Prescribed Performance Control of Marine Surface Vessel Trajectory Tracking in Finite-Time with Full-State Constraints and Input Saturation

Xiyun Jiang,Yuanhui Wang

doi:10.3390/jmse9080866

Xiyun Jiang, Yuanhui Wang

Open Access

https://doi.org/10.3390/jmse9080866

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Abstract

This manuscript mainly solves a fully actuated marine surface vessel prescribed performance trajectory tracking control problem with full-state constraints and input saturation. The entire control design process is based on a backstepping technique. The prescribed performance control is introduced to embody the analytical relationship between the transient performance and steady-state performance of the system and the parameters. Meanwhile, a new finite time performance function is introduced to ensure that the performance of the system tracking error is constrained within the preset constraints in finite time, and the full-state constraints problem of the system can be solved simultaneously in the entire control design, at the same time without introducing additional theory and parameters. To solve the non-smooth input saturation function matrix is not differentiable, the smooth function matrix is introduced to replace the non-smooth characteristics. Combining the Moore-Penrose generalized inverse matrix to design the virtual control law, the dynamic surface control is introduced to avoid the complicated virtual control derivation process, and finally the actual control law is designed using the properties of Nussbaum function. In addition, in view of the uncertainties in the system, a fractional disturbance observer is designed to estimate it. With the proposed control, the full-state will never be violated constraints, and the system tracking error satisfies transient and steady-state performance. Compared with other methods, the simulation results show the effectiveness and advantages of the proposed method.

Highlights

In recent years, the trajectory tracking control of surface vessels has interested a wide range of scholars, becoming a theoretical and practical research topic
The barrier Lyapunov function method can ensure that the system full-state will not violate the constraints, but this method can only solve the convergence region of the tracking error in theory, and cannot effectively restrict the dynamic process of the tracking error over time, which makes it difficult to satisfy the requirements of the dynamic characteristics of the control system, i.e., it ignores the transient performance and steady-state error performance of the system
The control design method in this paper is mainly based on backstepping technique, combined with prescribed performance and disturbance observer to solve the problem of finite time constraint of marine surface vessel trajectory tracking

Summary

Introduction

The trajectory tracking control of surface vessels has interested a wide range of scholars, becoming a theoretical and practical research topic. In reference [16], a new performance function is constructed to solve finite-time prescribed performance trajectory tracking problem of dynamic positioning ship. Reference [17] solves a class of nonlinear system control problems that require dynamic performance of the system It constructs a new type of performance function to make the tracking error converge in finite-time and satisfy the transient and steady-state requirements. The control design method in this paper is mainly based on backstepping technique, combined with prescribed performance and disturbance observer to solve the problem of finite time constraint of marine surface vessel trajectory tracking.

Preliminaries

Problem Formulation

Fractional Order Disturbance Observer Design

Simulations

Discussion

Conclusions