Although a couple of robust cooperative controllers have been proposed to achieve the multi-tug towing of unactuated offshore platform with uncertainties and unknown disturbances, the convergence performance of towing control system is unsatisfactory. To surmount this challenge, this research aims to improve the convergence performance of multi-tug towing system based on fixed-time stability theory. Initially, a fixed-time extended state observer (FxESO) is designed to estimate the uncertainties and disturbances. Based on the FxESO, a fixed-time virtual controller is proposed to acquire desired drag force for the offshore platform to track the expected trajectory. Subsequently, the desired drag force is allocated to the desired towline tensions of tugs by the quadratic programming algorithm, and the corresponding desired towline length is calculated through the towline catenary model. Then, the desired position of each tug is obtained based on the desired towline length and the current position information of the platform and tug. Based on the desired positions of tugs, a fixed-time distributed cooperative controller is designed to achieve the multi-tug towing of offshore platform within the fixed time. Finally, simulations and comparisons have verified the progressiveness and effectiveness of the proposed method.

This paper addresses the problem of safety-critical path-guided herding control for multiple-input multiple-output multi-agent systems under incomplete state measurement, safety constraints, and limited communication resources. Specifically, an output-feedback finite-time neural predictor is proposed to identify both model uncertainties and unknown state information. Subsequently, a distributed path-guided herding control strategy is designed, including patrolling, gathering, enclosing, and expelling. Control barrier functions are formulated as safety constraints, and a quadratic optimization problem is established. By using the neurodynamic optimization to solve the optimization problem, the optimal control law satisfying both safety constraints and state constraints is generated. Furthermore, a dynamic event-triggered communication method is proposed to reduce unnecessary communication, especially during the transient phase. By using the proposed herding control approach, the collision-free herding is guaranteed for input-to-state stability, and simulation results are provided to demonstrate the effectiveness of the approach.

The International Maritime Organization (IMO) proposed the concept of a maritime autonomous surface ship (MASS), which could integrate perception, decision-making, and control functions to implement autonomous navigation in complicated environments. It is recognized as the fundamental component of the future new generation of shipping systems. The development of MASS requires the use of specific test tools and use cases for the evaluation of the safety, reliability, and functional performance of its navigation system. At present, the lack of standardized, modular, and serial testing paradigms and methods for MASS impedes the development and improvement of related products and applications. Therefore, it is essential to develop a practical and applicable testing framework. This paper presents a functional analysis of autonomous navigation systems and provides a comprehensive overview of current research status, potential solutions, and future challenges. Moreover, this paper also takes a step towards facilitating the functional testing of autonomous surface vehicles by proposing a hybrid virtual-real framework consisting of scenario generation, virtual simulation, model-scaled physical experiment, validation and evaluation. The research opportunities and future aspects are also addressed. This work may serve as a reference for academic and industrial researchers to investigate new methods and to develop prototype systems for future autonomous surface ships.

This article investigates the pursuit–evasion problem of multiple underactuated autonomous surface vehicles (ASVs) under velocity and collision avoidance constraints. A safety–critical pursuit–evasion game (PEG) method based on min–max optimization and neural network dynamic control is proposed. Specifically, an allocation strategy is designed at first based on the position information of the pursuing and evading ASVs to achieve a rational and efficient allocation of pursuit targets by minimizing pursuit distances. Next, a nominal PEG guidance law is proposed by combining model predictive control (MPC) with min–max optimization methods. Then, the nominal guidance law is optimized based on a heading-constrained control barrier function (CBF) such that a safety–critical guidance law for collision avoidance can be achieved. Finally, a predicator-based neural network is developed to estimate the uncertainty and external disturbance, and a dynamic control law is proposed to track the guidance signals without using any model parameters. It is proven that the closed-loop system is input–to–state stable (ISS), and the ASV system is safe. A robot-operating-system (ROS)-based simulation results demonstrate the effectiveness of the proposed safety–critical PEG method based on min–max optimization and neural network dynamic control.

This paper investigates the safety-certified cooperative path following problem for second-order nonlinear systems with multiple-input multiple-output strict-feedback form subject to safety, state, and input constraints. A safety-certified learning control approach is proposed to achieve collision-free cooperative path following based on command optimization, online learning, and self-triggered communication. Specifically, an extended-state-observer-aided learning neural predictor is developed to simultaneously identify nonlinear functions and unknown input gains without measuring state derivatives. Control barrier functions are then employed to ensure safety through forward invariant sets. Next, command optimization is utilized to generate the optimal virtual control signals that satisfy safety constraints, state constraints, and input constraints. A neurodynamic optimization technique is employed to solve the quadratic optimization problem in real time. Additionally, a self-triggered mechanism is introduced in path variable coordination to reduce the listening and triggering times. By using the proposed safety-certified cooperative path following approach, a safe formation is guaranteed for input-to-state safety. Simulation results are provided to illustrate the effectiveness of the proposed method.Note to Practitioners—This paper addresses the safety-certified cooperative path following problem of multi-agent systems, which has practical implications in various applications. These applications include formation patrol, cargo transportation, search and rescue missions, swarm robotics, and agricultural tasks. By coordinating the movements of multiple agents, cooperative path following enhances efficiency in these scenarios. The challenges posed by safety, state, and input constraints are commonly encountered in practical. To address these challenges, the command optimization approach is proposed in this paper. The optimization problem is efficiently solved in real-time using neurodynamic optimization technique. Furthermore, to enhance feasibility in a limited communication environment, a self-triggered mechanism is introduced to reduce the communication burden. Therefore, the aforementioned effective scheme is suitable for implementation in industrial applications.

