A Novel Fixed-Time Trajectory Tracking Strategy of Unmanned Surface Vessel Based on the Fractional Sliding Mode Control Method

Abstract

A novel sliding mode control method is proposed to achieve the trajectory tracking of the Unmanned Surface Vessel (USV) and effectively deal with the unmodeled dynamics and external unknown disturbances. First, a fixed-time fractional-order sliding mode control (FTFOSMC) strategy is proposed, combined with the fixed-time control theory and fractional-order control theory based on the sliding mode control method. The FTFOSMC strategy can improve the convergence velocity of the system, and effectively track the desired path, weakening the “chattering” effect in sliding mode control systems. Second, a fixed-time fractional-order sliding mode control strategy combined with the radial basis function neural network (RBF-FTFOSMC) was designed, which can effectively estimate the lumped uncertainties, such as the disturbance of external wind, wave, and current, and the unmodeled dynamics of the USV model. Then, the stability and effectiveness of the designed control strategy are guaranteed by the Lyapunov theory and the corresponding lemmas. Finally, a rigorous simulation experiment is designed to validate the effectiveness and stability of the proposed control strategy. The simulation results show that the control strategy can effectively achieve trajectory tracking of the USV, reduce the “chattering” phenomenon of sliding mode, and effectively estimate the lumped uncertainties.

Computational Methods for Parameter Identification in 2D Fractional System with Riemann–Liouville Derivative

“…In order to simplify the description of the numerical algorithm to be implemented, we present the difference schema (11) in matrix form, so we introduce the following matrices:…”

“…The matrices from the difference scheme ( 16) are large, so the obtainedsystem of equations is time-consuming to solve. Hence, we applied the alternating direction implicit method (ADIM) to the difference scheme (11), which significantly reduces the computation time (details can be found in [27]). This is an important issue in the case of inverse problems, where a direct problem should be solved many times.…”

“…This is an important issue in the case of inverse problems, where a direct problem should be solved many times. Let us write the scheme (11) in the form of the directional separation product:…”

“…Numerical scheme ( 17) is split into two parts and solved, respectively, first in the direction x, and afterwards in the direction y. With this approach, the resulting matrices for the systems of equations have significantly lower dimensions than in the case of the scheme (11). The numerical algorithm has two main steps:…”

“…In addition to applications in electronics, neural networks, and sensors, fractional calculus is also used in modeling of thermal processes [6,7], in modeling of anomalous diffusion [8,9], in medicine [10], and also in control theory [11,12]. Authors of the study in [6] model heat transfer in a two-dimensional plate using Caputo operator.…”