Hybrid controller based on data and physical modeling using Neural ODE networks

Combining model-based (MB) and data-based (DB) techniques can offer significant benefits in control system design. However, achieving high performance requires a robust and efficient hybridization (MB+DB). A well-designed hybrid controller with these characteristics can be particularly advantageous for systems with only partial physical knowledge. Another motivation for this hybrid approach is the rapid advancement of AI, which enables high efficiency and diverse modeling possibilities. In this paper, we propose an adaptation of neural ODEs to incorporate prior physical dynamics. Specifically, during the forward phase, the system's physical model is propagated in parallel with a neural ODE network, while, in the backward phase, the network's training mechanism is adjusted to account for the prior dynamics; thus, using the ODE solver and the adjoint method naturally fuses the ODE equations of the prior physics and the network. This approach has broad applicability, and, in this article, it is used to design and train both a system identifier and a neuro-controller, demonstrating strong performance in modeling and tracking, when compared with a tuned classical PID controller in the benchmark tasks (see section 5.2), the proposed controller achieves reductions exceeding 75% in both settling time and maximum control effort, meanwhile, the learning process consistently converges from multiple initial conditions within reduced training iterations. These results highlight the effectiveness of the proposed hybrid Neural ODE framework as a general and efficient solution for control problems involving limited physical insight and available data, respectively. The proposed method can be applied to various common control challenges involving partial knowledge of system dynamics and available data.