This paper focuses on a distributed cooperative guidance model-free control method for a cluster of under-actuated disk-type autonomous underwater gliders (AUGs) in the presence of unknown kinetic model parameters and ocean disturbances. Firstly, a distributed cooperative motion generator is designed to generate reference path points, and then a cooperative control method is proposed based on the update path parameters. Secondly, a three-dimensional (3D) guidance law is constructed by employing closed 3D vector fields. Finally, data-driven filtered adaptive extended state observers (DFAO) are proposed to deal with the unknown input gains, internal uncertainties and external disturbances of the disk-type AUGs, and an adaptive kinetic control law is designed by using the knowledge learned from the observers. Simulation results demonstrate the effectiveness of the proposed 3D distributed cooperative guidance model-free control method for disk-type AUGs subject to fully unknown kinetics. Note to Practitioners—The disk-type AUG has the characteristic of long operational endurance, capable of functioning continuously for several months when fully loaded. Consequently, this type of glider offers an advantage in establishing oceanic sensor networks. To achieve this goal, two technical challenges arise: the coordination among multiple gliders and the anti-disturbance control of individual glider. Our research focuses on distributed cooperative guidance and model-free control issues for multiple underwater gliders. First, we propose a distributed cooperative guidance scheme to maintain a specific formation among the gliders. Additionally, while ensuring control effectiveness, we employ data-driven methods to estimate uncertain kinetic model parameters. Our approach is not only theoretically viable but also ready for industrial application, thus filling a gap in underwater glider technology.

This article addresses the coordinated path-following (CPF) control under human supervision for marine vehicles (MVs) with unknown disturbances. A human-in-the-loop coordinated path-following (HCPF) control architecture is proposed based on the robust exact differentiator (RED) observer and the output feedback continuous twisting control (OFCTC) method. Specifically, a human manipulation is introduced into a virtual leader to regulate its path update speed in response to sudden circumstances for the follower MVs. All follower MVs synchronize indirectly with the human-in-the-loop virtual leader over a communication graph. Then, the path-following control problem is transformed into the controls of a second-order along-track error dynamic and a third-order cross-track error dynamic. By using the path-following errors only, the RED observers are developed to recover the unknown states of the error dynamics. Finally, the OFCTC laws are designed to achieve the individual path following in finite time regardless of the lumped disturbances. The stability of the closed-loop system is analyzed by employing the cascade theory. A salient feature of the proposed HCPF control architecture is that the CPF for MVs can be implemented under the supervision and intervention of human. Simulation results are given to illustrate the effectiveness of the proposed HCPF control method.

In this paper, a finite set model predictive control method based on data-driven neural network predictors (DNNPs) is proposed for pulse width modulation (PWM) rectifiers with fully unknown parameters. First, DNNPs are structured based on concurrent learning such that model uncertainties and input gains are identified simultaneously. Secondly, based on the information estimated by the predictors, a finite set model predictive power controller is designed, which is responsible for simplifying the rolling optimization and reducing the computational complexity. Finally, the stability analysis is provided based on input-to-state stability theory, and simulation results are provided to prove the effectiveness of the proposed method.

This article addresses the safety-critical receding-horizon planning and formation control of autonomous surface vehicles (ASVs) in the presence of model uncertainties, environmental disturbances, as well as stationary and moving obstacles. A three-level formation control architecture is proposed with a safety-critical formation trajectory generation module at its high level, a collision-free guidance module at its middle level, and an anti-disturbance control module at its low level. Specifically, a safety-critical formation trajectory generator is designed by leveraging collaborative neurodynamic optimization to plan safe formation trajectories to track a given trajectory and avoid stationary obstacles in a receding-horizon manner. Based on control barrier functions, a collision-free line-of-sight guidance law is developed to generate safe guidance commands to avoid collision with moving obstacles and other vehicles. An anti-disturbance control law is customized with a finite-time convergent observer for a vehicle to follow the guidance command signals. Simulation and hardware-in-the-loop experimental results are elaborated to validate the efficacy of the proposed method for the receding-horizon planning and formation control of ASVs.

