The Koopman operator framework provides a new direction to the analysis and synthesis of systems with complex dynamics. This chapter provides a comprehensive review of exploiting resolvent operators for Koopman operators, also known as Koopman resolvents, with the aim of understanding complex dynamical systems and their connection to numerical methods that directly estimate the properties from data. Existing literature and open problems are also provided.

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Koopman Resolvents

  • Yoshihiko Susuki

摘要

The Koopman operator framework provides a new direction to the analysis and synthesis of systems with complex dynamics. This chapter provides a comprehensive review of exploiting resolvent operators for Koopman operators, also known as Koopman resolvents, with the aim of understanding complex dynamical systems and their connection to numerical methods that directly estimate the properties from data. Existing literature and open problems are also provided.