Efficient ODE Substructure Identification of the Acrobot under Partial Observability using Neural Networks and Direct Multiple Shooting

Abstract

Motion control and automation can benefit from models that accurately predict the behavior of mechatronic systems to enhance efficiency and performance. Uncertain nonlinear physical phenomena however hinder to fully capture the system behavior with classical physics-based models. The emerging availability of data has caused a surge in the use of data-driven techniques, yet it is expensive to acquire a sufficiently rich data-set of a given system. This paper presents a hybrid model that integrates physical laws, in the form of ordinary differential equations (ODE), and neural network layers, as the unknown ODE substructures, for uncertain mechatronic systems. We focus to enhance the hybrid model’s predictive capabilities for systems that are subject to multiple unknown phenomena and partial state observations. To discover these unknown dynamics we use the framework of direct multiple shooting. This allows to formulate the problem of aligning observed time-series with model responses as a constrained optimization problem. Furthermore, this formulation allows to deal with incomplete state observations, which would otherwise be unattainable with classical approaches. We apply and validate the proposed methodology to identify the friction in both joints of an acrobot of which only measurements in one joint are available. Numerical experiments show that our model can discover detailed representations of the friction characteristics in both joints and has accurate multistep predictive capabilities.