Underactuated Marine Surface Vessels Research Articles

Fault-tolerant control of underactuated MSVs based on neural finite-time disturbance observer: An Event-triggered Mechanism

This paper deals with the problem of fault-tolerant control synthesis for underactuated marine surface vessels (MSVs) with dynamic uncertainties, external time-varying disturbances, and input saturation. In control design, with the help of neural networks (NNs) to reconstruct the dynamic uncertainty of the system, a novel nonlinear finite-time disturbance observer (FTDO) is established to reconstruct the compound uncertainty online, including unknown time-varying disturbances, approximation errors, bias faults and parts of loss-of-effectiveness (LOE) faults. Combining finite-time control (FTC) theory, event-triggered control (ETC) technology and backstepping design method, a new fault-tolerant control scheme for underactuated MSVs is designed. Based on the Lyapunov stability theory, it is proved that all signals in the closed-loop tracking system are bounded, and the tracking error of the underactuated MSVs converges to a small set near the origin in finite-time. The effectiveness of the proposed novel fault-tolerant control scheme is verified by computer simulation.

Adaptive neural dynamic surface composite control for path following of underactuated vessels with fixed-time convergence

The article discusses the path following control issue for underactuated marine surface vessels (MSVs) subject to nonlinear uncertainties. Firstly, the tracking goal of MSVs will be changed from the earth-fixed position to the line-of-sight (LOS) angle with the aid of LOS approach. To deal with the nonlinear uncertainties existing in MSVs, radial basis function neural networks (RBFNNs) are utilized. In particular, the fixed-time serial–parallel estimation models are used to boost the approximation of RBFNNs and determine whether RBFNNs really estimate the unknown nonlinearities by using the forecast and the track biases to change the weight of RBFNNs. Then, a fixed-time filter is produced to handle the ‘explosion of complex’ issue and improve the structure of the developed controller. In addition, the function tanh with smooth derivative function is utilized to overcome the singularity issue of the virtual controller derivations caused by fixed-time control. Finally, an adaptive neural fixed-time dynamic surface composite control method is developed for the path following control problem based on the adaptive backstepping control technique. The stability analysis results show the yaw angle ψ converges to the LOS angle ψs when t≥TS where Ts given later is not determined by the system initial variables. The system internal variables also reach a bounded compact set, which indicates the RBFNNs indeed estimate the uncertainties existing in MSVs by using fixed-time serial–parallel estimation models. And comparation simulation results also certificate the utilizability of the developed controller.

Online recorded data-based finite-time composite neural trajectory tracking control for underactuated MSVs.

This paper presents an online recorded data-based composite neural finite-time control scheme for underactuated marine surface vessels (MSVs) subject to uncertain dynamics and time-varying external disturbances. The underactuation problem of the MSVs was solved by introducing the line-of-sight (LOS) method. The uncertain dynamics of MSVs are approximated by the composite neural networks (NNs). A modified prediction error signal is designed by virtue of online recorded data. The weight updating law of NN is driven by both tracking error and prediction error, introducing additional correction information to the weights of NN, thus improving the learning ability of the NN. Furthermore, disturbance observers can be devised to estimate the compound disturbances consisting of the approximation errors of NNs and external disturbances. Moreover, the smooth function is inserted into the design of the control scheme, and the finite-time composite neural trajectory tracking control of MSVs is achieved. The stability of the MSVs trajectory tracking closed-loop control system is guaranteed rigorously by the Lyapunov approach, and the tracking error will converge to the set of residuals around zero within a finite time. The simulation tests on an MSV verify the effectiveness of the proposed control scheme.

Finite time PAILOS based path following control of underactuated marine surface vessel with input saturation

In this article, the line-of-sight (LOS)-based on the control principle of path following is presented to apply to a marine surface vessel (MSV) with an unknown time-varying sideslip angle. The input saturation and the uncertain model are taken into account. The presented finite-time predictor-based adaptive integral line-of-sight (FPAILOS) guidance principle can estimate the unknown time-varying sideslip angle while compensating for the drift force. The FPAILOS guidance law offers the desired yaw angle. The drift force can be caused by the ocean currents, which are taken into account in the kinematic model for the MSV. For the input saturation problem, we select the finite-time auxiliary system to limit inputs. Designing path following control signals adopts the finite-time dynamic surface control (FDSC) method. The finite-time low-frequency learning-based fuzzy system is designed to solve the uncertain model problem for the MSV. Finally, the stability of the system is demonstrated and numerical simulations are performed, where the objective is to evaluate the proposed theoretical results. With the presented control strategy, the track errors can converge into arbitrary small neighborhoods around zero in finite time.

