Learning Dissipative Neural Dynamical Systems
This work addresses a specific challenge in control theory and machine learning for ensuring stability in learned models, but it is incremental as it builds on existing neural dynamical systems with a novel constraint-handling approach.
The paper tackles the problem of learning neural dynamical models that approximate unknown dissipative nonlinear systems while preserving dissipativity, a hard constraint with no existing techniques. It proposes a two-stage method involving unconstrained learning followed by weight and bias perturbations, resulting in a guaranteed dissipative model that closely fits system trajectories.
Consider an unknown nonlinear dynamical system that is known to be dissipative. The objective of this paper is to learn a neural dynamical model that approximates this system, while preserving the dissipativity property in the model. In general, imposing dissipativity constraints during neural network training is a hard problem for which no known techniques exist. In this work, we address the problem of learning a dissipative neural dynamical system model in two stages. First, we learn an unconstrained neural dynamical model that closely approximates the system dynamics. Next, we derive sufficient conditions to perturb the weights of the neural dynamical model to ensure dissipativity, followed by perturbation of the biases to retain the fit of the model to the trajectories of the nonlinear system. We show that these two perturbation problems can be solved independently to obtain a neural dynamical model that is guaranteed to be dissipative while closely approximating the nonlinear system.