Learning Deep Dissipative Dynamics
This work addresses stability and robustness issues in dynamical systems for fields like robotics and fluid dynamics, offering a novel method to enforce dissipativity, though it builds on existing theoretical foundations.
The study tackled the problem of ensuring dissipativity in neural network-learned dynamical systems, which is crucial for stability and energy conservation, by proposing a differentiable projection method that strictly guarantees these properties and demonstrating its robustness in robotic and fluid dynamics applications.
This study challenges strictly guaranteeing ``dissipativity'' of a dynamical system represented by neural networks learned from given time-series data. Dissipativity is a crucial indicator for dynamical systems that generalizes stability and input-output stability, known to be valid across various systems including robotics, biological systems, and molecular dynamics. By analytically proving the general solution to the nonlinear Kalman-Yakubovich-Popov (KYP) lemma, which is the necessary and sufficient condition for dissipativity, we propose a differentiable projection that transforms any dynamics represented by neural networks into dissipative ones and a learning method for the transformed dynamics. Utilizing the generality of dissipativity, our method strictly guarantee stability, input-output stability, and energy conservation of trained dynamical systems. Finally, we demonstrate the robustness of our method against out-of-domain input through applications to robotic arms and fluid dynamics. Code is https://github.com/kojima-r/DeepDissipativeModel