This article addresses cooperative target enclosing of underactuated autonomous surface vehicles (ASVs) subject to obstacles. Each ASV suffers from input constraints in addition to unknown kinetics induced by model nonlinearities, unknown input gains, and external disturbances. A safety-critical cooperative target enclosing control method is proposed for surrounding a maneuvering target vehicle. Specifically, a finite-time fuzzy predictor is presented to learn the unknown kinetics with the integral of historical vehicle data. By using a distributed target estimator to recover the target position, a nominal distributed target enclosing control law is developed to achieve a circumnavigation formation. To avoid collisions between ASVs and obstacles/team members, input-to-state safe high-order control barrier functions are first introduced for encoding safety constraints. Based on the safety constraints and input constraints, a quadratic programming problem is formulated, and an optimal safety-critical control law is obtained by using projection neural networks to track the optimal solution. The closed-loop control system is proven to be input-to-state stable via Lyapunov theory. Moreover, the multiple ASV systems are proven to be input-to-state safe regardless of high-order relative degree. The salient contributions of the proposed approach lie in finite-time fuzzy learning and collision-free target enclosing control under disturbances. Simulation results validate the effectiveness of the proposed safety-critical model-free control method for cooperatively surrounding a maneuvering target.

This article investigates the yaw angle tracking control of an autonomous surface vehicle (ASV) subject to fully unknown internal dynamic, external disturbance, and unknown control input gain. A model-free adaptive antidisturbance autopilot control method is proposed for an ASV without using any model parameters. Specifically, by utilizing real-time and historical data, a data-driven concurrent learning extended state observer (CLESO) method is designed to estimate the unknown ASV model parameters and ensure the convergence of the estimation without requiring persistent excitation. Then, a model-free yaw angle tracking controller is designed based on the data-driven CLESO method. Through Lyapunov stability analysis, the closed-loop system is proven to be input-to-state stable. Simulation and experimental results validate the effectiveness of the proposed CLESO method for the yaw angle tracking of an ASV with fully unknown dynamic model.

This article addresses multitarget circumnavigation with autonomous surface vehicles (ASVs) subject to model nonlinearities, environmental disturbances, and physical constraints in the presence of stationary/moving obstacles. A neurodynamics-driven distributed optimization method is proposed to achieve safety-certified cooperative circumnavigation guided by multiple targets. Specifically, a cooperative circumnavigation guidance law based on a finite-time distributed observer is designed for surrounding multiple targets. Based on the geometric characteristics of multitarget circumnavigation, three collision-avoidance rules are formulated with respect to obstacles, targets, and ASVs; and three types of control barrier functions are derived to encode the coupled safety constraints into state constraints. A distributed command governor optimization problem is formulated to generate optimal commanded guidance signals within the globally coupled state constraints. To compute optimal commands in real time, multiple recurrent neural networks (RNNs) are employed to solve a distributed optimization problem. An event-triggered communication scheme is designed for the communication among RNNs with reduced communication burden. A predictor-based fuzzy control law is designed to track safe velocity commands. The closed-loop system is proven to be input-to-state stable. Simulation results are elaborated to demonstrate the effectiveness of the safety-certified control method for ASVs to circumnavigate multiple targets with guaranteed safety.

This paper presents a finite control set model free predictive control method for doubly fed induction generator for direct current generation system. The system model is fully unknown, and only the input and output data are measured. Firstly, data-driven neural network predictors are proposed to reconstruct the system model. Filtered data of system states are recorded and used to update the neural network parameters. The system of the data-driven NN predictors is proved to be input-to-state stable. Then, a finite control set model free predictive controller is designed based on the perdiction model. The optimal control actions are selected based on the receding horizon optimization with a finite control set. Simulation results show the effectiveness of the proposed model free predictive control of doubly fed induction generator based on data-driven neural network predictors.

This article addresses the cooperative multitarget encircling control of underactuated autonomous surface vehicles with unknown kinetics subject to velocity and input constraints. A distributed observer is designed for the vehicles to estimate the geometric center of the area covered by multiple moving targets. Based on the target center estimate, a multitarget encircling guidance law is developed to form encircling trajectories around the targets. A data-driven fuzzy predictor is designed for learning the vehicle kinetics, including model input gains, with available data. Based on the learned model, a nominal control law is developed to track reference guidance signals. In order to satisfy the velocity and input constraints, a feasibility condition for velocities is derived based on a control barrier function, and a neurodynamics-based optimal control law is developed based on the feasibility condition and input constraint. The bounded input-to-state stability of the closed-loop control system is theoretically proved. Simulation results are elaborated to substantiate the effectiveness of the proposed control approach for circumnavigating multiple moving targets.

