlinear disturbance observers to deal with the disadvantages mentioned above. Radial basis function neural networks (RBFNN) are designed to tackle unknown nonlinear functions, and the disturbance observers are introduced to compensate for the influence of the variable stiffness, disturbance, and the approximation error caused by NN. Simulations and experiments are independently implemented to demonstrate the effectiveness and feasibility of the proposed controller. Results exhibit that the integral absolute error‐index is reduced by 20.4% when the proposed method is deployed for the experiment with a multistep trajectory. [ABSTRACT FROM AUTHOR]

In this article, the prescribed performance tracking control problem is studied for interconnected nonlinear time‐delay systems with sensor and actuator faults. Based on the dynamic gain technique and the backstepping control method, a delay‐independent adaptive state feedback controller is designed. Besides, by embedding a smooth function into the controller, the unknown external disturbances, sensor and actuator faults are successfully compensated. Furthermore, we can deal with the asymmetric prescribed performance control with semi‐global or global requirements uniformly by selecting the initial value of the the scaling function. Based on Lyapunov theory, it is proved that the system output of each subsystem can closely track the desired signal and the boundedness of all signals in the closed‐loop systems can be ensured under the proposed control method. Finally, the effectiveness of the proposed control strategy is proved by two simulation examples. [ABSTRACT FROM AUTHOR]

As for a class of strict‐feedback nonlinear systems with simultaneous sensor and actuator faults, the article focuses on the problem of fixed‐time fault‐tolerant control. Both fixed‐time command filters and a compensation mechanism are utilized to cope with these issues of differential explosion and filter errors. Meanwhile, through the fusion of fixed‐time control, fuzzy logic systems, adaptive control and the backstepping technology, a n$$ n $$‐step design scheme is presented. Our proposed controller ensures the fixed‐time convergence of all the signals in the system even with sensor/actuator faults, and allows the designers to acquire the upper limit value of the fixed convergence time only by tuning the design parameters. And this scheme takes into account rapidity, adaptability and fault tolerance of the system simultaneously. Based on the numerical simulation analysis, it is shown that the better tracking performance can be achieved. So it is concluded that our strategy is effective. [ABSTRACT FROM AUTHOR]

This paper investigates adaptive fuzzy finite-time output feedback fault-tolerant tracking control problem for multiple-input multiple-output (MIMO) stochastic non-strict feedback nonlinear systems with non-affine nonlinear faults and states unmeasured. Firstly, high-gain fuzzy state observers are constructed to overcome the state unmeasured problem in the system. Secondly, the mean-value theorem and input compensation techniques are employed to decouple non-affine nonlinear faults, and the resulting unknown control coefficients problem is handled using Nussbaum functions. In addition, dynamic surface control techniques and error compensation mechanisms are considered in the controller design, which effectively decreases the computational complexity of the control scheme. By combining the adaptive backstepping technique with finite-time control, a novel adaptive fuzzy dynamic surface finite-time output feedback fault-tolerant tracking control algorithm is proposed. The designed controller guarantees that all signals in the stochastic systems are semi-global finite-time stable in probability (SGFSP) as well as the tracking errors can converge to a small neighborhood within the origin in finite-time. Finally, two simulation examples are introduced to verify the effectiveness of the suggested control strategy. [ABSTRACT FROM AUTHOR]

In this paper, a gradient dynamics-based control method is proposed to directly tackle the singularity problem in the backstepping control design of the TORA system. This method is founded upon the construction of an energy-like positive function, which includes an auxiliary variable in terms of the intermediate virtual control law. On this basis, a gradient dynamics is created to obtain a new virtual control command, which is capable of making the auxiliary variable gradually approach zero, thereby mitigating the issue of division by zero. The core innovation is the integration of the gradient dynamics into the recursive backstepping design to overcome the singularity problem and stabilize the system at the equilibrium quickly. In addition, it rigorously proves that all the signals in the closed-loop control system are uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around zero through a Lyapunov-based stability analysis. Comparative simulations demonstrate that the proposed approach not only avoids the singularity issue, but also achieves a better transient performance over other methods. [ABSTRACT FROM AUTHOR]

