Stability Margins of Neural Network Controllers
This work addresses the need for certifiable stability in neural network controllers for control systems, providing a method to enforce disk margins during training.
The paper presents a training method for neural network controllers that guarantees disk margin stability for linear time-invariant plants with uncertainties and nonlinearities described by integral quadratic constraints. The method alternates between reward maximization and a semidefinite programming projection step to enforce the stability margin.
We present a method to train neural network controllers with guaranteed stability margins. The method is applicable to linear time-invariant plants interconnected with uncertainties and nonlinearities that are described by integral quadratic constraints. The type of stability margin we consider is the disk margin. Our training method alternates between a training step to maximize reward and a stability margin-enforcing step. In the stability margin enforcing-step, we solve a semidefinite program to project the controller into the set of controllers for which we can certify the desired disk margin.