Global Bilinearization and Controllability of Control-Affine Nonlinear Systems: A Koopman Spectral Approach

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作者
Goswami, Debdipta [1 ,2 ]
Paley, Derek A. [2 ,3 ]
机构
[1] Univ Maryland, Dept Elect & Comp Engn, College Pk, MD 20742 USA
[2] Univ Maryland, Inst Syst Res, College Pk, MD 20742 USA
[3] Univ Maryland, Dept Aerosp Engn, Aerosp Engn Educ, College Pk, MD 20742 USA
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TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
This paper considers the problem of global bilinearization of the drift and control vector fields of a control-affine system. While there are linearization techniques like Carleman linearization for embedding a finite-dimensional non-linear system into an infinite-dimensional space, they depend on the analytic property of the vector fields and work only on polynomial space. The proposed method utilizes the Koopman Canonical Transform to transform the dynamics and ensures bilinearity from the projection of the Koopman operator associated with the control vector fields on the eigenspace of the drift Koopman operator. The resulting bilinear system is then subjected to controllability analysis using the Myhill semigroup method and Lie algebraic structures. The results are supported by a numerical example.
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页数:6
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