In order to suppress the influence of uncertain disturbances on the trajectory tracking of hydraulic manipulator, a composite control strategy for the cutting electro-hydraulic driving system (CEHDS) of the tunneling robot is presented, which synthesizes the advantages of neural networks technique, recursive backstepping and adaptive control theory. The Lagrangian model with actuator dynamics is derived based on the practical tunneling robot. The back-stepping method is utilized for the strictly feedback state-space model. To address the matched and unmatched lumped uncertainties, the radial-basis-function neural networks (RBFNNs) are employed to approximate the unmatched term which contains the nonlinear friction torque and external cutting load in the mechanical subsystem. The nonlinear disturbance observer (NDOB) is utilized to estimate the matched lumped uncertainty in the hydraulic subsystem. Simultaneously, the adaptive robust mechanism is proposed to compensate the residual disturbances. Based on the Lyapunov theorem, the stability and the bounded tracking error of the CEHDS are obtained. The simulation and experimental results validate the effectiveness of the proposed method in comparison with the common backstepping and PID-controller approaches. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive lateral control problem is considered for autonomous electric vehicles under denial-of-service (DoS) attacks. Autonomous electric vehicles require high-precision position and pose information for the lateral control, which can be obtained from the global positioning system (GPS). However, this kind of sensors is easily susceptible to malicious DoS attacks. To mitigate the performance degradation caused by DoS attacks on GPS, a state observer is designed based on the measurements of inertial measurement units (IMUs), such that the position and pose information of vehicles can be estimated. Then, by adopting the observer states and backstepping technique, a novel adaptive secure switching control scheme is proposed. Subsequently, a stability condition is derived, which guarantees that the tracking errors converge to a compact set, and the attack effects on system dynamic performance are weakened. The stability condition also reveals the relationships among the attack durations, design parameters, and tracking errors, which can be used to guide the selection of design parameters. Simulation results are provided to validate the effectiveness and robustness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paperinvestigates the distributed consensus control for nonlinear multi-agent systems with input quantization in a directed communication topology. A nonsingular adaptive finite-time control (NAFTC) scheme is proposed by combining the filtered backstepping method with neural network control. Both chattering and singularity problems of the control signals are avoided thanks to its C 1 continuity, so that the contradiction between discontinuous- and C 0 continuous finite-time control with input quantization does not exist in our scheme. At the same time, a novel inequality for the input-output relationship of hysteresis quantizer is derived, which can simply handle the input quantization without requiring additional stability analysis. What is more, some common assumptions, such as Lipschitz assumption and Holder-continuity assumption, are not required in our scheme. Finally, stability analysis and numerical simulation are provided. [ABSTRACT FROM AUTHOR]

Summary: This article looks into the dynamic event‐triggered fixed‐time adaptive attitude control problem for nonlinear six‐rotor unmanned aerial vehicle (UAV) with external disturbances. The multiple six‐rotor UAVs considered are regarded as nonlinear multi‐agent systems (MASs), and each subsystem has multiple inputs. Under the framework of backstepping recursive design, an effective adaptive fixed‐time control method is proposed by combining neural networks (NNs) technology and fixed‐time theory. NNs are utilized to handle unknown nonlinearity and unmodeled parts in attitude systems. The hyperbolic tangent function is ushered to address the singularity problem that may occur in the derivative of the controller, thereby averting the phenomenon of chattering. For the sake of alleviating the correspondence burden of multiple UAVs attitude systems, a modified dynamic event‐triggered mechanism (DETM) is ushered. The developed controller swears for that all signals of the six‐rotor UAV attitude systems are bounded and the tracking errors converge to a small neighborhood of the origin within a fixed‐time interval. Eventually, with the help of simulation results, the effectiveness of the proposed control scheme was verified. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the position control issue of multi‐quadrotor unmanned aerial vehicle (QUAV) formation. Concerning the translational dynamic of a multi‐QUAV system, on the one hand, it is an under‐actuation dynamic; on the other hand, it does not satisfy the matching condition. These features will cause inevitable thorny in the formation position control design. Furthermore, because of the state coupling problem, the formation control of multi‐QUAV system is more challenging and knotty than the control of single QUAV system. To achieve this control, both backstepping technique and neural network (NN) approximation strategy are combined by introducing an intermediary control, where NN is employed to compensate the system uncertainty. However, since the traditional adaptive NN control methods need to train a large number of adaptive parameters for the high approximation accuracy, it will cause the heavy computing burden if traditional adaptive method is used for the QUAV formation control. The proposed adaptive NN strategy in this paper only requires training a scalar adaptive parameter, which is generated from the norm of NN weight vector or matrix, thereby significantly reducing computational burden. Finally, according to Lyapunov stability proof and computer simulation, it is demonstrated that the control tasks can be successfully accomplished. [ABSTRACT FROM AUTHOR]

