Distributionally Robust Planning with $\mathcal{L}_1$ Adaptive Control

TL;DR

This paper introduces DRP-$ ext{L}_1$AC, a hierarchical control framework combining adaptive control and distributionally robust planning to ensure safe autonomous operation under uncertainty.

Contribution

It develops a novel integration of $ ext{L}_1$-adaptive control with distributionally robust MPC using Wasserstein ambiguity sets, enabling certifiable safety without distribution samples.

Findings

Framework guarantees safety under combined uncertainties.

Uses Wasserstein duality for tractable reformulations.

Numerical experiments validate safety guarantees.

Abstract

Safe operation of autonomous systems requires robustness to both model uncertainty and uncertainty in the environment. We propose DRP-$\mathcal{L}_1$AC, 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. Environmental 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 environmental uncertainties.