Dynamic event-triggered trajectory tracking control for underactuated marine surface vessels with positive minimum inter-event time guarantees

This paper proposes a dynamic event-triggered trajectory tracking control scheme for underactuated marine surface vessels (MSVs) with positive minimum inter-event time (MIET) guarantees. Under the presented scheme, control inputs only need to transmit to actuators at the designed event triggering time. Additionally, the maximum signal transmission frequency can be prior known by designers. To facilitate the design of the above control architecture, an unified second-ordered tracking error dynamic system is firstly derived. Then, based on the transformed error dynamic system, an event-based adaptive control law is developed. To counteract external disturbances and unmodeled dynamics, the minimum-learning-parameter (MLP) based neural approximator is constructed to enhance system robustness. Finally, by introducing internal dynamic variables, a dynamic event-triggered mechanism (DETM) is established to manage communications between the control module and actuators. Compared with existing event-triggered methods, the proposed event-driven method is dynamic and more flexible to satisfy network bandwidth requirements. Besides, MIETs of the presented DETM are also proved to be strictly positive and computable from control parameters. Theoretical analysis and simulation results verify the validity and effectiveness of the proposed DETM based control scheme.

Event-triggered finite-time tracking control of underactuated MSVs based on neural network disturbance observer

In this work, a trajectory tracking control issue is discussed for the underactuated marine surface vessels (MSVs) with uncertain dynamic and unknown external disturbances. In the control design, the neural network approximation technology is applied to reconstruct the unknown dynamic, and a finite-time disturbance estimator is established to reconstruct the lumped uncertainties including the unknown external disturbance and approximation error online. Under the design framework of line-of-sight, a new finite-time trajectory tracking control scheme for underactuated MSVs is developed combining the finite-time control theory with the backstepping design method. The developed control scheme has the following remarkable characteristics: (1) it realizes the fast and accurate online reconstruction of lumped uncertainties; (2) it can release the requirement of online disturbance estimation technology on an accurate MSV motion model and expand the application range of online disturbance estimation technology; (3) the unnecessary wear and tear of actuators is suppressed by introducing the event-triggered control (ETC) approach. Based on the Lyapunov theory, it is proved that all signals in the closed-loop tracking control system are bounded. Finally, the effectiveness of the proposed control scheme is verified by the simulation and comparison.

Composite learning tracking control for underactuated marine surface vessels with output constraints.

In this paper, a composite learning control scheme was proposed for underactuated marine surface vessels (MSVs) subject to unknown dynamics, time-varying external disturbances and output constraints. Based on the line-of-sight (LOS) approach, the underactuation problem of the MSVs was addressed. To deal with the problem of output constraint, the barrier Lyapunov function-based method was utilized to ensure that the output error will never violate the constraint. The composite neural networks (NNs) are employed to approximate unknown dynamics. The prediction errors can be obtained using the serial-parallel estimation model (SPEM). Both the prediction errors and the tracking errors were employed to construct the NN weight updating. Using approximation information, the disturbance observers were designed to estimate unknown time-varying disturbances. The stability analysis via the Lyapunov approach indicates that all signals of unmanned marine surface vessels are uniformly ultimate boundedness. The simulation results verify the effectiveness of the proposed control scheme.

Event-Triggered Adaptive Neural Fault-Tolerant Control of Underactuated MSVs With Input Saturation