The problem of retargeting rigid body attitude with attitude constraints has been extensively investigated, whereas the challenge persists in maneuvering rigid-body attitude with multiple concurrent attitude constraints and finite sequential actuator faults. Finite sequential actuator faults, which can reduce controllability or destabilize the system, necessitate the implementation of fault-tolerant control strategies. Therefore, this paper aims to address the issue of redirecting spacecraft attitude subject to multiple attitude constraints and finite sequential actuator faults comprehensively. Firstly, we represent spacecraft attitude using unit quaternions and employ an artificial potential function to effectively handle multi-attitude constraints. The negative gradient direction guides the rigid-body spacecraft towards seamless convergence with the desired attitude. Our proposed unwinding strategy effectively avoids unwinding phenomena during large-angle spacecraft reorientation as well. Additionally, we design an adaptive compensation strategy for finite sequential actuator faults that enables real-time calculation of the fault compensation matrix under such actuator faults. Importantly, we propose an improved adaptive fault-tolerant back-stepping controller integrated with a potential function that effectively addresses both attitude constraints and finite sequential actuator faults simultaneously. Subsequently, stability analysis is conducted on the proposed controller to ensure its stability in practical applications rigorously. Finally, numerical simulations are performed meticulously to demonstrate the effectiveness and robustness of our proposed controller. [ABSTRACT FROM AUTHOR]

Reconfigurable variable stiffness actuator (RVSA) has attracted increasing attention in robotics due to its safety, compliance, and robustness. However, the control of the RVSA is challenging due to nonlinear factors such as high-order nonlinear dynamic, model uncertainties, time-varying model parameters, and disturbances. In this paper, firstly, a lightweight RVSA structure with both passive and active nonlinear variable stiffness characteristic is developed. Secondly, a dynamic surface backstepping control method based on a radial basis neural network and disturbance observer (DSBC-RBFNN-DOB) is proposed to achieve position control of the lightweight RVSA with matched and unmatched uncertainties. To address solve the "complexity explosion" and noise problems in traditional backstepping control, the dynamic surface backstepping control (DSBC) method is used to design the controller. Then, a method based on radial basis neural network (RBFNN) and disturbance observer (DOB) are used to compensate for the matched and unmatched uncertainties in the link and motor. In this method, the matched uncertainties are compensated using RBFNN, and the DOB is integrated to compensate RBFNN approximation errors and unmatched uncertainties. Through Lyapunov stability analysis, the semi-global boundedness of the controller is proven. Finally, the proposed method is simulated and actually implemented, verifying the effectiveness of the method. Simulation and experimental results show that the root mean square error (RMSE) of the proposed method is only 0.97277° and 0.6418°, respectively. Compared with PID, DSBC, and DSBC-RBFNN, the error reduction percentages in simulation (experiment) are 85.6 % (88.9 %), 49.4 % (88.4 %) and 36.1 % (80.0 %) respectively. • A lightweight reconfigurable variable stiffness actuator with smaller mass and more compact structure is proposed.. • A dynamic surface backstepping control method based on neural network and disturbance observer is proposed. • A method of uncertainty and disturbance estimation combining neural network and disturbance observer is proposed. • Experiments and simulations were conducted under the condition of actively changing stiffness. [ABSTRACT FROM AUTHOR]

This document is a summary of a special issue of the Journal of Marine Science & Engineering titled "Intelligent Ships and Waterways: Design, Operation and Advanced Technology." The special issue focuses on advanced technologies for the design and sustainable operation of intelligent ships and waterways. It includes 20 research articles and 2 review articles covering topics such as waterway and port monitoring, ships' navigation environment perception, ships' navigation decision making and motion planning, and ships' motion modeling and control problems. The articles discuss various methods and technologies, including artificial intelligence, big data analysis, mixed reality, building information modeling, and digital twins, to improve the safety, efficiency, and sustainability of intelligent ships throughout their lifetime. The articles also address specific challenges in navigation safety, ship collision risk identification, ship identification in marine radars, collision risks between merchant and fishing vessels, situational awareness in inland waterways, ship trajectory prediction, oil spill detection, port terminal monitoring, and more. The authors of the articles have provided their contributions to the document. [Extracted from the article]