This article addresses the safety-critical containment maneuvering of multiple underactuated autonomous surface vehicles (ASVs) in the presence of multiple stationary/moving obstacles. In a complex marine environment, every ASV suffers from model uncertainties, external disturbances, and input constraints. A safety-critical control method is proposed for achieving a collision-free containment formation. Specifically, a fixed-time extended state observer is employed for estimating the model uncertainties and external disturbances. By estimating lumped disturbances in fixed time, nominal containment maneuvering control laws are designed in an Earth-fixed reference frame. Input-to-state safe control barrier functions (ISSf-CBFs) are constructed for mapping safety constraints on states to constraints on control inputs. A distributed quadratic optimization problem with the norm of control inputs as the objective function and ISSf-CBFs as constraints is formulated. A recurrent neural network-based neurodynamic optimization approach is adopted to solve the quadratic optimization problem for computing the forces and moments within the safety and input constraints in real time. It is proven that the error signals in the closed-loop control system are uniformly ultimately bounded and the multi-ASVs system is guaranteed for input-to-state safety. Simulation results are elaborated to substantiate the effectiveness of the proposed safety-critical control method for ASVs based on neurodynamic optimization with control barrier functions.

Autonomous marine vehicles (AMVs), including autonomous surface and underwater vehicles, are versatile means to explore, exploit, monitor, and protect marine resources and environments. Motion control is a fundamental enabling technique for state-of-the-art AMV development. Especially, guidance is a critical component in AMV motion control. In recent years, line-of-sight (LOS) guidance, as an efficient guidance method, has attracted tremendous interest from both theoretical and practical perspectives. In this paper, an overview of recent advances in LOS guidance for AMV path following is provided. First, a control objective for the path following of an AMV with a kinematic model is specified. Next, major LOS guidance laws for path following are reviewed in detail. Then, LOS guidance laws applicable to coordinated path following of multiple AMVs are elaborated. Finally, six challenging issues for future research are addressed.

This article addresses the distributed formation control of multiple under-actuated autonomous surface vehicles (ASVs) in a receding-horizon setting. The ASVs are subject to physical constraints, in addition to stationary and moving obstacles. A barrier-certified distributed model predictive control method is proposed with the capability of avoiding collision with stationary and moving obstacles and neighboring ASVs. Specifically, a data-driven neural predictor is used to learn unknown functions in ASV kinetics. A nominal distributed receding-horizon position control law is developed based on the learned unknown function to achieve the desired formation within physical constraints. To ensure the safety requirement, a barrier-certified control law is designed based on control barrier functions to generate the signals of optimal surge force and heading angle within the safety constraints. A receding-horizon heading control law is designed based on the data-driven neural predictor to track the desired heading signals. Constrained quadratic programming problems are formulated based on barrier functions for barrier-certified distributed formation control and solved via neurodynamic optimization using one-layer recurrent neural networks. Thus, the proposed control method is able to ensure obstacle avoidance in the formation control of multiple ASVs in the presence of stationary and moving obstacles. Simulation results are elaborated to validate the efficacy of the proposed barrier-certified distributed model predictive control method for ASV formation.

This article addresses the path-guided flocking control of unmanned surface vehicles (USVs) suffering from fully unknown kinetics. A model-free learning and anti-disturbance control method is developed to achieve path-guided flocking without using prior knowledge of model nonlinearities, ocean disturbances, or control input gains. Specifically, data-driven concurrent learning extended state observers (CLESOs) based on fuzzy systems are presented to estimate the unknown kinetics of USVs. With the proposed CLESO, a model-free path-following control law is proposed for a leader USV to follow a parameterized path. Then, model-free flocking control laws based on potential functions are proposed for follower USVs to avoid collisions and maintain network links within available communication ranges. Through cascade stability analysis, the closed-loop system is proven to be globally asymptotically stable. Simulation results substantiate the proposed CLESO-based anti-disturbance control approach for path-guided flocking of a swarm of USVs.

This article investigates the model-free containment control of multiple underactuated unmanned surface vessels (USVs) subject to unknown kinetic models. A novel cooperative control architecture is presented for achieving a containment formation under switching topologies. Specifically, a path-guided distributed containment motion generator (CMG) is first proposed for generating reference points according to the underlying switching topologies. Next, guiding-vector-field-based guidance laws are designed such that each USV can track its reference point, enabling smooth transitions during topology switching. Finally, data-driven neural predictors by utilizing real-time and historical data are developed for estimating total uncertainties and unknown input gains, simultaneously. Based on the learned knowledge from neural predictors, adaptive kinetic control laws are designed and no prior information on kinetic model parameters is required. By using the proposed method, the fleet is able to converge to the convex hull spanned by multiple virtual leaders under switching topologies regardless of fully unknown kinetic models. Through stability analyses, it is proven that the closed-loop control system is input-to-state stable and the tracking errors are uniformly ultimately bounded. Simulation results verify the effectiveness of the proposed cooperative control architecture for multiple underactuated USVs with fully unknown kinetic models.

