Event-Triggered Asymptotic Tracking Control of Underactuated Ships With Prescribed Performance

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.