UC Berkeley

Neural network controllers have shown remarkable performance in control tasks, but their deployment in safety-critical applications is hindered by a lack of formal robustness guarantees. We propose methods to synthesize and verify neural network controllers robust to both model uncertainty and exogenous disturbances. We consider robustness specifications through the framework of dissipativity, which naturally accommodates exogenous disturbances, and ensure these dissipation inequalities hold for model perturbations characterized by integral quadratic constraints (IQCs). We first propose linear matrix inequality-based methods for verifying robust dissipation inequalities, and a reinforcement learning framework that alternates learning steps with semidefinite programming to train robust neural network controllers that maximize reward. We then propose a counterexample guided training procedure for neural network controllers, paired with a branch-and-bound-based verification approach where nonlinearities are treated without IQC over-approximation and only the uncertainties are described by IQCs, reducing conservatism. Finally, we explore two facets of the problem of characterizing uncer­tainties. First, we address the problem of discrete uncertainty sets, and propose a clustering method to decompose large finite sets of perturbations into a few small sets of perturbations, for which controllers can be designed using the approaches described above. Second, to address the conservatism of quadratic multipliers for characterizing known nonlinearities, we propose integral polynomial constraints (IPCs), a natural generalization of IQCs to polynomial multipliers, and demonstrate their utility in sum of squares programming for estimating regions of attraction.