Real-time optimal control with shallow recurrent decoder networks

Matteo Tomasetto, Andrea Manzoni, J. Nathan Kutz

Keywords: optimal control problems, shallow recurrent decoder networks, reduced order modeling, sparse sensing, imitation learning

TL;DR: In this work, we employ SHallow REcurrent Decoder networks-based Reduced Order Modeling to control high-dimensional and parametric dynamics in real-time, relying solely on limited sensors monitoring the state evolution

Abstract: Controlling dynamical systems in real-time across multiple scenarios is critical to enable adaptive control strategies, ensuring stability and efficiency. However, parametric optimal control problems require several system simulations to tailor optimal actions in response to varying scenarios, which are often computationally demanding -- or even intractable -- due to the high-dimensionality of spatio-temporal dynamics. In this work, we exploit SHallow REcurrent Decoder networks-based Reduced Order Modeling (SHRED-ROM) to synthesize a real-time policy for high-dimensional and parametric dynamics, relying solely on limited state sensor readings. After training the model on few optimal examples given by an expert demonstrator, as typically considered in imitation learning, SHRED-ROM mimics the expert behavior with effective distributed control actions in real-time and in new scenarios, mitigating the curse of dimensionality. The performance of the proposed policy is finally assessed on a challenging density control test case.

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Submission Number: 31