Physics-informed deep Koopman operator for Lagrangian dynamic systems

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外文摘要：Accurate mechanical system models are crucial for safe and stable control.Unlike linear systems,Lagrangian systems are highly nonlinear and difficult to optimize because of their unknown system model.Recent research thus used deep neural networks to generate linear models of original systems by mapping nonlinear dynamic systems into a linear space with a Koopman observable function encoder.The controller then relies on the Koopman linear model.However,without physical information constraints,ensuring con-trol consistency between the original nonlinear system and the Koopman system is tough,as the learning process of the Koopman observation function is unsupervised.This paper thus proposes a two-stage learning algorithm that uses structural subnetworks to build a physics-informed network topology to simultaneously learn the Koopman observable functions and the system energy representation.In the Koopman matrix learning session,a quadratic-constrained optimization problem is solved to ensure that the Koopman rep-resentation satisfies the energy difference matching hard constraint.The proposed energy-preserving deep Lagrangian Koopman(EPDLK)framework effectively represents the dynamics of the Lagrangian system while ensuring control consistency.The effectiveness of EPDLK is compared with those of various Koopman observable function construction methods in multistep prediction and trajectory tracking tasks.EPDLK achieves better control consistency by guaranteeing energy difference matching,which facilitates the appli-cation of the control law generated on the Koopman system directly to the original nonlinear Lagrangian system.

外文关键词：

Koopman operatorLagrangianphysics-informednonlinearmodel predictive control(MPC)

作者：

Xuefeng WANG、Yang CAO、Shaofeng CHEN、Yu KANG

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作者单位：

Department of Automation,University of Science and Technology of China,Hefei 230027,China

State Key Laboratory of Fire Science,University of Science and Technology of China,Hefei 230027,China

Institute of Advanced Technology,University of Science and Technology of China,Hefei 230027,China

基金：

National Natural Science Foundation of ChinaChina Postdoctoral Science FoundationFundamental Research Funds for the Central Universities

项目编号：

620330122023M733384WK2100000044

出版年：

2024

DOI：

10.1007/s11432-022-4050-4

中国科学:信息科学(英文版)

中国科学院

中国科学:信息科学(英文版)

CSTPCDEI

影响因子：0.715

ISSN：1674-733X

年,卷(期)：2024.67(9)