This paper is devoted to the event-triggered consensus control for a class of uncertain multiple Euler-Lagrange (EL) systems with actuator faults. Different from the related works where strict conditions are imposed on system uncertainties and the measurements of the leader's output, more serious uncertainties are involved since all the system dynamic matrices are unknown while both actuator faults and external disturbance are considered; and moreover, fewer measurements of the leader's output are required since its time derivatives are not necessarily available for feedback. Mainly because of these, the consensus problem is hard to solve by straightforwardly extending the existing results. To solve the control problem, a dynamic gain with a smart choice of its updating law is introduced to overcome the serious uncertainties and the sampling error of the control signal. By incorporating the dynamic gain into the vectorial backstepping procedure, an adaptive consensus controller joined with an event-triggered mechanism is designed for each follower to ensure the consensus of the multi-agent system in the sense that all the states of the closed-loop system are bounded while the output of each follower tracks the leader's output. Finally, the effectiveness of the proposed method is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Permanent magnet synchronous motor (PMSM) is a multivariable and highly coupled nonlinear system, which is prone to chaotic behavior during actual operation. In order to suppress the chaotic behavior of the PMSM, this work designs a free-will arbitrary time adaptive controller based on the inverse step derivation, adaptive control theorem and Lyapunov stability theory. Firstly, the corresponding coordination transformations are designed according to the PMSM. Secondly, the bounded problem of the controlled system is analyzed by using the Lyapunov stability theory, and the free-will arbitrary time adaptive controller is designed by backstepping derivation. Finally, numerical simulation verifies that the designed controller quickly stabilizes the system state variables to the output signals and proves that the controller is free-will arbitrary time stable for all closed-loop signals. [ABSTRACT FROM AUTHOR]

In this article, we present an innovative approach for controlling nonlinear switched systems (NSSs) with strict feedback utilizing adaptive neural networks (ANNs). Our methodology encompasses several facets, addressing key challenges inherent to these systems. To commence, we tackle the constrained nature of NSSs with strict feedback by designing a barrier Lyapunov function. This function ensures that all states within the switched systems remain within prescribed constraints. Additionally, we harness neural networks (NNs) to approximate the unknown nonlinear functions inherent to the system. Furthermore, we deploy an ANN state observer to estimate unmeasurable states. Our approach then proceeds to develop a cost function for the subsystem. Building upon this, we apply the Hamiltonian–Jacobi–Bellman (HJB) solution in conjunction with observer and behavior critic architectures, all rooted in backstepping control (BC) principles. This integration yields both a virtual optimal controller and a real optimal controller. Furthermore, we introduce a novel ANN event‐triggered control (ETC) strategy tailored explicitly for strictly feedback systems. This strategy proves highly effective in reducing the utilization of communication resources and eliminating the occurrence of Zeno behavior. Our analysis provides formal proof that all states within the closed‐loop system exhibit half‐leaf consistency and are ultimately bounded, regardless of arbitrary switching conditions. Finally, we substantiate the efficacy and viability of our control scheme through comprehensive numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive cooperative formation controller is developed to force a swarm of nonholonomic mobile robots with limited sensing ranges to move along the desired reference trajectory in a predetermined formation, while maintaining communication connectivity among the initial user-specified connected robots and guaranteeing no collision between the robots. Both kinematic models and dynamic systems with parametric uncertainties are discussed. The presence of parametric uncertainties is handled by adaptive control technique. A novel artificial potential function, which is based on a 4 times differential pseudo bump function, is constructed to achieve collision avoidance and connectivity maintenance. The control design is based on a fusion of potential function, adaptive backstepping technique, and Lyapunov synthesis. The cooperative formation controller is proven to be stable and can guarantee that there is no collision between any robots and the initial connectivity of the communication network can be always maintained. The proposed formation control approach is decentralized in the sense that the control action on each robot depends only on information from its neighbours and the desired trajectory of the group. Comparative simulation and experiment studies are performed to show the effectiveness of the proposed formation controller. [ABSTRACT FROM AUTHOR]

This article concentrates on the problem of adaptive event-triggered control with double-side event-triggering mechanisms for a family of switched nonlinear systems with measurement sensitivity. In order to circumvent the negative effect of intermittent transmission and sensor measurement sensitivity on the output, an extended system is constructed by introducing a first-order output filter. Then, an input-driven neural switched observer is designed to estimate unmeasurable system states. To deal with the mutual interaction between the triggering and the switching mechanisms and their negative effect on the positive lower bound of inter-execution intervals, an incremental compensation is incorporated in the event-triggering mechanism (ETM) at the output sensor side. At last, a novel event-triggered control scheme built on both sides of the controller and output is proposed, which exhibits superior efficacy compared to the one-side event-triggered control scheme. By using the methods of the average dwell time (ADT) and the backstepping design, it is guaranteed that all signals of the switched closed-loop system are semiglobally uniformly ultimately bounded (SGUUB), and the Zeno phenomenon is excluded. The efficacy of the proposed methodology is validated by using a numerical simulation and a one-link robot system. [ABSTRACT FROM AUTHOR]

