Time-varying Environmental Disturbances Research Articles

An adaptive internal model control approach for unmanned surface vehicle based on bidirectional long short-term memory neural network: Implementation and field testing

This paper investigates a practical adaptive internal model control (IMC) for an unmanned surface vehicle (USV) with unknown time-varying nonlinear model parameters and environmental disturbances. Firstly, an internal model of the USV is presented using the Bidirectional Long Short-Term Memory (BiLSTM) neural network. Then, an adaptive neural IMC controller is designed for the trajectory tracking of USV by using the IMC method. The internal model and the controller are updated by an error threshold algorithm. The proposed control scheme comprises of a trajectory guidance module via the Line-of-Sight (LOS) guidance method and a tracking control module designed by IMC theory. Under the proposed control scheme, the development processes of the vehicle platform and the control algorithms are described, and accurate tracking control can be achieved. Finally, the results of simulation and field experiments are presented and discussed to validate the effectiveness of the proposed control scheme.

PSO-Based Predictive PID-Backstepping Controller Design for the Course-Keeping of Ships

Ship course-keeping control is of great significance to both navigation efficiency and safety. Nevertheless, the complex navigational conditions, unknown time-varying environmental disturbances, and complex dynamic characteristics of ships pose great difficulties for ship course-keeping. Thus, a PSO-based predictive PID-backstepping (P-PB) controller is proposed in this paper to realize the efficient and rapid course-keeping of ships. The proposed controller takes the ship’s target course, current course, yawing speed, as well as predictive motion parameters into consideration. In the design of the proposed controller, the PID controller is improved by introducing predictive control. Then, the improved controller is combined with a backstepping controller to balance the efficiency and stability of the control. Subsequently, the parameters in the proposed course-keeping controller are optimized by utilizing Particle Swarm Optimization (PSO), which can adaptively adjust the value of parameters in various scenarios, and thus further increase its efficiency. Finally, the improved controller is validated by carrying out simulation tests in various scenarios. The results show that it improves the course-keeping error and time-response specification by 4.19% and 9.71% on average, respectively, which can efficiently achieve the course-keeping of ships under various scenarios.

A Deep Reinforcement Learning-Based Path-Following Control Scheme for an Uncertain Under-Actuated Autonomous Marine Vehicle

In this article, a deep reinforcement learning-based path-following control scheme is established for an under-actuated autonomous marine vehicle (AMV) in the presence of model uncertainties and unknown marine environment disturbances is presented. By virtue of light-of-sight guidance, a surge-heading joint guidance method is developed within the kinematic level, thereby enabling the AMV to follow the desired path accurately. Within the dynamic level, model uncertainties and time-varying environment disturbances are taken into account, and the reinforcement learning control method using the twin-delay deep deterministic policy gradient (TD3) is developed for the under-actuated vehicle, where path-following actions are generated via the state space and hybrid rewards. Additionally, actor-critic networks are developed using the long-short time memory (LSTM) network, and the vehicle can successfully make a decision by the aid of historical states, thus enhancing the convergence rate of dynamic controllers. Simulation results and comprehensive comparisons on a prototype AMV demonstrate the remarkable effectiveness and superiority of the proposed LSTM-TD3-based path-following control scheme.

Distributed Event-Triggered Fixed-Time Leader–Follower Formation Tracking Control of Multiple Underwater Vehicles Based on an Adaptive Fixed-Time Observer

This paper focuses on the fixed-time leader–follower formation control of multiple underwater vehicles (MUVs) in the presence of external disturbances. First, an adaptive fixed-time disturbance observer (AFxDO) is developed to deal with unknown time-varying environmental disturbances. The developed AFxDO guarantees the fixed-time convergence property of the disturbance observation error and no prior information on the external disturbances or their derivatives is required. Then, with the aid of the developed AFxDO, a distributed event-triggered fixed-time backstepping controller was developed to achieve the leader–follower formation tracking control of MUVs. To solve the “explosion of complexity” problem inherent in the conventional backstepping, a nonlinear filter is introduced to obtain the derivative of the virtual control law. Furthermore, to reduce the communication burden, the event-triggered mechanism is integrated into the formation tracking controller. The stability analysis shows that the closed-loop MUV system is practical fixed-time stable. Finally, simulation results demonstrate the effectiveness of the proposed scheme.

