船舶动力定位反步逆最优控制

Inverse optimal backstepping control of dynamic positioning ships

针对动力定位船舶定点定位过程中的高低频运动特性,设计了一种基于无源滤波的反步逆最优控制器.首先建立船舶的非线性方程,再利用线性化方程对应的Riccati方程对船舶非线性方程进行反步变换,最后基于Lyapunov函数设计了未建模扰动环境力自适应律和渐进稳定的控制律,同时满足了局部性能指标和全局性能指标.该方法从一个新的角度解决定点定位过程中船舶非线性系统最优控制的问题,避免了传统H∞鲁棒控制需要求解Hamilton-Jacobi-Isaacs(HJI)方程的问题,保证了整个滤波和控制系统的稳定性.同时还研究了误差和控制权矩阵Q和R对系统性能的影响,确保了船舶低速定位过程中的能耗最优.动力定位船舶定点定位的仿真结果验证了该方法的有效性.

In view of the characteristics of high and low frequency motion in ship dynamic locating and positioning,an inverse optimal backstepping controller is designed cascaded with a passive filter.Firstly,the nonlinear equation of the ship is established.Then,the Riccati equation corresponding to the linear equation is used to carry out the backstepping transformation of the nonlinear equation.Finally,the adaptive law and the asymptotic stable control law for disturbed environmental force without modeling are designed based on the Lyapunov function,which meets both the local cost function and global cost function.This new approach obtains a solution of the optimal control of nonlinear system in a new direction,avoids solving the Hamilton-Jacobi-Isaacs（HJI）equation in traditional H∞ controller design and simultaneously guarantees the stability of filter and controller.The influences of error and control weight matrix Qand Ron the system performance are discussed,and the optimal energy consumption during dynamic positioning of ship at slow speed is achieved.The simulation results of a dynamic locating and positioning ship show the effectiveness of this approach.