Toward Improving the Distributional Robustness of Risk-Aware Controllers in Learning-Enabled Environments

This paper is concerned with designing a risk-aware controller in an unknown and dynamic environment. In our method, the evolution of the environment state is learned using observational data via Gaussian process regression (GPR). Unfortunately, these learning results provide imperfect distribution information about the environment. To address such distribution errors, we propose a risk-constrained model predictive control (MPC) method that exploits techniques from modern distributionally robust optimization (DRO). To resolve the infinite dimensionality issue inherent in DRO, we derive a tractable semidefinite programming (SDP) problem that upper-bounds the original MPC problem. Furthermore, the SDP problem is reduced to a quadratic program when the constraint function has a decomposable form. The performance and the utility of our method are demonstrated through an autonomous driving problem, and the results show that our controller preserves safety despite errors in learning the behaviors of surrounding vehicles.