Finite-time trajectory tracking control of dynamic positioning ship based on discrete-time sliding mode with decoupled sampling period

In this paper, the finite-time trajectory tracking control problem of a dynamic positioning ship with model uncertainty and time-varying environmental disturbances is investigated based on the discrete-time sliding mode with decoupled sampling period. To overcome the influence of the sampling period variation on the system’s control effect, a finite-time discrete sliding mode controller with decoupled sampling period is designed based on the new discrete-time adaptive fast power reaching law. The sampling period condition that guarantees the finite-time convergence of the system is given. A new finite-time high-order discrete disturbance observer is proposed to estimate model uncertainty and environmental disturbance, which reduces the dependence of the observer’s estimation accuracy on the sampling period. To realize the transformation from position tracking to velocity tracking in a finite time, a new finite-time discrete virtual velocity controller is designed. The proposed control strategy decouples the sampling period and enables the finite-time trajectory tracking control of the dynamic positioning ship over a wider sampling period range. The stability analysis demonstrates that all tracking errors of the closed-loop system can converge to a small domain near zero in a finite time. Two simulation examples verify the effectiveness of the proposed control method.

Event-triggered coordinated trajectory tracking control for multiple fully-actuated MSVs under prescribed performance constraints and limited transmission resources

This paper addresses the challenging problem of event-triggered coordinated formation trajectory tracking control for multiple fully-actuated marine surface vehicles (MSVs) affected by uncertain lumped dynamics, time-varying marine environmental disturbances, and prescribed performance constraints, as well as limited transmission resources. A prescribed performance constraint is initially imposed on the neighborhood errors to overcome these issues. The radial basis function neural networks (RBF NNs) and virtual parametric method are adopted to handle the uncertain lumped dynamics and time-varying marine environmental disturbances. Meanwhile, an auxiliary dynamic system is also introduced to compensate for filtering errors. Additionally, a unique event-triggered transmission strategy is devised by innovatively constructing a lumped state term, effectively reducing the burden on the transmission network and conserving resources among the MSVs. A triggering threshold condition is constructed to ensure Zeno-free behavior in the sense that guarantees the lower bound of the release intervals is always larger than zero. The overall Lyapunov theoretical synthesis reveals the boundedness of all closed-loop signals. Finally, the effectiveness and advantages of the designed strategy for event-triggered coordinated trajectory tracking control are verified through numerical simulation.

Adaptive backstepping fast terminal sliding mode control of dynamic positioning ships with uncertainty and unknown disturbances

Considering the complexity of the operating environment of marine ships, higher demands are placed on the positioning accuracy and positioning performance of Dynamic Positioning (DP) systems. This paper designs an Adaptive Backstepping Fast Terminal Sliding Mode Control (ABFTSMC) to solve the problems of low positioning accuracy, slow convergence, and poor anti-interference performance in ship positioning due to uncertainty of dynamic model parameters and unknown time-varying environmental disturbances. A Fast Terminal Sliding Mode Control (FTSMC) is combined with backstepping techniques to ensure the robustness of the system to uncertainties and disturbances. Meanwhile, an adaptive law is used to estimate the unknown uncertainty terms. Moreover, the Lyapunov stability criterion is used to prove the convergence and stability of the designed controller. Multiple simulation results show that ABFTSMC has better control performance compared with Adaptive Backstepping Control (ABC) and Adaptive Backstepping Sliding Mode Control (ABSMC). All the comparisons could fully verify the effectiveness and superiority of the proposed control method.

Robust trajectory tracking and control allocation of X-rudder AUV with actuator uncertainty

This paper proposes a robust trajectory tracking control method for an X-rudder autonomous underwater vehicle subject to imprecise model parameters, unknown disturbances, and actuator uncertainty. The control scheme consists of a kinematics controller, dynamics controller, and rudder allocator constructed using backstepping techniques. The kinematics controller employs a line-of-sight guidance law, while the dynamics controller uses integral sliding mode and a Radial Basis Function Neural Network to handle modeling errors and unknown disturbances. Finally, a Recursive Least Square Control Allocation method is developed to minimize the allocation error considering the uncertainty in the control effectiveness matrix by solving a dual second-order cone programming problem. Simulation results demonstrate that the RBFNN-based trajectory tracking method achieves satisfactory performance in the presence of time-varying environmental disturbances, and the Recursive Least Square Control Allocation method effectively deals with actuator uncertainty.

