基于改进Koopman算子在线预估器的海洋浮体路径跟踪预测控制算法  

Path-following predictive control of marine floating body based on online predictor of Koopman operator

作　　者：丁博文 付东飞[1] 金志豪 黎明[1,2] DING Bo-wen;FU Dong-fei;JIN Zhi-hao;LI Ming(College of Engineering,Ocean University of China,Qingdao 266404,China;Institution of Marine Engineering and Technological Innovation,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国海洋大学工程学院,山东青岛266404 [2]中国海洋大学海洋工程与技术创新研究院,山东青岛266100

出　　处：《控制与决策》2025年第3期863-870,共8页Control and Decision

基　　金：山东省自然科学基金项目(ZR2022MF280).

摘　　要：针对具有强非线性动力学特性的海洋浮体路径跟踪问题,提出基于改进Koopman算子在线预估器的模型预测控制(MPC)算法.在算子可观测函数中引入状态时延变量与状态导数,将浮体动态系统提升到希尔伯特空间,使其高维线性化模型包含更多系统模态.据此提出基于Koopman算子的线性预估器,该数据驱动方法通过在提升空间中解决最小二乘问题,对系统的输入-输出数据进行非线性变换.将扩展动态模式分解得到的线性模型作为MPC控制器的内模,以此方式设计的MPC优化问题与一般线性动态系统的MPC优化问题具有相同的计算复杂度.此外,既可以以线性的方式对状态和控制输入施加线性不等式约束,也可以施加源自海洋浮体动态特性的非线性约束.为了减少计算时间,在线预测器采用增量更新策略.将所提出控制方案应用于海洋浮体的路径跟踪控制,并通过仿真实验验证其有效性.To tackle the path-following problem of marine floating bodies with strong nonlinear dynamics,this paper proposes a model predictive control(MPC)scheme based on an online predictor using Koopman operator learning.By introducing delayed states and corresponding derivatives into the observable function,the system dynamics are lifted to Hilbert space,where the linear model of marine floating body is more accurate.Thereby,a linear predictor is designed based on the Koopman operator,in which this data-driven approach relies on nonlinear transformation of system inputoutput measurements by solving the least squares problem in the lifting space.Then,the linear model obtained from the extended dynamic mode decomposition is used as the internal model of the MPC controller.Therefore,the MPC optimization problem designed in this way has the same computational complexity as the one in the linear MPC scenario.Moreover,both linear inequality constraints and nonlinear constraints arising from the dynamic characteristics of marine floating bodies can be imposed in a linear manner on the state and control inputs.To reduce computation time,an incremental update strategy is used by the online predictor.The proposed control scheme is applied to the pathfollowing of a marine floating body,and extensive experiments are conducted to verify its effectiveness.

关 键 词：海洋浮体 Koopman算子 模型预测控制 路径跟踪 扩展动态模式分解 增量更新 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]