$\mathcal{L}_1$-Certified Distributionally Robust Planning for Safety-Constrained Adaptive Control
This addresses safety-critical control for autonomous systems, representing an incremental advance through integration of existing methods.
The paper tackles the problem of ensuring safe operation of autonomous systems under simultaneous model and environmental uncertainty by proposing a hierarchical framework that integrates distributionally robust model predictive control with L1-adaptive control, achieving certifiable safety with tractable reformulations.
Safe operation of autonomous systems requires robustness to both model uncertainty and uncertainty in the environment. We propose a hierarchical framework for stochastic nonlinear systems that integrates distributionally robust model predictive control (DR-MPC) with $\mathcal{L}_1$-adaptive control. The key idea is to use the $\mathcal{L}_1$ adaptive controller's online distributional certificates that bound the Wasserstein distance between nominal and true state distributions, thereby certifying the ambiguity sets used for planning without requiring distribution samples. Environment uncertainty is captured via data-driven ambiguity sets constructed from finite samples. These are incorporated into a DR-MPC planner enforcing distributionally robust chance constraints over a receding horizon. Using Wasserstein duality, the resulting problem admits tractable reformulations and a sample-based implementation. We show theoretically and via numerical experimentation that our framework ensures certifiable safety in the presence of simultaneous system and environment uncertainties.