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In this paper, a new event-triggered optimal trajectory tracking control method based on goal representation heuristic dynamic programming (GrHDP) is proposed for underactuated ships, which achieves the promising tracking performance, the minimized control energy consumption and the communication resource saving together. The adaptive event-triggered mechanism is designed from the performance perspective based on the internal reinforcement signals and the optimal value function. The trajectory tracking control algorithm is derived based on GrHDP value iteration by using three neural networks (NNs), and the underactuated problem can thereby be solved. Then, the approximation error between the GrHDP value iteration function and the optimal cost is theoretically analyzed, and the convergence of the GrHDP value iteration algorithm is proved. We discuss in detail the uniformly ultimately bounded (UUB) stability of the closed-loop system. A theoretical analysis is conducted on the parameter selection of the triggering condition, which compromises the communication resources and the control performance. The optimality of the proposed control scheme is finally verified through simulation. • The proposed scheme can achieve the optimal tracking performance of the underactuated ship. • The fast training and convergence of NNs can be ensured by using GrHDP. • The underactuated problem can be solved by using NN learning. [ABSTRACT FROM AUTHOR]

This article proposes a novel active non-singular integral terminal sliding mode fault tolerant control scheme based on compound iterative learning observer (CILO-NITSM-FTC) for the trajectory tracking control problems of autonomous underwater vehicles (AUVs), which accompanied by nonlinear dynamics and possible thruster failures. The designed compound iterative learning observer (CILO) can effectively estimate the values of nonlinear dynamics and reconstruct the faults of the thrusters. Compared to the existing adaptive non-singular integral terminal sliding mode-based fault tolerant control (ANITSM-FTC), which is a passive fault tolerant control method essentially, the mentioned CILO-NITSM-FTC in this paper presents faster rate of convergence and more accurate control precision. In the design process of CILO, radial basis function neural network (RBFNN) is adopted to estimate the nonlinear dynamics, then approximation errors of neural network, thruster faults and external disturbances are considered as global disturbances. The estimated values obtained from CILO can be used to perform feedforward compensation on the designed controller to complete the reconstruction of thruster faults. Through rigorous mathematical proof and comparative numerical simulation experiments, the superiority and practicability of CILO-NITSM-FTC proposed in this paper are verified. • A CILO-NITSM-FTC method is proposed for the trajectory tracking control of AUVs. • A compound iterative learning observer (CILO) is designed based on ILO and RBFNN. • The designed CILO can estimate nonlinear dynamics and reconstruct faulty system. • The proposed CILO-NITSM-FTC has better control performance than existing ANITSM-FTC. [ABSTRACT FROM AUTHOR]

The autonomous surface vehicle (ASV) is supposed to be able to adapt unknown environments without human interference. This paper investigates the problem of trajectory tracking control for ASVs in the present of parameter uncertainties, disturbances, input quantization and actuator saturation. The neural network (NN) approximation and an adaptive sliding mode control (SMC) strategy are combined for the ASVs with a priori unknown upper bound of parameter uncertainties, external disturbances and saturation errors. The NN is adopted to approximate the unknown continuous uncertainties and disturbances in the system. The adaptive law for the SMC parameter can guarantee no overestimation of the robust control parameter with respect to unknown upper bounds of the NN approximation errors and the saturation error. By adding the NN approximation into the adaptive SMC laws, the robust control parameter and the chattering can be reduced. Uniformly ultimately bounded (UUB) for sliding variables and tracking errors can be guaranteed by Lyapunov proof. Simulation examples are given to illustrate the improved performance with the proposed approach. The comparisons on the proposed control method with other algorithms are given by using the integrated absolute error (IAE) and integrated time absolute error (ITAE). • This paper investigates the problem of trajectory tracking control for ASVs. • A switched quantizer integrating logarithmic quantizer and uniform quantizer is used. • The neural network technique is incorporated into the adaptive sliding mode control. • The assumption of prior knowledge of the upper bound of saturation error is relaxed.. [ABSTRACT FROM AUTHOR]

Safety and stability are two primary factors that affect the task execution performance of autonomous underwater vehicles (AUVs), especially when they operate in a disturbed environment. The unknown disturbances and unmodeled dynamics will severely degrade the performance, resulting in unsafe and unstable behaviors. This paper presents a safety-critical control framework for AUVs in the presence of unknown disturbances using a neural network function approximator. The high-order control barrier functions (CBFs) are utilized to address the safe constraints of relative degree two. A nominal controller is designed in which the unknown lumped disturbances are compensated by a radial basis function neural network, thus ensuring that the tracking errors are uniformly ultimately bounded. Besides, the function approximation and the associated bounded approximation errors are adopted to estimate the unknown lumped disturbance terms in the second-order derivative of CBFs, which alleviates the mismatch of the forward invariance condition for the safety set. The minimally invasive quadratic program (QP) is formulated to make minimal sacrifice on the performance of nominal controller. The proposed method encompasses a straightforward structure for disturbance estimation, alongside a highly efficient explicit estimating rule that promotes rapid convergence. Integrated with computationally efficient QP, the proposed method demonstrates substantial promise for real-time implementation. Comparative numerical results with disturbance observer and input-to-state safety-based robust methods reveal an improved trade-off between safety and control performance. • A simple structure function approximator is proposed to address the safety-critical control problem with unknown disturbance. • The explicit updating law ensures efficient convergence. • The conservatism of the proposed method is reduced compared with the worst-case compensation. • The approximation error bound of the nominal controller is utilized to estimate the high-order CBF condition, resulting in a better trade-off between safety and control performance. [ABSTRACT FROM AUTHOR]

