Finite-time Formation Control Methods For Multiple Dynamic Positioning Ships

With the deep development of marine resources,dynamic positioning technology has also been rapid development.However,taking into account the limited operational capacity and operating range of a single-vessel,the multi-vessel cannot only improve the efficiency of maritime tasks,but also perform special operations.In recent years,with the control of multiple ships has gradually become the hotspot of ship control research,the finite-time formation control for multiple ships,as a branch of ship control,has attracted wide attention and research.In this paper,We study the trajectory of the dynamic positioning ships with a certain formation in a limited time;and the marine environment is changing rapidly.In the actual sea operation,the complexity of the marine environment becomes the difficulties in the study of finite time motion control for multi-vessels.In this paper,the finite time motion control of coordinated formation of multiple ships will be divided into several steps.Firstly,the background and significance of the subject matter studied in this paper are briefly described.This paper describes the process of coordinated formation control in the process of multi-agent system movement,and the advantages of finite time convergence of motion control of multi-agent system and the advantages of system coordination and finite time control in real engineering application.This paper focuses on the research progress of the coordination control of multi-DP ships at home and abroad,and the development of finite time control methods in recent years.At the same time,it analyzes the difficulties and problems encountered in the research processes,and the main research contents of this paper.Secondly,the basic content of the multi-DP ship system coordination formation in the limited time control is studied.Firstly,the establishment of the mathematical model of the DP ship is analyzed.Then,the theoretical basis and theorem of the graph topology are described.The information communication between the vessels is described by the mathematical method of the strong connected graphs.And it has introduced the relevant convergence theorem and stability theorem of the knowledge and proof process of the matrix theory involved in the research of the thesis,so that the formulaic derivation of the later chapter have the basis.Thirdly,for the multi DP system virtual leader ship,taking into account the limitations of the undirected graph,using directed graph form,motion design of coordinated formationcontrol law of formation tracking control of multi DP leader ship to sea duty need.The coupling error of the absolute error between the follower ship and the pilot ship and the synchronization error of the following ship is taken as the systematic error,the accuracy of trajectory tracking control error is improved;The design of the coordinated formation control law is based on terminal sliding mode control,the system coupling error can converge to zero in finite time;However,the equation of the sliding surface is nonlinear,aiming at the disadvantage of slow convergence of the system state and the singularity of the control force,the formation control law of the terminal sliding mode is presented,the fast terminal sliding mode control law and nonsingular fast terminal sliding mode control law are proposed.Based on Lyapunov stability analysis shows that the control law can realize multi DP ship tracking system pilot ship motion and trajectory in finite time method and finite time convergence theorem,finally,the state variables of the system are simulated to prove controller is effective.Fourthly,in view of the difficulty of complex marine environment disturbance,a finite time disturbance observer is designed to observe the disturbance in real time.The finite time convergence theorem and Lyapunov theorem are used to prove the finite time convergence of the disturbance observer;A nonsingular fast terminal sliding mode control law is designed based on the disturbance estimation value,and the tracking process of multi DP following ship is controlled,and it is proved that the system state can be obtained with finite time convergence.Finally,the simulation verifies the effectiveness and correctness of the terminal sliding mode observer and controller.Finally,the research contents and results of this thesis are summarized,the paper also points out the shortcomings of the thesis and the future research direction.