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In this paper, the event-based triggering method is adopted to investigate the secure consensus issue of multiple autonomous underwater vehicles (AUVs) under denial-of-service (DoS) attacks. DoS attack is a form of time-sequence-based cyber attack, which can destroy the normal service of the control target or network. First, based on an event-triggered mechanism, a novel secure control protocol is proposed. Second, the upper bounds of attack duration and attack frequency are given to ensure that multiple AUVs under DoS attacks can reach consensus. Third, an event-triggered mechanism with exponential variables is developed to avoid the continuous update of the controller, thereby reducing the burdens of communication and calculation. Zeno behavior can be strictly ruled out for each AUV under this triggering mechanism. Finally, the simulation results illustrate the feasibility of the proposed scheme.

The problem of prescribed-time containment control of unmanned underwater vehicles (UUVs) with faults and uncertainties is considered. Different from both regular finite-time control and fixed-time control, the proposed prescribed-time control strategy is built upon a novel coordinate transformation function and the block decomposition technique, resulting in the followers being able to move into the convex hull spanned by the leaders in prespecifiable convergence time. Moreover, intermediate variables and the control input terms are also shown to remain uniformly bounded at the prescribed-time. To reduce the magnitude of the bounds, a novel fixed-time observer for the fault is proposed. Two numerical examples are provided to verify the effectiveness of the proposed prescribed-time control strategy.

In contrast to the majority of model-based terminal sliding mode control (TSMC) approaches that rely on the plant physical model and/or data-driven adaptive pointwise model, this study treats the unknown dynamic plant as a total uncertainty in a black box with enabled control inputs and attainable outputs (either measured or estimated), which accordingly proposes a model-free (MF) nonsingular terminal sliding mode control (MFTSMC) for higher-order dynamic systems to reduce the tedious modelling work and the design complexity associated with the model-based control approaches. The total model-free controllers, derived from the Lyapunov differential inequality, obviously provide conciseness and robustness in analysis/design/tuning and implementation while keeping the essence of the TSMC. Three simulated bench test examples, in which two of them have representatively numerical challenges and the other is a two-link rigid robotic manipulator with two input and two output (TITO) operational mode as a typical multi-degree interconnected nonlinear dynamics tool, are studied to demonstrate the effectiveness of the MFTSMC and employed to show the user-transparent procedure to facilitate the potential applications. The major MFTSMC performance includes (1) finite time (2.5±0.05 s) dynamic stabilization to equilibria in dealing with total physical model uncertainty and disturbance, (2) effective dynamic tracking and small steady state error 0±0.002, (3) robustness (zero sensitivity at state output against the unknown bounded internal uncertainty and external disturbance), (4) no singularity issue in the neighborhood of TSM σ=0, (5) stable chattering with low amplitude (±0.01) at frequency 50 mHz due to high gain used against disturbance d(t)=100+30sin(2πt)). The simulation results are similar to those from well-known nominal model-based approaches.

Based on a line-of-sight (LOS) guidance law for a curve parametrized path, a finite-time backstepping control is proposed for the kinematic path-following of an underactuated autonomous surface vehicle (ASV). Finite-time observer is utilized to estimate the unknown external disturbances accurately. The first-order Levant differentiator is introduced into the finite-time filter technique, such that the output of filter can not only approximate the derivative of the virtual control, but also avoid the singularity problem of real heading control. The integral terminal sliding mode is employed to improve the tracking performance and converging rate in the surging velocity control. By virtue of Lyapunov function, all the signals in the closed-loop system can be guaranteed uniformly ultimate boundedness, and accurate path-following task can be fulfilled in finite time. The simulation results and comparative analysis validate the effectiveness and robustness of the proposed control approach.

This paper proposes a new trajectory tracking scheme for the constrained nonlinear underwater vehicle-manipulator system (UVMS). For overcoming the unmodeled uncertainties, external disturbances, and constraints of control inputs in the operation of UVMS, a modified constrained H∞ controller with a basic computed-torque controller (CTC) and a new designed nonlinear disturbance observer (NDO) are proposed. The CTC gives the nominal model-based control. The NDO is designed based on the system dynamics and used to online provide the estimation of the lumped disturbances. However, the designed NDO is an observer of biased estimation, i.e., it has a blind domain of disturbance estimation which cannot be rejected. In order to reject the biased estimation, the modified constrained H∞ controller is designed but with new features. To the best of our knowledge, the conventional H∞ robust controller is generally designed by calculating the Riccati equation offline and ignoring the constraints of control inputs made by the physical actuators, which are poor in handling the time-varying environment. In order to solve these issues, the modified constrained H∞ robust controller online optimized by grey wolf optimizer (GWO) is designed to ensure the control system has a compensation of the biased estimation, a satisfied constrained control input, and a fast calculation. In this paper, we modify the prior method of offline calculating the Riccati equation of the conventional H∞ robust controller to be an online optimization scheme and proposed a new constrained evaluation function. The new constrained evaluation function is online optimized by the GWO, which can both find out the constrained suboptimal control actions and compensate the biased estimation of the NDO for the UVMS. The whole system stability is proved. The effectiveness of the fast online calculation, tracking accuracy, and lumped disturbances rejection is shown by a series of UVMS simulations.

