Learning Exactly Linearizable Deep Dynamics Models

TL;DR

This paper addresses the challenge of safely controlling nonlinear systems learned from data by introducing Exactly Linearizable (EL) models that guarantee linearization through dynamic feedback. The EL architecture uses bijective neural networks for the coordinate transformation $\Phi$, the internal input mapping $\Psi$, and a convex partially input convex network for the output map $\Xi$, enabling $\,\dot{\xi}=A\xi+Bv+c$ with a wide expressive range beyond traditional Hammerstein–Wiener models. Control is performed by solving linear-quadratic regulator (LQR) problems in the transformed coordinates and enforcing hard constraints via integral control barrier functions (I-CBF), leading to a fast, convex quadratic program (QP) at runtime. Experimental results on a high-fidelity engine simulator show that EL models yield superior predictive accuracy over S--HW, and the constraint-aware controller satisfies input/output bounds while maintaining good regulation, demonstrating practical impact for automotive control under safety constraints. Overall, the work advances learning-based control by marrying exact linearization with convex, real-time constraint handling for complex nonlinear systems.

Abstract

Research on control using models based on machine-learning methods has now shifted to the practical engineering stage. Achieving high performance and theoretically guaranteeing the safety of the system is critical for such applications. In this paper, we propose a learning method for exactly linearizable dynamical models that can easily apply various control theories to ensure stability, reliability, etc., and to provide a high degree of freedom of expression. As an example, we present a design that combines simple linear control and control barrier functions. The proposed model is employed for the real-time control of an automotive engine, and the results demonstrate good predictive performance and stable control under constraints.

Figures (9)

• Figure 1: Exactly linearizable model
• Figure 2: Network structure of exactly linearizable model
• Figure 3: Controller implementation
• Figure 4: Controller design
• Figure 5: Engine air path and combustion system

Theorems & Definitions (7)

• Definition 1
• Definition 2
• Theorem 3
• Definition 4: Ames2019
• Theorem 5: Sontag1998
• Theorem 6
• proof