This paper studies the non-singular practical fixed-time neural adaptive control issues for multi-input and multi-output (MIMO) nonlinear systems with non-strict feedback form. Neural networks (NN) are used to estimate the unknown nonlinearities and deal with the problem of an algebraic loop. Under the framework of the backstepping control design, a practical fixed-time adaptive NN control method is developed by using the adding power integration technology. According to the Lyapunov function theory, it is proved that the closed-loop system is practical fixed-time stable, and the system can track the desired reference signal within a fixed time. Finally, the proposed practical fixed-time control method is applied to a multi-motor control platform, which proves the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper is devoted to adaptive trajectory tracking of quadrotor systems with full-state constraints and random disturbances. The command-filtering technology combined with error compensation mechanisms is proposed to deal with the "explosion of complexity" problem in traditional backstepping design and reduction of the filtering errors. The Barrier Lyapunov functions (BLFs) are constructed to ensure that all system states do not violate the boundary of its constraints. The command-filtered adaptive fuzzy controller is designed such that the state constraints are not breached almost surely, all signals in the closed-loop system are bounded almost surely, and the first-order moment of the tracking error converges to an arbitrarily small neighborhood of zero by parameters tuning. Finally, the effectiveness of the proposed control method is illustrated by simulation results. [ABSTRACT FROM AUTHOR]

This article investigates the finite‐time recoil control problem of deepwater drilling riser systems with nonlinear friction force, tension force and saturation input. For the friction force, a new approximation model based on radial basis function neural networks is presented, which not only can ensure a better approximation effect than the sine‐function type and exponential‐polynomial‐function type computational models, but also can be easily used for control design. Different from the existing linear optimal control methods, a neural‐network‐based adaptive backstepping control method is proposed to deal with the nonlinear friction and tension forces, which can achieve better recoil control responses. An auxiliary system combining with the change of coordinates is employed to compensate the saturation input effect. To prolong the average release interval of control input while preserving satisfied control performance, a new switched event‐triggered control (ETC) scheme is developed, in which the triggering conditions are switched between the fixed and relative thresholds based on the strength of control signal. With the event‐triggered controller, the practical finite‐time stability condition of recoil control system is derived and the Zeno behavior is avoided. Numerical results are given to show the advantages of the proposed methods in handling the model nonlinearities, finite‐time stability and ETC performance of riser‐tension systems. [ABSTRACT FROM AUTHOR]

Summary: This article investigates the adaptive finite‐time control design with performance assurance for nonlinear Markov jumping systems. First, the radial basis function neural networks are applied to tackle unknown nonlinear terms. Subsequently, within the framework of the command‐filtered backstepping control, the new error compensation signals are devised to remove the effect caused by filter error. Additionally, an adaptive finite‐time prescribed performance control law with an event‐triggered mechanism is developed to achieve a balance between tracking performance and bandwidth consumption, which ensures that the closed‐loop system is practically finite‐time stable in mean square and guarantees that the tracking error adjusts to the predetermined area. Finally, two simulation examples are provided to verify the validity and superiority of the devised scheme. [ABSTRACT FROM AUTHOR]

A novel full state‐constrained integrated guidance and control (IGC) schema for aerial interceptors under input saturation with tunnel‐prescribed performance is proposed. To achieve an appointed‐time engagement with less overshoot phenomenon, the tunnel‐prescribed performance control (TPPC) technique is applied to generate virtual guidance laws, where the tracking of desired line of sight (LOS) angles possesses predefined‐time convergent property. For the sake of the flight safety of interceptors in a practical flight environment, the physical limitations on the flight angles and the angular rates of attitude systems are taken into consideration. The integral barrier Lyapunov function (iBLF) technique is adopted to ensure all the attitude states within a user‐defined domain. The nominal virtual commands are generated adaptively by the backstepping method combined with some novel dynamic surfaces. To further eliminate the possible input saturation, a novel one‐order auxiliary system is constructed to compensate for the discrepancy of the virtual input commands. All the signals in the closed‐loop system are strictly proven to be bounded by Lyapunov theory. The simulation results show the effectiveness of the proposed IGC schema by comparison with other IGC laws. [ABSTRACT FROM AUTHOR]