For an actual control system, the position information is usually an indispensable physical quantity for feedback control, while in an actual project, the position quantity is generally constrained. This paper discusses the distributed leader-following consensus control problem of networked Euler-Lagrangian systems (ELSs) both with unknown control directions and position constrains under a directed topology. Two novel types of barrier Lyapunov functions together with a Nussbaum-type gain function are employed to design distributed leader-following consensus protocol under a directed graph in this paper. One Lyapunov function is used to ensure that all the signals in the closed-loop system are bounded and the other is designed to prove that the consensus tracking errors of all the followers are uniformly ultimately bounded (UUB) and can be adjusted arbitrarily small. Meanwhile, according to the analysis of the tracking procedure, the security problem of position constraints are always satisfied. Finally, simulation examples are given to verify the effectiveness of the proposed algorithms in this paper.

This study aims to address the three-dimensional path planning problem of autonomous underwater vehicle (AUV) in the environment of ocean current and seabed terrain obstacles, based on five biological swarm intelligent algorithm. Firstly, a three-dimensional seabed environment model and a Lamb vortex current environment model are established. Subsequently, a three-dimensional path planning mathematical model is established by considering the navigation distance, seabed terrain constraints and ocean current constraints. Furthermore, five biological swarm intelligent optimization algorithms are applied to solve the multi-objective nonlinear optimization problem. Finally, the experimental results show that the optimal path performance of the particle swarm optimization (PSO) algorithm is better than other algorithms. The planning speed of PSO algorithm is the fastest, and the robustness of WPA algorithm is the best. However, the planning time is the longest. The PSO algorithm is more suitable for three-dimensional path planning of AUV under the influence of seabed terrain obstacles and ocean currents.

This paper deals with the circular formation control problem of multiagent systems for achieving any preset phase distribution. The control problem is decomposed into two parts: the first is to drive all the agents to a circle which either needs a target or not and the other is to arrange them in positions distributed on the circle according to the preset relative phases. The first part is solved by designing a circular motion control law to push the agents to approach a rotating transformed trajectory, and the other is settled using a phase-distributed protocol to decide the agents’ positioning on the circle, where the ring topology is adopted such that each agent can only sense the relative positions of its neighboring two agents that are immediately in front of or behind it. The stability of the closed-loop system is analyzed, and the performance of the proposed controller is verified through simulations.

Rub-impact between the rotating and static parts is a more common fault. The occurrence of faults is often accompanied by the generation of nonlinear phenomena. However, it is difficult to find out because the nonlinear characteristics are not obvious at the beginning of the fault. As a new frequency domain-based method, nonlinear output frequency response functions (NOFRFs) use the vibration response to extract the nonlinear characteristics of the system. This method has a better recognition rate for fault detection. Also, it has been applied in structural damages detection, but the high-order NOFRFs have the characteristics that the signals are weak and the features are difficult to extract. On this basis, the concept of the weighted contribution rate of the NOFRFs is proposed in this paper. The variable weighted coefficients with orders are used to amplify the influence of high-order NOFRFs on the nonlinearity of the system so as to extract its fault characteristics. The new index RI is proposed based on Clenshaw–Curtis quadrature formula to eliminate the effect of artificially selected weighted coefficients on sensitivity. Especially in the early stage of the fault, the new index varies greatly with the deepening of the fault. Both simulation and experimental results verify the validity and practicability of the new index. The new index has certain guiding significance in the detection of mechanical system faults.

This paper solves a fixed-time trajectory tracking control problem for a marine surface vessel in the presence of model uncertainties, external disturbances, input saturation and prescribed performance constraints. Firstly, a fixed-time disturbance observer (FXDO) is designed, which not only realizes fixed-time stability, but also solves the design method problem in the existing disturbance observer. Secondly, a fixed-time nonsingular terminal sliding mode manifold (FXNTSMM) with simple structures is designed, whereby the designed FXNTSMM reduces the calculation burden of the system. Thirdly, a fixed-time trajectory tracking control scheme in the presence of model uncertainties, external disturbances, input saturation and prescribed performance constraints is proposed based on the FXDO, the FXNTSMM and a prescribed performance function, and the entire constrained closed-loop control system is with fixed-time stability, simplicity and nonsingularity. Finally, several numerical simulation results are presented to demonstrate the effectiveness of the proposed trajectory tracking control scheme.