Koopman-Based Optimal Tracking Control of Nonlinear Dynamical Systems
作者单位：School of IoT EngineeringJiangnan University Wuxi Institute of Technology
会议名称：《第40届中国控制会议》
会议日期：2021年
学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070104[理学-应用数学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程]
关 键 词：Koopman operator data-driven control dynamical mode decomposition deep neural network linear quadratic tracking control
摘 要：A data-driven procedure to approximate the Koopman operator is a leading technology in researching the properties of nonlinear dynamical systems. The Koopman operator is an infinite-dimensional linear operator that can be used to predict and control a nonlinear system in a linear manner. In this paper, the reformulation and control problems of complex nonlinear dynamical systems are explored. The extended dynamical mode decomposition method and the deep neural network method are applied, respectively, to obtain a finite approximation of the Koopman operator. Then, we present Koopman-based optimal tracking controller for nonlinear dynamical systems by using the linear quadratic tracking control strategy. Finally, simulation results demonstrate that the linear embedding of nonlinear systems by data-driven procedure can approximate the states of the nonlinear systems and the desired output of nonlinear systems can be optimally tracked based on the designed controller of the linear embedding system.