This paper focuses on the adaptive asymptotic tracking control problem for an autonomous underwater vehicle (AUV) with un-modeled dynamics and unknown input saturation by combining the backstepping control strategy and the neural network (NN) method. In our controller, a novel single neural network-based backstepping control method is proposed to address the uncertain problem, and the input saturation issue is overcome in virtue of a hyperbolic tangent function. The approximation error of the neural network is also compensated by a new adaptive mechanism in order to achieve the zero-error regulation. Furthermore, the nonlinear transformation is incorporated into the backstepping-based framework to improve the AUV performance. And then, the performance analysis illustrates that the designed controller can realize the asymptotic stability of the AUV system. Finally, the effectiveness of our control strategy is validated through simulation results. • A single neural network-based asymptotic adaptive backstepping control strategy is proposed for the trajectory tracking of autonomous underwater vehicles. • The approximation error of the neural network is compensated by using the adaptive mechanism to achieve the zero-error regulation. • The nonlinear transformation is incorporated into the adaptive backstepping scheme to improve the AUV performance. • The asymptotic stability of the AUV system is proven based on the Lyapunov stability theorem. [ABSTRACT FROM AUTHOR]

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. • A coordinate transformation solves the underactuation problem and simplifies controller design. • The event triggering control significantly reduces the frequency of control execution without affecting control performance. • The control scheme can achieve stable tracking without any priori information about the USV mass, hydrodynamic parameters and external disturbances. [ABSTRACT FROM AUTHOR]

In this paper, a path-following control (PFC) problem of an underactuated surface vehicle (USV) is scrutinized based on an interval type-3 fuzzy logic system (IT3FLS). The suggested method is able to tackle the main limitations of the singleton fuzzy controller in terms of the approximation ability for uncertainties and exogenous disturbances of a complex nonlinear USV. Since a novel structure is employed for the FLS, the control policy is capable of ensuring robust performance against uncertainties with a wide range of variations and higher volumes of complex disturbances. Moreover, surge-guided line-of-sight (SGLOS) and auxiliary dynamics are utilized to design surge and heading control policies, adjusting the velocity of a vehicle and its position at each moment respective to the predefined path. Predictive compensators are designed to enhance the robustness by reducing the approximation error signals while the stability analysis of both tracking and approximation error signals are investigated based on the Lyapunov approach and Barbalat's lemma. Finally, simulation results demonstrate the effectiveness of the suggested improved fuzzy-based control strategy to solve a PFC problem. • A novel type-3 fuzzy-based controller is proposed subject to uncertainties. • The uncertainties are approximated via an online scheme consisting of adaptive rules. • A nonlinear predictive compensator is designed to reduce the approximation error. • The robust stability of the closed-loop scheme is guaranteed. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time adaptive dynamic positioning (DP) control problem of an unmanned surface vehicle (USV) with prescribed performance subject to time-varying disturbances, unknown model parameters and input saturation. First, the error transformation is performed to provide a framework for the design of model-free prescribed performance DP controller, which eliminates the need for accurate prior information of the model and external disturbances. Then, a saturated-command-deviation based compensated law is proposed by incorporating the fuzzy supervisory approach to account for the excess control efforts resulted by input saturation. Subsequently, the fuzzy logic systems (FLS) integrated with minimum learning parameters technique are employed to approximate the model-based and high-order terms, such that the explosion of computational complexity is removed and requirements for accurate modeling are eliminated. Meanwhile, to suppress the negative effects induced by time-varying disturbances and unknown approximation errors, the adaptive technique is adopted to estimate the upper boundary of compounded disturbances online. Finally, by incorporating the softening sign signal and piecewise function into recursive backstepping procedure, a DP controller is developed to avoid potential singularity and achieve finite time convergence. Theoretical analysis and simulation results successfully illustrate the effectiveness of the proposed scheme. • A model-free finite time prescribed performance controller is developed for dynamic positioning of USV subject to time-varying disturbances, unknown model parameters and input saturation. • A saturated-command-deviation based controller is proposed to deal with input saturation by employing the fuzzy supervisory approach. • Dynamic positioning with prescribed performance is achieved in a finite time. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for depth precision control of under-actuated autonomous underwater vehicles (AUV) subject to model uncertainties, ocean currents, and input constraints. Specifically, a transformation is made to convert the input constraint problem into a state constraint problem. Subsequently, an observer-based guidance law is developed to deal with the drift affected by unknown ocean currents by using an extended disturbance observer (EDO). An adaptive neural controller is then designed using the DSC technique and an advanced modified integral barrier Lyapunov function (mIBLF) to guarantee that all states are confined within the given constraint. Besides, a novel nonlinear disturbance observer is introduced to cope with external disturbances and neural network approximation errors. It is proved that all closed-loop signals are uniformly ultimately bounded by Lyapunov stability theory. Finally, comparative simulations are carried out to verify the effectiveness and outstanding characteristics of the proposed method. • A new approach for depth control of AUV subject to model uncertainties, ocean currents, and input constraints is suggested. • A transform converts the input constraint into a state constraint problem. Then an EDO observer is constructed. • An adaptive neural learning law is designed using modified Lyapunov function (mIBLF) to ensure all states are confined. • A nonlinear disturbance observer is used to cope with external disturbances and neural-based approximation errors. • Comparative simulations are carried out to verify the effectiveness of the proposed neural control technique. [ABSTRACT FROM AUTHOR]

