Koopman-Based Feedback Design With Stability Guarantees

2024/07/09 by Robin Strässer, Manuel Schaller, Karl Worthmann +2 · 12 citations
Engineering · #Control Systems and Identification #Advanced Control Systems Optimization

paper · doi:10.1109/tac.2024.3425770

Abstract

We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for approximation errors due to finitely many data samples. To simplify practical usage across various applications, we provide a tutorial-style exposition of the feedback design and its stability guarantees for single-input systems. Moreover, we extend this controller design to multi-input systems and more flexible nonlinear state-feedback controllers using gain-scheduling techniques to increase the guaranteed region of attraction. As the proposed controller design is framed as a semidefinite program, it allows for an efficient solution. Further, we enhance the geometry of the region of attraction through a heuristic algorithm that establishes a connection between the employed Koopman lifting and the dynamics of the system. Finally, we validate the proposed feedback design procedure by means of numerical examples.

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• Two Roads to Koopman Operator Theory for Control: Infinite Input Sequences and Operator Families
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