Minimum-learning-parameter-based adaptive finite-time trajectory tracking event-triggered control for underactuated surface vessels with parametric uncertainties

For the problem of trajectory tracking control of underactuated surface vessels (USVs) affected by input saturation, parametric uncertainties, time-varying marine environmental disturbances, and limited transmission resources, a robust adaptive finite-time event-triggered control scheme is presented in this paper. First, a coordinate transformation is constructed to tackle the underactuation problem of the USV and enables the USV control law to be devised in vector form, which simplifies the design and makes it more suitable for computer processing. A continuous auxiliary dynamic system is constructed to handle the input saturation problem. The minimum learning parameter (MLP) technique is used to approximate the parametric uncertainties of the model. An adaptive law is devised to update online the upper bound of the combination of external disturbances and the approximation error generated by the MLP. Additionally, a finite-time control scheme is presented by introducing a robustifying term in the virtual control law, which improves the control performance; an introduced event triggering mechanism in the channel from the controller to the actuator decreases both the transmission burden and the control execution frequency without affecting the control performance. The theoretical analysis reveals that the devised robust adaptive finite-time event-triggered control scheme enables the USVs to track the desired trajectory in a finite time with a small number of control executions, while ensuring the closed-loop stability of the system and avoiding Zeno behavior. The simulations verify the effectiveness and the superiority of the presented control scheme.

Adaptive generalized predictive control for dynamic positioning system of ships with model unknown parameters

This paper proposes an adaptive generalized predictive control for dynamic positioning of ships with unknown model parameters and unknown time-varying environmental disturbances. The controlled auto-regressive integrated moving average (CARIMA) model is employed to describe the movements of ships with model parameter and disturbance uncertainties. The recursive least square method with forgetting factor is utilized to design adaptive laws to estimate the CARIMA model parameters online. Considering both the positioning accuracy and the change intensity of control increments, a cost function is constructed. The optimal control increments that minimize the cost function are obtained by using Lagrange multiplier method. Then, the adaptive control law is designed to maintain ship’s position and heading at desired values. Finally, simulation studies in different cases are carried out and simulation results demonstrate the effectiveness of the proposed control scheme.

Fast terminal sliding-mode control based on unknown input observer for the tracking control of underwater vehicles

The control of underwater vehicles is always challenging due to nonlinear dynamics, unmodeled dynamics, system uncertainty, and environmental disturbances. In this paper, a robust control scheme is designed for the tracking control of underwater vehicles with system uncertainty and time-varying environmental disturbances. First, the dynamic model of underwater vehicles is simplified to an explicit expression for the inertia matrix without the need for complex hydrodynamic coefficients. Then, according to the invariant manifold theorem, a single-parameter unknown input observer (UIO) is designed to estimate uncertainty. Based on the simplified model and UIO, a fast terminal sliding mode control with an inverse function (IFTSMC) is designed. The finite-time stability of the closed-loop system is proved. Finally, to evaluate the performance of the proposed control scheme, comparative numerical simulations are conducted with 20% dynamic uncertainty and time-varying interference. The results indicate that the proposed control scheme is effective and robust under dynamic uncertainty and time-varying disturbances.

Finite-Time Controller Design for the Dynamic Positioning of Ships Considering Disturbances and Actuator Constraints

Focusing on dynamic positioning (DP) systems for ships, which are subject to environmental disturbances and actuator constraints, this paper presents a finite-time controller that uses a disturbance observer with the aid of a backstepping technique. First, to estimate the time-varying and unknown environmental disturbances in finite time, two sliding-mode disturbance observers are constructed. Specifically, an adaptive disturbance observer (ADO) effectively decreases undesired chattering without the need for prior information on environmental disturbances. Then, to handle the actuator constraints, the designed control forces are distributed into multiple actuators using a control allocation algorithm to obtain the actual forces. Next, an auxiliary dynamic system is built to compensate for velocity tracking errors induced by the mismatch of the DP control law and thruster forces. Then, with the designed ADO and the auxiliary dynamic system, a finite-time controller with a fast exponential-reaching law is designed; this ensures that the positioning errors and the sliding surface converge to zero at a fast convergence rate. Finally, numerical simulations are presented: these present a cable-laying ship experiencing wind, currents, and waves in different sea states. The results show the effectiveness of the presented control scheme.

