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arXiv · 2507.14455

Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking

Chun-Ming Yang·Pranav A. Bhounsule
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Abstract

Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear state space system using this approach as long as its behavior is consistent in modes and timings. We extend time-delay embeddings to generate a linear model of two periodic hybrid systems: the bouncing pendulum and the simplest walker with control inputs. This leads to a state history augmented linear quadratic regulator (LQR) which uses current and past state history for feedback control. Example code can be found at https://github.com/Chun-MingYang/koopman-timeDelay-lqr.git

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Chun-Ming Yang, Pranav A. Bhounsule. 2025-07-19. Koopman Operator Based Time-Delay Embeddings and State History Augmented LQR for Periodic Hybrid Systems: Bouncing Pendulum and Bipedal Walking. https://arxiv.org/abs/2507.14455

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