This paper investigates the tracking control problem of marine surface vessels (MSVs) in the presence of uncertain dynamics and external disturbances. The facts that actuators are subject to undesirable faults and input saturation are taken into account. Benefiting from the smoothness of the Gaussian error function, a novel saturation function is introduced to replace each nonsmooth actuator saturation nonlinearity. Applying the hand position approach, the original motion dynamics of underactuated MSVs are transformed into a standard integral cascade form so that the vector design method can be used to solve the control problem for underactuated MSVs. By combining the neural network technique and virtual parameter learning algorithm with the vector design method, and introducing an event triggering mechanism, a novel event-triggered indirect neuroadaptive fault-tolerant control scheme is proposed, which has several notable characteristics compared with most existing strategies: 1) it is not only robust and adaptive to uncertain dynamics and external disturbances but is also tolerant to undesirable actuator faults and saturation; 2) it reduces the acting frequency of actuators, thereby decreasing the mechanical wear of the MSV actuators, via the event-triggered control (ETC) technique; 3) it guarantees stable tracking without the a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> knowledge of the dynamics of the MSVs, external disturbances or actuator faults; and 4) it only involves two parameter adaptations—a virtual parameter and a lower bound on the uncertain gains of the actuators—and is thus more affordable to implement. On the basis of the Lyapunov theorem, it is verified that all signals in the tracking control system of the underactuated MSVs are bounded. Finally, the effectiveness of the proposed control scheme is demonstrated by simulations and comparative results.

Path following of a class of underactuated mechanical systems via immersion and invariance‐based orbital stabilization

SummaryThis article aims to provide a new problem formulation of path following for mechanical systems without time parameterization nor guidance laws, namely, we express the control objective as an orbital stabilization problem. It is shown that it is possible to adapt the immersion and invariance technique to design static state‐feedback controllers that solve this problem. In particular, we select the target dynamics adopting the recently introduced Mexican sombrero energy assignment method. To demonstrate the effectiveness of the proposed method we apply it to control underactuated marine surface vessels.

Finite-Time Path Following Control of an Underactuated Marine Surface Vessel with Input and Output Constraints

This paper develops a finite-time path following control scheme for an underactuated marine surface vessel (MSV) with external disturbances, model parametric uncertainties, position constraint and input saturation. Initially, based on the time-varying barrier Lyapunov function (BLF), the finite-time line-of-sight (FT-LOS) guidance law is proposed to obtain the desired yaw angle and simultaneously constrain the position error of the underactuated MSV. Furthermore, the finite-time path following constraint controllers are designed to achieve tracking control in finite time. Additionally, considering the model parametric uncertainties and external disturbances, the finite-time disturbance observers are proposed to estimate the compound disturbance. For the sake of avoiding the input saturation and satisfying the requirements of finite-time convergence, the finite-time input saturation compensators were designed. The stability analysis shows that the proposed finite-time path following control scheme can strictly guarantee the constraint requirements of the position, and all error signals of the whole control system can converge into a small neighborhood around zero in finite time. Finally, comparative simulation results show the effectiveness and superiority of the proposed finite-time path following control scheme.

FAILOS guidance law based adaptive fuzzy finite-time path following control for underactuated MSV

An adaptive fuzzy finite-time path following control design is presented for the underactuated marine surface vessel (MSV) under the condition of the time-varying ocean currents and time-varying large sideslip angle in this paper. The proposed FAILOS guidance law can not only calculate the desired heading angle but also estimate time-varying ocean currents and time-varying large sideslip angle simultaneously. It is the first time that the fuzzy logic system is introduced into the guidance system of MSV's path following control problem. Then the adaptive fuzzy finite-time path following controllers are established via backstepping technique, and the unknown lumped disturbances are estimated by the adaptive fuzzy logic system. The new saturation compensators are adopted to handle the input saturation problem and meet with finite-time convergence requirement of the whole control system. It has been demonstrated that the proposed adaptive fuzzy finite-time path following controllers can drive the vessel to follow the predefined path and tracking error can converge to a small neighborhood around origin in finite time. Simulation studies and comparisons are carried out to demonstrate the validity of the proposed control approach.

Adaptive NN event-triggered control for path following of underactuated vessels with finite-time convergence

This paper investigates the problem of path following of underactuated marine surface vessels (MSVs) with uncertain nonlinear dynamics. First, the tracking target of the vessel is reduced from tracking the earth-fixed position to tracking the line-of-sight (LOS) angle by LOS method. Then, by employing the radial basis function neural network (RBFNN) to deal with the uncertain nonlinear dynamics, an adaptive NN fast power reaching law is developed for the path following problem based on the backstepping design methodology. Thereafter, the event-triggered technique is incorporated into the control design to synthesize an adaptive NN event-triggered controller with the fast power reaching convergence rate. By combining with the presented event-triggered mechanism, the controller is only updated when the triggering condition is satisfied. Therefore, both the update frequency of the controller and actuator loss are greatly reduced comparing with the traditional time-triggered controller. Theoretical analysis via Lyapunov method indicates that the tracking error can converge to zero within a finite time, meanwhile it also shows that Zeno behavior can be avoided. Simulation results with comparations illustrate the validity and superiority of the proposed controller.

