1. Koopman Linear Quadratic Regulator Using Complex Eigenfunctions for Nonlinear Dynamical Systems.
- Author
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Gibson, Andrew J., Calvisi, Michael L., and Yee, Xin C.
- Subjects
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NONLINEAR dynamical systems , *EIGENFUNCTIONS , *VECTOR spaces , *NONLINEAR oscillators , *OPERATOR theory , *FUNCTION spaces , *LINEAR dynamical systems - Abstract
Koopman operator theory has gained interest in the past decade as a framework for rigorously transforming nonlinear dynamics on the state space into linear dynamics on Koopman-invariant function spaces. These Koopman-invariant spaces can be approximated purely through data-driven methodologies, which then enables future state prediction and the application of classical linear control to strongly nonlinear systems. Recently in literature, the linear quadratic regulator (LQR) was developed for systems represented through eigenfunctions of the Koopman operator. However, the controller was limited to using real-valued eigenfunctions for conservative systems. In this paper, we extend the Koopman LQR framework to use multiple complex eigenfunctions. We illustrate in several examples that our proposed extension enables Koopman LQR to control dissipative systems and to drive different nonlinear oscillators to stabilize at nonequilibrium points and follow arbitrarily prescribed targets, which was not possible using a single real-valued Koopman eigenfunction. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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