Generalized Momenta-Based Koopman Formalism for Robust Control of Euler-Lagrangian Systems
Rajpal Singh, Aditya Singh, Chidre Shravista Kashyap, Jishnu Keshavan
AI summary
Problem
Conventional Koopman modeling of Euler-Lagrangian systems relies on explicit position-velocity states, which forces computationally expensive bilinear formulations, demands large datasets, and complicates integration with linear controllers.
Approach
The authors reformulate Euler-Lagrangian dynamics using generalized positions and momenta to decouple control inputs from nonlinear state dependencies, enabling the learning of only passive dynamics via tailored neural networks and integrating a linear observer for real-time disturbance compensation.
Key results
- Decoupling control from state-dependent dynamics via momentum-based representation to enable efficient linear Koopman models
- Learning only passive dynamics to drastically reduce trainable parameters and improve data efficiency
- Dual neural architectures enabling flexible embedding learning from actuated or unactuated data
- Linear GESO integration with MPC for real-time disturbance estimation and compensation
Why it matters
It provides a scalable, data-efficient, and robust pathway for learning-based control of complex robotic systems, directly benefiting researchers and engineers developing model predictive controllers for nonlinear dynamics.
Abstract
This paper presents a novel Koopman operator formulation for Euler–Lagrangian dynamics that employs an implicit generalized momentum-based state space representa- tion, which decouples a known linear actuation channel from state-dependent dynamics and makes the system more amenable to linear Koopman modeling. By leveraging this structural separation, the proposed formulation only requires to learn the unactuated dynamics rather than the complete actuation- dependent system, thereby significantly reducing the number of learnable parameters, improving data efficiency, and lowering overall model complexity. In contrast, conventional explicit formulations inherently couple inputs with the state-dependent terms in a nonlinear manner, making them more suitable for bilinear Koopman models, which are more computationally expensive to train and deploy. Notably, the proposed scheme enables the formulation of linear models that achieve superior prediction performance compared to conventional bilinear mod- els while remaining substantially more efficient. To realize this framework, we present two neural network architectures that construct Koopman embeddings from actuated or unactuated data, enabling flexible and efficient modeling across different tasks. Robustness is ensured through the integration of a linear Generalized Extended State Observer (GESO), which explicitly estimates disturbances and compensates for them in real-time. The combined momentum-based Koopman and GESO frame- work is validated through comprehensive trajectory tracking simulations and experiments on robotic manipulators, demon- strating superior accuracy, robustness, and learning efficiency relative to state-of-the-art alternatives.