Improved adaptive integral line-of-sight guidance law and adaptive fuzzy path following control for underactuated MSV

This paper presents an adaptive fuzzy path following control law based on an improved adaptive integral line-of-sight (IAILOS) guidance law for the underactuated marine surface vessel (MSV) exposed to the time-varying ocean currents and time-varying sideslip angle. Initially, the IAILOS guidance law is proposed which can not only calculate the desired yaw angle but also estimate the time-varying ocean currents and time-varying sideslip angle simultaneously. Furthermore, the adaptive fuzzy path following control law is established by combining with the estimator to cope with the MSV’s attitude tracking control and velocity tracing control problem via backstepping technique. Specifically, the dynamic uncertainties and unknown environment disturbances are compensated by the fuzzy logic system with fuzzy updating law based on estimation error rather than tracking error. Additionally, two high-order tracking differentiators (TDs) are designed to construct derivatives of virtual control vector and reduce computational complexity inherent in backstepping method. It is proved that the proposed adaptive fuzzy path following control law can drive the vessel to track the desired path and tracking error can converge to an arbitrarily small compact set, while guaranteeing all signals in the closed-loop control system are uniformly ultimately bounded. Finally, simulation results and comparisons are carried out to demonstrate the effectiveness of the proposed control approach.

Adaptive Neural-Based Finite-Time Trajectory Tracking Control for Underactuated Marine Surface Vessels With Position Error Constraint

This paper addresses the trajectory tracking control problem of an underactuated marine surface vessel with position error constraint, finite-time convergence requirement, model uncertainties, and external disturbances. A barrier Lyapunov function is incorporated with the backstepping control scheme to handle the position error constraint. The command filters and auxiliary systems are designed to avoid the tedious analytical computation of the virtual control laws. Furthermore, an adaptive radial basis function neural network is adopted to provide the estimation of the unknown hydrodynamic damping term, and a disturbance observer is designed to compensate for the lumped disturbances including the neural approximation errors and external ocean disturbances. We show that under the proposed control scheme, the tracking errors of the vessel can converge to a small neighborhood around 0 within finite time, while the constraint on the vessel position is never violated during the maneuver, and all closed-loop signals are proved to be bounded. Finally, a numerical simulation is provided to illustrate the effectiveness and superiority of the proposed control scheme.

Finite-Time Trajectory Tracking Control for Uncertain Underactuated Marine Surface Vessels

This paper concerns the finite-time trajectory tracking control problem for an underactuated marine surface vessel (MSV) suffering from the external disturbance and parameter uncertainties. First, the virtual velocity command is proposed based on a novel piecewise function. It will be illustrated that the position tracking error can be stabilized to small regions in finite time once the desired velocity commands are tracked. Then, an adaptive tracking controller is developed such that sway and yaw velocities can converge to the desired ones in finite time. Utilizing the proposed control strategy, global finite-time stability can be ensured for the position and velocity tracking errors even in the presence of external disturbances and parameter uncertainties. Finally, the effectiveness of the proposed controller is illustrated by numerical simulation.

High-Gain Observer-Based Line-of-Sight Guidance for Adaptive Neural Path Following Control of Underactuated Marine Surface Vessels

This paper presents an adaptive neural network dynamic surface control law with time-varying sideslip compensation, which includes a geometric kinematic control design and a dynamic control design, for path following of underactuated marine surface vessels (MSVs) in the presence of unmeasured states, model uncertainties, unknown ocean environmental disturbances, and input saturation. First, a high gain observer based line-of-sight guidance law, capable of estimating and compensating the time-varying sideslip angle induced by the unknown time-varying ocean disturbances, is proposed to generate the desired heading for the dynamic control system of the MSV. Next, considering the input saturation, adaptive neural network dynamic surface velocity control laws, in which the model uncertainties and unknown ocean environmental disturbances of the system are compensated by adaptive radial basis function neural network and the problem of input saturation is solved by introducing auxiliary dynamic systems, are designed to realize the dynamic control target of the path following. The proposed control strategy of path following compensates the ocean environmental disturbances from the perspective of both the geometric kinematics and the dynamics, and all error signals of a closed-loop control system are proven to be uniformly ultimately bounded. The simulations validate the effectiveness of the proposed control strategy for path following of MSVs.