Neural network feedback linearization target tracking control of underactuated autonomous underwater vehicles with a guaranteed performance

In this paper, an adaptive neural network-based feedback-linearizing controller is proposed to force an underactuated autonomous underwater vehicle (AUV) to follow a target with desired relative distance and angles in three-dimensional space. Towards this end, a new input-output model of the AUV is developed by defining a proper set of look-ahead position variables in a cone-shaped area in the front of the vehicle. Then, a nonlinear saturated PID-type controller is designed such that target tracking errors converge to a neighborhood of the zero while the prescribed transient and steady-state performance characteristics including desirable overshoot/undershoot, convergence rate and steady-state accuracy are guaranteed. This technique effectively prevents undesirable transient state behaviour of the vehicle while reducing the risk of actuators saturation. A combination of multi-layer neural networks (NNs) and adaptive robust control (ARC) techniques is used to handle the compensation of model uncertainties including unknown parameters, time-varying environmental disturbances induced by waves and ocean currents and NN approximation errors. A Lyapunov-based stability synthesis is presented to ensure the semi-global uniform ultimate boundedness of the proposed closed-loop control system with a guaranteed prescribed performance. Finally, simulation results are given to show the effective performance of the AUV for practical applications.

Event-based adaptive horizon nonlinear model predictive control for trajectory tracking of marine surface vessel

This study investigates the trajectory tracking problem of fully actuated marine surface vessels (MSVs). First, an optimal problem for trajectory tracking of MSV is established. Model uncertainty, time-varying environmental disturbances, and actuator saturation are considered in this problem. For the control algorithm, considering that the traditional nonlinear model predictive control (NMPC) algorithm requires large amounts of computational resources, it is not easy to transmit the control signal to the system in real-time in practice. Meanwhile, due to the limited bandwidth of the system, the large amount of data transmission may lead to congestion and loss of signal transmission. Therefore, a novel event-based adaptive horizon nonlinear model predictive control (EAHNMPC) scheme is proposed to relieve the computation burden and reduce the signal transmission frequency for the MSV's trajectory tracking. Moreover, stability proof of adaptive predictive horizon control is given, and simulation experiments under different cases are performed. The results show that the proposed scheme has better control performance and computational performance than other approaches.

Swarm Control for Connectivity-Preserving and Collision-Avoiding Unmanned Surface Vehicles Subject to Multiple Constraints

This paper investigates swarm control for unmanned surface vessels subject to multiple constraints. These constraints can be summarized as model parameter uncertainty, the unavailability of velocity measurements, time-varying environmental disturbances, input saturation and output constraints. Firstly, to recover unmeasured velocity information, to identify unknown vehicle dynamics and to estimate time-varying environmental disturbances, a neural adaptive state observer is designed for each vessel. Secondly, to avoid complex calculations, a second-order linear tracking differentiator is employed to generate a smooth reference signal and to extract the time derivative of the kinematic control law. Thirdly, to solve the input saturation, an auxiliary dynamic system is introduced. Fourthly, the barrier Lyapunov function is used to achieve connectivity preservation, collision avoidance and swarm control. Meanwhile, by using the estimated velocities of vessels, an output feedback controller is designed. The stability of the closed-loop system is proved. The simulation results show the effectiveness of the proposed swarm control strategy.

