This article studies the model-based event-triggered control (ETC) for the tracking activity of the underactuated surface vessel (USV). Following this ideology, the continuous acquisition of states is no longer needed, and the communication traffic is reduced in the channel of sensor to controller. The control laws are fabricated in the frame of an adaptive model, which is renewed with the states of the original system whenever the triggering condition is violated. In the scheme, both internal and external uncertainties are approximated by the neural networks (NNs). To decrease the computing complexity, the minimum learning parameters (MLPs) are involved both in the adaptive model and the derived controller. The adaptive laws of only two MLPs are devised, and their updating only happens at triggering instants. Using the MLPs, an adaptive triggering condition is further derived. To avoid the ``Zeno'' phenomenon in small tracking errors, a dead-zone operator is designed for the triggering condition. Furthermore, we incorporate the dynamic surface control (DSC) into the controller design, such that the jumping of virtual control laws at triggering instants is smoothed and the problem of ``complexity explosion'' is circumvented. Through the techniques of the impulsive dynamic system and the direct Lyapunov function, the parameter setting for the DSC is derived to guarantee the semiglobal uniformly ultimate boundedness (SGUUB) of all the error signals in the closed-loop system. Finally, the effectiveness of the proposed scheme is validated through the simulation.

This paper investigates the adaptive fuzzy outputfeedback path-following control of autonomous surface vessels (ASVs) via the event-triggered mechanism, in which the fuzzy logic systems (FLSs) are employed to approximate the uncertainties. By transforming the estimation errors, an adaptive fuzzy observer is established to estimate the kinematic states of the ASV, and a serial-parallel estimation model is fabricated based on this observer. By combining the tracking errors with the prediction errors between the observer and the serial-parallel estimation model, the composite adaptive laws are devised for the weights of the FLSs. Then, the event-triggered controller is developed in the channel of sensor to controller, in which the estimated kinematic states, the positional coordinates and the heading angle of the ASV are sampled only when the triggering condition is violated. In this paper, we put forward the problem of jumps of virtual control laws at the triggering instants, which commonly exists in the backstepping-based event-triggered control (ETC) in the channel of sensor to controller. To solve this problem, the dynamic surface filters are employed to generate the continuous substitutes for the virtual control laws. The proposed scheme can guarantee at least the similar control performance compared with its continuous alternatives while it importantly reduces the communication burden through the ETC, and can enhance the estimation accuracy of the observer by applying the composite learning. All the errors are ensured to be semiglobally uniformly ultimately bounded (SGUUB) in the closedloop system. Finally, the effectiveness of the proposed scheme is verified through the numerical experiment.

This paper addresses the issue of waypoints-based path-following control for sailboats. Based on the parameterized line-of-sight framework, a novel guidance principle for the sailboat is developed, which comprises the mechanisms to observe the crab angle and generate the reference heading angle. For the crab angle observation, the approach with double reduced-order extended state observers and a saturation operator is developed, which involves the consideration of the intense sway. For the heading angle generation, three modes are devised, i.e., the path-following mode, the characteristic tacking mode, and the gybing mode. Sign functions are employed to describe tacking and gybing maneuvers of the sailboat such that rational switching of the reference heading angle is guaranteed, and no linguistic command is required. Matching with the proposed guidance principle, an adaptive neural control law is thereafter developed with the outputs landing in rudder angles. The echo state networks (ESNs) are introduced to offset model uncertainties and environmental disturbances with minimum parameters learning. By introducing two time-varying systems, all the errors in the closed-loop system are proved to be semiglobal uniformly ultimate bounded. Finally, the effectiveness of the proposed scheme is testified in MATLAB simulation.

Adapting to the navigational high-precision tracking tasks, this paper develops an event-triggered adaptive neural asymptotic tracking control framework for underactuated ships. The prescribed performance control (PPC) technique is employed to address spatial constraints in navigation, where the positional tracking errors are transformed via the transformation functions. By using the approximation of radial basis function neural networks (RBF NNs) in the form of minimum learning parameters (MLPs), the uncertainties coming from the unknown model dynamics, the environmental disturbances and the derivation of virtual control laws are offset all together, and a succinct computation is guaranteed. Assisted by the property of neural basis function, the “algebraic loop” problem in the backstepping design is released. To achieve the asymptotic tracking performance, the hyperbolic tangent functions are incorporated into the control laws, which are characterized by the integral-bounded terms. The event-triggered control (ETC) is designed in the controller-to-actuator (CA) channel. Two separate triggering conditions are constructed for the surge and the yaw motions respectively, which are characterized by the compound thresholds composed of a variable and a constant. The “Zeno” behaviors can thereby be avoided. The proposed scheme has three notable characteristics: 1) the computational complexity is reduced by using the MLP technique with lumped uncertainties; 2) the high-precision tracking performance can be achieved through the asymptotic tracking control; 3) the practical problems of spatial constraints and communication burdens can be solved by fabricating a uniform control framework including PPC and ETC. With the aid of direct Lyapunov candidates and the Barbalat’s lemma, the asymptotic convergence of all the tracking errors is proved. Finally, a numerical experiment corroborates the feasibility of the proposed scheme.