Negative Imaginary Neural ODEs: Learning to Control Mechanical Systems with Stability Guarantees
This work addresses control stability for mechanical systems, offering a novel neural method with guarantees, though it appears incremental as it builds on existing NI theory and neural ODE frameworks.
The authors tackled the problem of stabilizing mechanical systems by proposing a negative imaginary neural ODE (NINODE) controller that ensures asymptotic stability under certain conditions, demonstrated through an example with a nonlinear mass-spring system.
We propose a neural control method to provide guaranteed stabilization for mechanical systems using a novel negative imaginary neural ordinary differential equation (NINODE) controller. Specifically, we employ neural networks with desired properties as state-space function matrices within a Hamiltonian framework to ensure the system possesses the NI property. This NINODE system can serve as a controller that asymptotically stabilizes an NI plant under certain conditions. For mechanical plants with colocated force actuators and position sensors, we demonstrate that all the conditions required for stability can be translated into regularity constraints on the neural networks used in the controller. We illustrate the utility, effectiveness, and stability guarantees of the NINODE controller through an example involving a nonlinear mass-spring system.