This article deals with the problem of network-based path-tracking control of an underactuated unmanned surface vehicle subject to model uncertainties and unknown disturbances over a wireless network. A two-level network-based control architecture is proposed, including a local inner loop and a remote outer loop. In the remote outer loop, an event-triggered line-of-sight guidance law is designed to achieve path tracking while reducing the network burden for the remote control at the kinematic level. In the local inner loop, an extended state observer is employed to estimate the unknown disturbances due to the model uncertainties and environmental disturbances. Based on the estimated information from the extended state observer, an event-triggered anti-disturbance control law is developed to reduce the execution rate of actuators at the kinetic level. The stability of the closed-loop path-tracking system is proved based on the input-to-state stability and cascade stability theory. The effectiveness of the proposed network-based method for path tracking of the USV is verified via experiments.

This article addresses the cooperative target enclosing problem of ring-networked underactuated autonomous surface vehicles (ASVs). The target velocity is unavailable, and the ASVs are subject to sideslip effects, unknown control gains, and uncertain kinetics. The control objective is to drive a fleet of ASVs to surround a moving target at a desired range and maintain a spaced formation. An integrated distributed guidance and model-free control method is presented based on extended state observers (ESOs) and a data-driven fuzzy predictor. Specifically, by using two ESOs to estimate the unknown relative kinematics induced by the unknown target velocity and unknown sideslip and a distributed target estimator to recover the target position, intermediate range keeping and phase keeping guidance laws are designed to achieve a circular motion and an evenly spaced formation, respectively. Next, a model-free fuzzy control law is developed based on a data-driven fuzzy predictor, which learns the unknown control gains and uncertain kinetics simultaneously. Finally, the closed-loop control system is proven to be input-to-state stable through Lyapunov analysis. The salient feature of the proposed method is that cooperative circumnavigating a maneuvering target with unknown velocity can be achieved without the global target information and knowledge of vehicle kinetics. Simulation results validate the effectiveness of the proposed distributed guidance and control method for cooperative target enclosing of ASVs.

This article addresses an output-feedback flocking control problem for a swarm of autonomous surface vehicles (ASVs) to follow a leading ASV guided via a parameterized path. The leading and following ASVs are subject to completely unknown model parameters, external disturbances, and unmeasured velocities. A data-driven adaptive anti-disturbance control method is proposed for establishing a flocking behavior without any prior knowledge of model parameters. Specifically, a data-driven adaptive extended state observer (ESO) is proposed such that unknown input gains, unmeasured velocities, and total disturbance are simultaneously estimated. For the leading ASV, an output-feedback path-following control law is developed to follow a predefined parameterized path. For following ASVs, an output-feedback flocking control law is developed based on an artificial potential function for collision avoidance and connectivity preservation, in addition to a distributed ESO for estimating the velocity of the leading ASV through a cooperative estimation network. The simulation results are discussed to substantiate the efficacy of the proposed path-guided output-feedback ASV flocking control based on data-driven adaptive ESOs without measured velocity information.

Autonomous surface vehicles (ASVs) are marine vessels capable of performing various marine operations without a crew in a variety of cluttered and hostile water/ocean environments. For complex missions, there are increasing needs for deploying a fleet of ASVs instead of a single one to complete difficult tasks. Cooperative operations with a fleet of ASVs offer great advantages with enhanced capability and efficacy. Despite various application potentials, coordinated motion control of ASVs pose great challenges due to the multiplicity of ASVs, complexity of intravehicle interactions and fleet formation with collision avoidance requirements, and scarcity of communication bandwidths in sea environments. Coordinated control of multiple ASVs has received considerable attention in the last decade. This article provides an overview of recent advances in coordinated control of multiple ASVs. First, some challenging issues and scenarios in motion control of ASVs are presented. Next, coordinated control architecture and methods of multiple ASVs are briefly discussed. Then, recent results on trajectory-guided, path-guided, and target-guided coordinated control of multiple ASVs are reviewed in detail. Finally, several theoretical and technical issues are suggested to direct future investigations including network-based coordination, event-triggered coordination, collision-free coordination, optimization-based coordination, data-driven coordination of ASVs, and task-region-oriented coordination of multiple ASVs and autonomous underwater vehicles.

This article addresses the problem of distributed path following of multiple under-actuated autonomous surface vehicles (ASVs) with completely unknown kinetic models. An integrated distributed guidance and learning control architecture is proposed for achieving a time-varying formation. Specifically, a robust distributed guidance law at the kinematic level is developed based on a consensus approach, a path-following mechanism, and an extended state observer. At the kinetic level, a model-free kinetic control law based on data-driven neural predictors via integral concurrent learning is designed such that the kinetic model can be learned by using recorded data. The advantage of the proposed method is two-folds. First, the proposed formation controllers are able to achieve various time-varying formations without using the velocities of neighboring vehicles. Second, the proposed control law is model-free without any parameter information on kinetic models. Simulation results substantiate the effectiveness of the proposed robust distributed guidance and model-free control laws for multiple under-actuated ASVs with fully unknown kinetic models.