This paper investigates a distributed adaptive finite‐time containment control scheme for multiple unmanned aerial vehicles subject to external disturbances and input saturation. Combined with a novel indicator of the saturation degree designed by the hyperbolic tangent function, an adaptive method is proposed to deal with the input saturation issue, which considers both symmetry and asymmetry saturation. Moreover, to address the problem of the "explosion of terms" inherent in the traditional backstepping controller design, a fixed‐time sliding mode differentiator is utilized to approximate the derivative of the virtual signal in the command‐filtered backstepping method. Finally, the convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations. [ABSTRACT FROM AUTHOR]

Considering the complexity of communication environment in reality, this paper investigates the adaptive output consensus problem for heterogeneous nonlinear multi‐agent system (MAS) under random link failures, in which connection of each link may suffer from link failure. The major challenge lies in dealing with the coupling among different nonlinearities and integrator orders of heterogeneous agents while the distributed communication may fail randomly. Hence, a two‐level distributed adaptive control scheme based on the virtual model‐reference strategy will be presented. In the first level, virtual reference models are constructed to deal with the uncertainties caused by the random link failures, and a distributed consensus control strategy is designed based on the established communication observer of each agent. In the second level, an adaptive backstepping tracking controller drives each agent's output to follow its virtual reference model and compensate for the agent's uncertainties. The mean square stability of the controlled MAS has been rigorously proved. An illustrative example is presented to demonstrate the effectiveness of the given control scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of sampled-data adaptive tracking control for a class of switched nonlinear systems with prescribed performance is considered. In order to guarantee the system is stable and achieves the prescribed performance in sampled-data control, a coordinate transformation satisfying the prescribed performance is introduced. In addition, the neural networks (NNs) used to approximate the unknown nonlinear functions and the backstepping technique are applied to design the sampled-data controller and the adaptive laws. An upper bound on the sampling period is obtained to maintain the stability of the systems. It is confirmed that the designed sampled-data scheme ensures that all signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is limited to the prescribed performance function. The effectiveness of the designed control scheme is demonstrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this paper, for strict-feedback nonlinear systems with positive odd rational powers, the problem of adaptive fixed-time tracking control (FTTC) is considered. With the support of fixed-time theorem and adaptive backstepping method, this paper proposes a new globally adaptive FTTC strategy, which can overcome the singular problems caused by the derivation of virtual control signal. In addition, the proposed control scheme is a universal approach that can be applied to other types of nonlinear systems. Furthermore, the designed adaptive fixed-time tracking controller ensures the boundedness of all signals in the controlled system, and it guarantees the tracking error converges to a small neighbourhood near equilibrium in fixed-time. Finally, the simulation result further verifies the feasibility of the presented control scheme. [ABSTRACT FROM AUTHOR]

This article studies the passive tracking problem of a wearable exoskeleton for lower limb rehabilitation therapy in the face of unmodeled dynamics, interactive friction, disturbance, prescribed performance constraints, and actuator faults. Adaptive neural networks and a smooth performance function are incorporated to establish a novel fault-tolerant tracking scheme, which can not only compensate for the nonlinear uncertainties and disturbance, but also handle the actuator fault with guaranteed tracking performance. A state feedback controller is presented by using the full state information and an output feedback controller is developed when the angular velocity is unavailable. The differential explosion issue of the backstepping technique is resolved by constructing a first-order filter and the unmeasurable velocity is estimated by a nonlinear observer. Semiglobal uniform boundedness stabilities of the exoskeleton system are proved via the Lyapunov direct method. The tracking performances of the designed control approaches are tested by comparative simulations. [ABSTRACT FROM AUTHOR]

In this study, the problem of non-overshooting tracking control (NOTC) for a class of strict-feedback systems with prescribed finite-time (FT) is studied. In order to obtain a simple closed-loop system (CLS), we first propose a criterion lemma for prescribed FT stable control. A prescribed FT controller is designed by using backstepping and the proposed criterion lemma. According to the CLS, many conditions of NOTC are analyzed. Compared with the related results, the NOTC conditions obtained in this paper are relatively extensive, which reduces conservatism. The algorithm makes the system overshoot zero, so this result increases the accuracy. The final simulation results show that this algorithm is effective. • In the related research results of no overshoot control, the closed-loop system obtained by the existing prescribed finite-time control algorithm is very complicated. This leads to the failure to calculate the expression of tracking error through the closed-loop system, and then the control condition with non-overshooting cannot be obtained. Then, a new criterion lemma of prescribed finite-time control is proposed to design the control in this paper. Obviously, our closed-loop system is relatively simple. • In the related research results of non-overshooting control, the non-overshooting tracking control conditions obtained in this paper are relatively extensive, which reduces the conservatism of the existing algorithms. • Compared with mean-nonovershooting tracking control, the algorithm in this paper can make the overshoot of tracking error zero. Therefore, this result increases accuracy. [ABSTRACT FROM AUTHOR]

