Learning Neural Network Controllers with Certified Robust Performance via Adversarial Training
This work addresses the need for certified robustness in deploying neural network controllers for nonlinear dynamical systems, representing an incremental improvement over existing methods.
The paper tackles the problem of ensuring robust performance for neural network controllers in safety-critical settings by jointly synthesizing controllers and dissipativity certificates via adversarial training, achieving certified regions up to 78 times larger than a baseline method.
Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly synthesizing NN controllers and dissipativity certificates that formally guarantee robust closed-loop performance using adversarial training, in which we use counterexamples to the robust dissipativity condition to guide training. Verification is done post-training using alpha,beta-CROWN, a branch-and-bound-based method that enables direct analysis of the nonlinear dynamical system. The proposed method uses quadratic constraints (QCs) only for characterization of non-parametric uncertainties. The method is tested in numerical experiments on maximizing the volume of the set on which a system is certified to be robustly dissipative. Our method certifies regions up to 78 times larger than the region certified by a linear matrix inequality-based approach that we derive for comparison.