In this paper, a novel prescribed performance and full state constraints dynamic surface control (PP&FSC-DSC) scheme is proposed for trajectory tracking of unmanned surface vessel (USV) with model uncertainties, unknown nonlinear disturbances and full state and input constraints. Firstly, the restricted system with inequality constraints is transformed into the system with equality constraints by the modified asymmetric barrier Lyapunov function (MABLF) and then combined with the prescribed performance function, the vessel position tracking error meets the prescribed performance. Secondly, owing to use the dynamic surface technique and introduce an auxiliary dynamic system (ADS), the double advantages are established, i.e., the negative effects of the differential operation for the intermediate control law and input saturation of the intermediate control law are avoided. Thirdly, the model uncertainties are approximated by the neural network (NN), and the NN approximation error and unknown nonlinear disturbances is adaptively estimated. Finally, according to the Lyapunov stability theory, all signals are semi-globally uniformly ultimately bounded (SGUUB). The trajectory can be maintained with prescribed tracking performance and the full state can be constrained. The effectiveness of the proposed control protocol is validated by the simulation results. • For the constrained system including full state and input constraints, a novel modified asymmetric barrier Lyapunov function (MABLF) is proposed. • It is the first time to combine performance function with MABLF so that the overshoot and convergence speed of the system meet the prescribed condition. • An ADS with easily adjustable parameters is designed to solve the problem of input constrains. • Considering the model uncertainty and the unknown external environment disturbance, the neural network is used to approximate the model uncertainty. • The adaptive law is designed to estimate the bounds of the neural network approximation error and the unknown disturbance, so the robustness of the system is enhanced. [ABSTRACT FROM AUTHOR]

To promote the vigorous development of the marine technology, more and more scientific research institutes have begun to develop unmanned surface vehicles (USVs) with advanced control performance. This paper addresses trajectory tracking problem for state-constrained USV under the influence of actuator saturation and general disturbance uncertainties. An anti-windup system with auxiliary variables is employed to cope with actuator saturation. Besides, full-state constrains are not violated by combining the tan-type barrier Lyapunov function and backstepping method. Moreover, RBFNN is adopted to approximate some unknown uncertain function terms. By utilizing adaptive estimation technique, the unknown upper boundaries of disturbance uncertainties, input saturation difference, as well as RBFNN approximation error are compensated. The semi-global asymptotic convergence is guaranteed by rigorous theoretical analysis and Lyapunov proof. Finally, simulations results are given to verify the feasibility of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider trajectory tracking control for autonomous surface vehicles (ASVs) with unknown boundary model uncertainties and external disturbances. The neural networks (NNs) and the sliding mode control (SMC) with a switched adaptive law are combined for the first time. The NNs are used to approximate model uncertainties and external disturbances of ASVs. The parameters of the robust SMC term first increase until the sliding variable reaches a quasi sliding mode which bound is associated with the parameter of the barrier function (BF). Then the BF is selected as the parameter of the robust term for the SMC strategy to estimate the NN approximation error and to constrain the sliding variable inside the predefined quasi sliding mode. One salient feature of our approach is that the robust control parameter is no more than approximation error of NNs in sliding and steady phases of SMC. Simulation studies are performed to illustrate the advantage of the proposed control method. • The proposed method is composed of an adaptive sliding mode control (SMC) law and a neural network (NN). • The robust control parameter increases until the sliding variable reaches the quasi sliding mode. • Then a barrier function (BF) is used to estimate the NN approximation error. • The tracking errors can converge to a bounded region related to the parameter of the BF. [ABSTRACT FROM AUTHOR]