In this article, we address the disturbance/ uncertainty estimation of maritime autonomous surface ships (MASSs) with unknown internal dynamics, unknown external disturbances, and unknown input gains. In contrast to existing disturbance observers where some prior knowledge on kinetic model parameters such as the control input gains is available in advance, reduced- and full-order data-driven adaptive disturbance observers (DADOs) are proposed for estimating unknown input gains, as well as total disturbance composed of unknown internal dynamics and external disturbances. An advantage of the proposed DADOs is that the total disturbance and input gains can be simultaneously estimated with guaranteed convergence via data-driven adaption. We apply the proposed full-order DADO for the trajectory tracking control of an MASS without kinetic modeling and present a model-free trajectory tracking control law for the ship based on the DADO and a backstepping technique. We report the simulation results to substantiate the efficacy of the proposed DADO approach to model-free trajectory tracking control of an autonomous surface ship without knowing its dynamics.

This article addresses the distributed path maneuvering of underactuated unmanned surface vehicles (USVs) with collision avoidance and connectivity preservation. The USVs are guided by the multiple virtual leaders moving along the multiple parameterized paths and only a fraction of USVs have access to the virtual leaders. An observer-based finite-time control method is proposed to achieve a containment formation. Specifically, a finite-time extended state observer is employed to recover the unmeasured linear/angular velocities and estimate the total disturbances consisting of model uncertainties as well as ocean disturbances at first. Then, observer-based finite-time guidance laws using the information of neighbors are designed based on a containment scheme. An artificial potential field is incorporated into the distributed guidance law design to avoid collision and preserve connectivity. Finally, antidisturbance kinetic control laws are devised based on the finite-time convergent observers and nonlinear tracking differentiators. It is proven that all error signals in the closed-loop system are ultimately uniformly bounded, and the distributed path maneuvering formation pattern can be achieved in a finite time when USVs outside the collision avoidance and connectivity preservation region. Simulation results are given to verify the effectiveness of the proposed output feedback control method for the distributed path maneuvering of multiple USVs with position-yaw measurements only.

This paper investigates the distributed containment maneuvering problem for uncertain nonlinear multiagent systems in multiple-input multiple-output (MIMO) strict-feedback form. The follower agents are driven to achieve a collective motion guided by multiple parameterized paths, and a dynamic behavior can be independently prescribed for the group during maneuvering. A containment maneuvering controller is developed by utilizing a modular design method enabling decoupled estimation and control. Specifically, an estimator module is constructed by utilizing an echo state network to identify the unknown nonlinearities. Next, a controller module is constructed by employing a modified dynamic surface control method where a second-order nonlinear tracking differentiator is introduced to extract the derivative information of the virtual control law. Subsequently, a path update law is derived such that the virtual leaders are synchronized, and the desired speed profile for the group can be specified independently. By using a small-gain theorem and cascade stability theory, the entire closed-loop system is proved to be input-to-state stable, and the containment maneuvering errors are uniformly ultimately bounded. An application for the formation control of marine surface vehicles is provided to show the efficacy of the proposed controller for containment maneuvering of uncertain nonlinear MIMO strict-feedback systems.

This paper addresses the cooperative path following the problem of ring-networked under-actuated autonomous surface vehicles on a closed curve. A cooperative guidance law is proposed at the kinematic level such that a symmetric formation pattern is achieved. Specifically, individual guidance laws of surge speed and angular rate are developed by using a backstepping technique and a line-of-sight guidance method. Then, a coordination design is proposed to update the path variables under a ring-networked topology. The equilibrium point of the closed-loop system has been proven to be globally asymptotically stable. The result is extended to the cooperative path following the lack of sharing of a global reference velocity, and a distributed observer is designed to recover the reference velocity to each vehicle. Moreover, the cooperative path following the presence of an unknown sideslip is considered, and an extended state observer is developed to compensate for the effect of the unknown sideslip. Both simulation and experimental results are provided to illustrate the effectiveness of the proposed cooperative guidance law for the path following over a closed curve.

In this paper, a cooperative time-varying formation maneuvering problem with connectivity preservation and collision avoidance is investigated for a fleet of autonomous surface vehicles (ASVs) with position-heading measurements. Each vehicle is subject to unknown kinetics induced by internal model uncertainty and external disturbances. At first, a nonlinear state observer is used to recover the unmeasured linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based cooperative time-varying formation maneuvering control laws are designed based on artificial potential functions, nonlinear tracking differentiators, and a backstepping technique. The stability of closed-loop distributed formation control system is analyzed based on input-to-state stability and cascade stability. The salient features of the proposed method are as follows. First, cooperative time-varying formation maneuvering with the capability of connectivity preservation and collision avoidance can be achieved in the absence of velocity measurements. Second, the complexity of the cooperative time-varying formation maneuvering control laws is reduced without resorting to dynamic surface control. Third, the uncertainty and disturbance are actively rejected in the presence of position-heading measurements. Simulation results are given to substantiate the proposed output feedback control method for cooperative time-varying formation maneuvering of ASVs with connectivity preservation and collision avoidance.

