Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control

• URL: http://arxiv.org/abs/2509.19869v1
• Date: Wed, 24 Sep 2025 08:15:26 GMT
• Title: Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control
• Authors: Teruki Kato, Ryotaro Shima, Kenji Kashima,
• Abstract summary: Deep learning is increasingly used for enforce physical systems or systems where first-principles modeling is difficult.<n>We develop a new type of deep learning model that satisfies constraints on Jacobian entries--that monotonicity, and sign-definite positivity.<n>On a two-tank system hybrid, the proposed approach improves control inputs than existing methods.
• Score: 1.9116784879310027
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Deep learning is increasingly used for complex, large-scale systems where first-principles modeling is difficult. However, standard deep learning models often fail to enforce physical structure or preserve convexity in downstream control, leading to physically inconsistent predictions and discontinuous inputs owing to nonconvexity. We introduce sign constraints--sign restrictions on Jacobian entries--that unify monotonicity, positivity, and sign-definiteness; additionally, we develop model-construction methods that enforce them, together with a control-synthesis procedure. In particular, we design exactly linearizable deep models satisfying these constraints and formulate model predictive control as a convex quadratic program, which yields a unique optimizer and a Lipschitz continuous control law. On a two-tank system and a hybrid powertrain, the proposed approach improves prediction accuracy and produces smoother control inputs than existing methods.

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