Two-time scale path following of underactuated marine surface vessels: Design and stability analysis using singular perturbation methods

The paper aims to develop a novel path following control law for nonlinear vessel models in two-time scales. For the 4-DOF path following model, we explore that the guidance dynamics are much slower than the ship motion dynamics. Based on such characteristic, a singular perturbation method is used to decompose the full system into two-time-scale subsystems. The two-time-scale structure allows independent analysis of dynamics in each time scale. Separate control strategies for the quasi-steady-state subsystem and the boundary layer subsystem are designed to stabilize the full system, yielding a rudder angle control law which is compact and uncomplicated to implement in practice. Singular perturbation methods are utilized to provide mathematical expressions for the upper bound of the singularly perturbed parameter and establish the exponential stability of the full system. The paper proves that the control law is robust in the presence of bounded perturbations and unmodeled dynamics, resulting states converge into an invariant set arbitrarily closed to the origin. Simulation results show the effectiveness and robustness of the proposed method for path following. The primary benefit of the proposed method is the simplicity of implementation.

A self-tuning robust observer for marine surface vessels

The current work aims at developing a nonlinear, self-tuning, robust observer to estimate state variables pertinent to the control of under-actuated marine surface vessels. The state estimator combines the advantages of the variable structure systems theory with those of the self-tuning fuzzy logic algorithm. It does not require an exact knowledge of the system dynamics or the construction of a rule-based expert fuzzy inference system. However, the upper bounds of both modeling imprecision and external disturbances must be known. The convergence of the estimation process is guaranteed by forcing the tuning parameters to satisfy inequalities stemming from the sliding conditions. The observer has been implemented herein to provide accurate estimate of the state variables that are needed by an integrated guidance and control system for the autonomous operation of an under-actuated marine surface vessel. The observer along with the integrated guidance and control system have been tested on a six degree-of-freedom ship model that considers numerous uncertainties associated with wave excitation, nonlinear restoring forces, retardation forces, sea-current and wind resistive loads. The theoretical results prove that the proposed self-tuning observer can produce accurate estimates of the state variables in the presence of significant modeling imprecision and environmental disturbances. In addition, they illustrate the use of estimated state variables in the guidance and control system with minimal impact on the close-loop performance of the marine vessel.

A self-tuning guidance and control system for marine surface vessels

An integrated guidance and control system has been developed to enable underactuated marine surface vessels to operate autonomously and yield robust tracking performance in spite of significant external disturbances and modeling imprecision. A nonlinear ship model, accounting for all six degrees-of-freedom of the ship, has been used as a test bed to assess the performance of the proposed scheme. The controller combines the advantages of the variable structure systems (VSS) theory with the self-tuning fuzzy logic scheme. It does not require an accurate dynamic model of the ship or the construction of a rule-based expert system. Its asymptotic stability is ensured by knowing the upper bounds on modeling imprecision and external disturbances and by forcing the tuning parameters to satisfy the sliding conditions. The guidance system is based on the concepts of the variable radius line-of-sight (LOS) and the acceptance circle around the waypoints. The current system varies the LOS radius exponentially with the cross track error in order to achieve a fast convergence rate of the ship to its desired trajectory. The simulation results demonstrate the robust tracking characteristic of the integrated guidance and control system in spite of significant modeling uncertainties and environmental disturbances.

Straight Line Path Following for Formations of Underactuated Marine Surface Vessels

The problem of formation control and path following for underactuated 3-degrees-of-freedom (3-DOF) marine surface vessels is considered. The proposed decentralized controller makes the vessels asymptotically constitute a desired formation that follows a given straight line path with a given forward speed profile. The controller consists of a cross-track control law, based on line-of-sight guidance, and a nonlinear synchronization control law. The closed-loop dynamics of both the cross-track errors and the synchronization errors are analyzed in detail using nonlinear cascaded systems theory and the overall cascaded system is shown to be both uniformly globally asymptotically stable and uniformly globally exponentially stable under mild assumptions. The proposed control strategy is validated in experiments in both calm water and in waves using a scale model vessel.