This paper focuses on the output-feedback control for path-following of underactuated autonomous underwater vehicles subject to multiple uncertainties and unmeasured velocities. First, a novel extended state observer is proposed to estimate the mismatched lumped disturbance and recover the unmeasured velocities. Based on this premise, to overcome the limitation of relying solely on the accurate kinematic model, a disturbance observer-based stabilizing controller is developed. The difference in bandwidths between the observer and the vehicle dynamics allows for a mathematical setup amenable to standard singular perturbation theory. In the fast mode, a kinematic observer is designed to reject system uncertainty caused by unknown attack angular velocity and prohibitive path-tangential angular velocity, using a novel physical perspective. In the slow mode, an interconnected-system control law is proposed by integrating the backstepping technique with the time scale decomposition method. Furthermore, the stability of the overall closed-loop system is established. Finally, simulation results are presented to demonstrate the effectiveness of the proposed method for path-following of underactuated autonomous underwater vehicles in the vertical plane. • A novel ESO is developed to estimate the mismatched lumped disturbances and recover the unmeasured velocities by combining high-gain and singular perturbation techniques, leading to reduced complexity in stability analysis. • A DO is designed to estimate model uncertainties by utilizing the difference in bandwidths between the observer and state dynamics. The resulting singular perturbation analysis provides a new perspective on designing a DO in a straightforward manner. • An interconnected-system control law is proposed based on a time scale decomposition method to address the problem of the "explosion of terms" inherent in conventional backstepping. • The stability analysis enables the derivation of mathematical bounds on the control gains, offering guidance for selecting control gains to prevent controller ill-conditioning and/or closed-loop instability. [ABSTRACT FROM AUTHOR]

The system performance of grid-connected photovoltaic (PV) has a serious impact on the grid stability. To improve the control performance and shorten the convergence time, a predefined-time controller based on backstepping technology and dynamic surface control is formulated for the inverter in the grid-connected photovoltaic. The time-varying tuning functions are introduced into state-tracking errors to realize the predefined-time control effect. To address the “computational explosion problem” in the design process of backstepping control, dynamic surface control is adopted to avoid the analytical calculations of virtual control. The disturbances of the PV system are estimated and compensated by adaptive laws. The control parameters are chosen and the global stability of the closed-loop is ensured by Lyapunov conditions. Simulation results confirm the effectiveness of the proposed controller and ensure the predefined time control in the photovoltaic inverter. [ABSTRACT FROM AUTHOR]

In this study, dynamic formation tracking and interception are performed by controlling multi-agent using a Euler-like Lagrangian model. The purpose is to use the distance-based rigid graph method to control multi-agent, and ultimately achieve dynamic formation tracking and target interception of multi-agent. Initially, distance-based graph stiffness and back-stepping techniques were considered to address the formation control challenge. This method helps achieve the initial expected formation and effectively complete the formation mission. Leaders continue to chase the moving target, while followers stick to the expected arrangement. The leader then precisely tracks the moving target and surrounds it within the formation. By using Lyapunov stability theory with adaptive control, it is ensured that the total distance meets finite and consistent error limits. Finally, the numerical simulation of the interception plan was carried out by 6 multi-agents and 1 target at different times to verify the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper addressed the adaptive control problem for non-strict-feedback nonlinear systems with dead-zone and external disturbances. The design methodology integrated the backstepping technique with the approximation of unknown functions using an echo state network (ESN), enabling real-time adjustments. A comprehensive Lyapunov stability study was conducted to confirm the semi-globally uniformly ultimately boundedness (SGUUB) of all signals in the closed-loop system, ensuring that the tracking error converged to a small neighborhood of the origin. The effectiveness of the proposed method was further demonstrated through two examples, and error assessment criteria were utilized for comparisons with existing controllers. [ABSTRACT FROM AUTHOR]