This paper presents a design method for target enclosing of an underactuated autonomous surface vehicle to surround a maneuvering target with time-varying velocity, and both the target and the follower suffer from unknown ocean currents. Specifically, a target-enclosing controller is developed based on a line-of-sight (LOS) guidance and an ocean current estimator, where only the yaw rate is used to stabilize the circular motion around the target. Then, the proposed strategy is extended to the case where the target velocity is unavailable and the ocean currents time-varying. By using the relative range and angle information, an extended state observer is developed to estimate unknown relative velocities together with the ocean currents in real-time. Based on the estimated relative dynamics, a LOS, target-enclosing controller is developed without any velocity information of the target. The stability of the closed-loop system is analyzed via the Lyapunov theory. Both simulations and experiments are conducted to show the performance of the proposed LOS, target-enclosing controller for surrounding a maneuvering target.

In this paper, a consensus maneuvering problem for nonlinear multivehicle systems in strict-feedback form is investigated. The consensus maneuvering problem includes a geometric task and a dynamic task. The geometric task means that all trajectories of follower vehicles converge to a parameterized path. The dynamic task is to drive the system to satisfy a desired dynamic assignment. A consensus maneuvering controller is developed for each vehicle based on a modular design approach. First, an estimator module is designed based on an echo state network, which is used to estimate uncertain nonlinearities. Then, a controller module is designed based on a modified dynamic surface control method through the use of a second-order nonlinear tracking differentiator. Finally, a path update law is designed based on a distributed maneuvering error feedback and a filtering scheme. The proposed controller is distributed in the sense that the path information is accessed by a small number of follower vehicles only. The stability of the closed-loop system cascaded by the estimator module and the controller module is analyzed based on input-to-state stability theory and cascade theory. Simulation results are provided to demonstrate the efficacy of the proposed consensus maneuvering controllers for uncertain nonlinear strict-feedback systems.

This paper is concerned with the target tracking of underactuated autonomous surface vehicles with unknown dynamics and limited control torques. The velocity of the target is unknown, and only the measurements of line-of-sight range and angle are obtained. First, a kinematic control law is designed based on an extended state observer, which is utilized to estimate the uncertain target dynamics due to the unknown velocities. Next, an estimation model based on a single-hidden-layer neural network is developed to approximate the unknown follower dynamics induced by uncertain model parameters, unmodeled dynamics, and environmental disturbances. A bounded control law is designed based on the neural estimation model and a saturated function. The salient feature of the proposed controller is twofold. First, only the measured line-of-sight range and angle are used, and the velocity information of the target is not required. Second, the control torques are bounded with the bounds known as a priori. The input-to-state stability of the closed-loop system is analyzed via cascade theory. Simulations illustrate the effectiveness of the proposed bounded controller for tracking a moving target.

This paper presents a design method for output-feedback path-following control of under-actuated autonomous underwater vehicles moving in a vertical plane without using surge, heave, and pitch velocities. Specifically, an extended state observer (ESO) is developed to recover the unmeasured velocities as well as to estimate total uncertainty induced by internal model uncertainty and external disturbance. At the kinematic level, a commanded guidance law is developed based on a vertical line-of-sight guidance scheme and the observed velocities. To optimize guidance signals, optimization-based reference governors are formulated as bound-constrained quadratic programming problems for computing optimal reference signals. Two globally convergent recurrent neural networks called projection neural networks are used to solve the optimization problems in real-time. Based on the optimal reference signals and ESO, a kinetic control law with disturbance rejection capability is constructed at the kinetic level. It is proved that all error signals in the closed-loop system are uniformly and ultimately bounded. Simulation results substantiate the efficacy of the proposed method for output-feedback path-following of under-actuated autonomous underwater vehicles.

This paper presents a predictor-based neural dynamic surface control (PNDSC) design method for a class of uncertain nonlinear systems in a strict-feedback form. In contrast to existing NDSC approaches where the tracking errors are commonly used to update neural network weights, a predictor is proposed for every subsystem, and the prediction errors are employed to update the neural adaptation laws. The proposed scheme enables smooth and fast identification of system dynamics without incurring high-frequency oscillations, which are unavoidable using classical NDSC methods. Furthermore, the result is extended to the PNDSC with observer feedback, and its robustness against measurement noise is analyzed. Numerical and experimental results are given to demonstrate the efficacy of the proposed PNDSC architecture.