Nonsingular fast terminal sliding mode-based robust adaptive structural reliable position-mooring control with uncertainty estimation

This paper addresses a novel robust structural reliable position mooring scheme for a turret-moored floating production storage and offloading (FPSO) vessel subject to system uncertainties, environmental disturbances and unmeasurable velocity. A realistic mooring tension model considering buoys and different cable materials that can improve the capacity of the mooring system is derived. A sigmoid tracking differentiator (STD) is employed as a state observer to estimate the unmeasurable velocity. A structural reliability index is introduced to design a position mooring control law so that an FPSO vessel adequately uses a mooring system on the premise of safety to maintain position in an allowable region. It provides strong robustness and a fast transient response and suppresses chattering by merits of a backstepping method and an integral nonsingular fast terminal sliding mode surface (INFTSMS). An adaptive estimator is proposed to address the required unknown uncertainties and disturbances. Theoretical analysis proves the globally asymptotic stability of the whole system. Finally, comparative simulations on an FPSO vessel are conducted to illustrate the effectiveness and superiority of the proposed position mooring control scheme.

Model Reference Adaptive Control-Based Autonomous Berthing of an Unmanned Surface Vehicle under Environmental Disturbance

Surface-vehicle berthing is a complex and challenging task. It involves complicated ship dynamics owing to a large drift angle and the time-varying environmental disturbances induced by wind, wave, and current. Therefore, berthing requires state processing at each step and a controller that can respond to the non-linear behavior of the unmanned surface vehicle (USV). Herein, a systematic approach for the autonomous berthing of a USV is proposed. A state-machine approach is proposed to solve state transitions in the berthing step. A model reference adaptive controller was adopted to cope with the uncertainty of USV dynamics during berthing. Herein, the theoretical background and design of the adaptive controller are described. Simulation for the validation of the proposed method was conducted using the robot operating system Gazebo-based simulator. Finally, the respective performances of the proposed method and conventional controller were compared. Using the proposed berthing approach, an accurate and stable docking of small USVs became achievable.

Dynamical Sliding Mode Control for Robust Dynamic Positioning Systems of FPSO Vessels

The conventional proportional derivative (PD) control algorithm with appropriate gain scheduling is generally applied to a dynamic positioning (DP) system. However, finding appropriate gains through gain scheduling makes the DP system more complicated. A sliding-mode control algorithm controls an arbitrary point, such as the turret system on a floating production storage and offloading (FPSO) vessel. This algorithm was developed for DP and can be applied to FPSO vessels considering the uncertainty of the vessel dynamics, unknown time-varying environmental disturbances, and transient performance. To control an arbitrary point on the FPSO vessel using a DP controller, the Jacobian matrix in the kinematic equation is modified to present the arbitrary point in the control. The Lyapunov stability theory is applied in the design of the SM control algorithm to provide robustness to the control system. A time-domain simulation tool was developed to verify the effectiveness of the proposed SM control algorithm. The performance of the control algorithm was evaluated numerically to address its efficacy. The results were compared with those obtained using the conventional PD control algorithm.

Weather optimal area-keeping control for underactuated autonomous surface vehicle with input time-delay

The problem of the underactuated Autonomous Surface Vehicle (ASV) area-keeping control under unknown slow time-varying external environment disturbances and input time-delay, an integral time-delay sliding mode control algorithm based on weather optimal intermittent strategy is proposed in this article. Firstly, integral time-delay sliding mode control law is constructed, with controller parameters chosen according to the upper bound of time-delay. In the control law, a geometric updating rule is designed for the virtual suspension point, which enables ASV at a particular small area with a weather optimal heading. And, weather optimal intermittent strategy is developed to extend the area-keeping control method, while reducing ASV energy consumption. Besides, the closed-loop system is globally asymptotically stable through Lyapunov-Krasovskii analysis. Finally, the performance of the proposed algorithm is illustrated through the simulation examples.

Dynamic positioning of ship using backstepping controller with nonlinear disturbance observer

This paper studies the adaptive dynamic positioning control problem of the full-actuated ship with uncertain time-varying environmental disturbances. Considering the disturbances with unknown boundaries, the inversion control technique is combined with the disturbance observation compensation method to design the robust adaptive backstepping control law of the ship dynamic positioning system. The Lyapunov function is adopted to prove the errors of the ship’s position and heading angle are uniformly ultimately bounded using the designed control law. The nonlinear disturbance observer can adaptively estimate and compensate for uncertain external disturbances caused by winds, waves and currents. Afterward, the verification of the proposed controller through a typical CyberShip Ⅱ model subject to environmental disturbances is carried out using a hardware-in-the-loop simulation where a thrust distribution model is established. The simulation results show the effectiveness of the proposed control law.