This article studies an adaptive extended state observer (AESO) based prescribed‐time geometric attitude stabilization problem of quadrotors with endogenous uncertainties, exogenous disturbances, and actuator saturation, which can be estimated and compensated by AESOs. The employment of the geometric representation method for system attitude can effectively avoid ambiguity or singularity problems that may arise with other representations. The temporal and scale transformations are employed to solve the global boundedness problem on infinite time instead of the prescribed‐time convergence problem on finite time. By integrating the proposed controller with the backstepping technique, the system of quadrotors can be prescribed‐time stable. Further, a prescribed‐time geometric attitude control technique is devised such that the control signal is bounded and the state signals converge to a small domain near the equilibrium point in the prescribed time. The prescribed time is determined by the user and is independent of the initial conditions. The comparative simulations with different initial information are performed to demonstrate the effectiveness of the proposed design technique. [ABSTRACT FROM AUTHOR]

This article discusses the control problem of marine autonomous surface ships (MASS) under cross‐water scenarios, that is, from open water to restricted water, where several practical facts, such as uncertain dynamic, unknown disturbance and actuator wear suppression, are taken into account. To resolve such a control design challenge, the predefined performance control (PPC)‐based and barrier Lyapunov function (BLF)‐based ideas are employed, and a prespecified performance function (PPF) is designed to implement the transformation of cross‐water design. Under the adaptive backstepping design framework, with aid of PPC‐based and BLF‐based design ideas, an adaptive neural control solution is developed for MASS under cross‐water scenarios. Furthermore, to reduce the actuator wear and tear caused by high‐frequency corresponding control commands and hull vibration, a new multichannel concurrent event‐triggered protocol (ETP) is constructed in the controller‐actuator (C‐A) channel. Finally, a concurrent event‐triggered adaptive neural control scheme is proposed for MASS under cross‐water scenarios. The theoretical analysis indicates that all signals in the control system are ultimately bounded, and the Zeno behavior is avoided. The simulation and comparison results verify the effectiveness and superiority of the developed control scheme. [ABSTRACT FROM AUTHOR]

Quantized signal control has been widely recognized as an effective means for conserving communication resources. However, ensuring stability of quantization‐driven nonlinear systems becomes particularly challenging in the presence of intermittent denial‐of‐service (DoS) attacks and sensor failures. This article explores the stable control problem of quantized nonlinear systems subject to DoS attacks. When an attack exists, all signals are unmeasurable. During the dormant phase of a DoS attack, only the quantized output signal is measurable, while there is a deviation between the received signal and the ideal signal due to sensor failure. To address these challenges, a switch‐type quantized observer is designed in this article to estimate unmeasurable state signals. In addition, we integrate the first‐order dynamic filter into the back‐stepping design process, which not only avoid the obstacles arisen from non‐differentiable output signals, but also simplifies the design process. Furthermore, this article adopts a more flexible sector quantizer and derives a set of adaptive laws to compensate for unknown quantization parameters. It is shown that, by utilizing the estimated signal, the proposed quantized adaptive control is able to effectively fight against DoS attacks and also is fault‐tolerant to sensor failures, guaranteeing semi‐globally uniformly ultimately bounded for all closed‐loop signals. Finally, simulation results validate the effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

This study proposes a reinforcement learning‐based finite‐time cross‐media tracking control approach for a slender body cross‐media vehicle encountering unknown hydrodynamics, wind, and wave disturbances. Initially, a reinforcement learning framework consisting of the actor neural network and critic neural network is constructed. The critic neural network monitors the actions of the actor neural network and approximates the cost function, while the actor neural network estimates the unknown hydrodynamics and disturbances, minimising the cost function to optimise performance. Subsequently, the command filter featuring finite‐time convergence is formulated, effectively managing the corresponding filter error through a proposed error compensating signal. By integrating these techniques, a reinforcement learning‐based finite‐time control strategy is developed, circumventing the singularity issue inherent in traditional finite‐time backstepping strategies. Comparative analysis with existing methods demonstrates the strong robustness of the proposed scheme against unknown hydrodynamics and disturbances, ensuring finite‐time convergence of the system's states and optimising controller performance. Finally, simulations confirm the effectiveness and superiority of the presented approach. [ABSTRACT FROM AUTHOR]

This paper presents an alternative method to solve the control problem of an uncertain nonlinear system in strict-feedback form with a time delay. Instead of using Lyapunov–Krasovskii functionals, ordinary Lyapunov functionals are used to design the controllers. In order to address the completely unknown uncertainties of the system, including the unmodeled dynamics, time-delay nonlinearities, and external disturbances, command filters are applied to reconstruct the estimations of such uncertainties, and the negative feedback of these estimations can be used to reduce the influence of such uncertainties on the system. With the help of the backstepping technique and the Lyapunov stability criterion, it is proved that the system output tracks the target signal with a small error, and contrastive simulation results verify our method's effectiveness. [ABSTRACT FROM AUTHOR]