This paper is concerned with the cooperative path maneuvering of multiple underactuated autonomous surface vehicles (ASVs) moving along a parameterized path. Each vehicle is subject to uncertain kinematics and unknown kinetics induced by model uncertainty and ocean disturbances. A modular adaptive control method is presented to develop the cooperative controller such that a queue formation along the parameterized path can be achieved. First, two identification modules are developed such that the uncertain kinematics and unknown kinetics can be estimated by an adaptive term and echo state networks, respectively. Next, a cooperative path maneuvering controller module is designed based on a line-of-sight guidance scheme, tracking differentiators, and a path variable containment approach. The path variable containment approach is used to guarantee that the ASVs are evenly spaced between two virtual leaders moving along the path. Finally, the stability of the identification-controller pair is analyzed. Comparative studies are performed to validate the efficiency of the proposed method.

In this paper, a leader-following consensus scheme is presented for networked uncertain nonlinear strict-feedback systems with unknown control directions under directed graphs, which can achieve predefined synchronization error bounds. Fuzzy logic systems are employed to approximate system uncertainties. A specific Nussbaum-type function is introduced to solve the problem of unknown control directions. Using a dynamic surface control technique, distributed consensus controllers are developed to guarantee that the outputs of all followers synchronize with that of the leader with prescribed performance. Based on Lyapunov stability theory, it is proved that all signals in closed-loop systems are uniformly ultimately bounded and the outputs of all followers ultimately synchronize with that of the leader with bounded tracking errors. Simulation results are provided to demonstrate the effectiveness of the proposed consensus scheme.

In this brief, a neural dynamic surface control algorithm is proposed for three-phase pulse width modulation voltage source rectifier with the parametric variations. Neural networks are employed to approximate the uncertainties, including the parametric variations and the unknown load-resistance. The actual control laws are derived by using the dynamic surface control method. Furthermore, a linear tracking differentiator is introduced to replace the first-order filter to calculate the derivative of the virtual control law. Thus, the peaking phenomenon of the filter is suppressed during the initial phase. The system stability is analyzed by using the Lyapunov theory. Simulation results are provided to validate the efficacy of the proposed controller.

This paper considers cooperative dynamic positioning (CDP) of multiple offshore vessels in the presence of dynamical uncertainties, time-varying ocean disturbances and unmeasured velocity, aimed at collectively holding a relative formation and reaching a reference position. K-filter observers are first designed to estimate the unmeasured velocity information of each vessel, and then observer based CDP controllers are developed with the aid of dynamic surface control (DSC) technique, neural network and iterative learning approach. The formation among vehicles can be guaranteed if the graph induced by the vessels and the reference point contains a spanning tree. It is proved by Lyapunov analysis that the proposed control laws can ensure that all the signals in the closed-loop systems are uniformly ultimately bounded, and tracking errors converge to a small neighborhood of origin.

This paper considers the coordinated pattern tracking of multiple marine surface vehicles in the presence of uncertain kinematics and kinetics. Distributed pattern tracking controllers depending on the information of neighboring vehicles are derived based on a backstepping technique, neural networks and an identifier. Specifically, the identifier is devised to precisely estimate the time-varying ocean currents at the kinematic level. Neural networks together with adaptive filtering methods are employed to extract the low frequency content of the model uncertainty and ocean disturbances at the kinetic level. The benefit of the proposed design results in adaptive pattern tracking controllers over any undirected connected graphs with guaranteed low frequency control signals, which facilitates practical implementations. The stability properties of the multi-vehicle systems are established via Lyapunov analysis, and the pattern tracking errors converge to an adjustable neighborhood of origin. An example is given to show the performance of the proposed approach.

This paper addresses the leader-follower synchronization problem of uncertain dynamical multiagent systems with nonlinear dynamics. Distributed adaptive synchronization controllers are proposed based on the state information of neighboring agents. The control design is developed for both undirected and directed communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case where a neighborhood observer is proposed based on relative output information of neighboring agents. Then, distributed observer-based synchronization controllers are derived and a parameter-dependent Riccati inequality is employed to prove the stability. This design has a favorable decouple property between the observer and the controller designs for nonlinear multiagent systems. For both cases, the developed controllers guarantee that the state of each agent synchronizes to that of the leader with bounded residual errors. Two illustrative examples validate the efficacy of the proposed methods.

This paper addresses the distributed robust stabilization problem for a class of uncertain nonlinear multiagent systems subject to dynamical uncertainties and external disturbances. A distributed adaptive controller is developed, based on the local information of the neighboring agents. The proposed controller can be implemented in a distributed manner for any undirected connected communication networks without requiring the accurate model of each agent. The proposed distributed neural controller guarantees that all signals in the closed-loop network are uniformly ultimately bounded. An example is given to show the efficacy of the proposed control method.