We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of robust stability can be obtained based on a proposed semidefinite programming feasibility problem. The method is able to certify a large set of stabilizing controllers by exploiting problem-specific structures; furthermore, we analyze and establish its (non)conservatism. Empirical evaluations on two decentralized control tasks, namely multi-flight formation and power system frequency regulation, demonstrate that the reinforcement learning agents can have high performance within the stability-certified parameter space, and also exhibit stable learning behaviors in the long run.
@article{arxiv.1810.11505,
title = {Stability-certified reinforcement learning: A control-theoretic perspective},
author = {Ming Jin and Javad Lavaei},
journal= {arXiv preprint arXiv:1810.11505},
year = {2018}
}