Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control
This work addresses the challenge of ensuring physical consistency and convexity in deep learning-based control for complex systems like hybrid powertrains, representing an incremental improvement over prior methods.
The paper tackled the problem of deep learning models failing to enforce physical structure and convexity in control applications, resulting in inconsistent predictions and discontinuous inputs. The result was a method that improved prediction accuracy and produced smoother control inputs on a two-tank system and a hybrid powertrain compared to existing methods.
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.