Robust adaptive control is vital for keeping robots safe while actively reducing uncertainty in unfamiliar settings. However, traditional methods are often conservative since they fail to account for guaranteed future parameter learning during planning and struggle to scale to high-dimensional systems. In this work, we present A-SLS, a learning-aware robust adaptive model predictive control (RAMPC) framework based on system-level synthesis. A-SLS forecasts future parameter uncertainty and preserves correlations between process disturbances, parameter error, and estimate updates to construct tight, guaranteed reachable sets that account for future information gain. We also develop a GPU-accelerated A-SLS solver to enable real-time performance. Across nonlinear robotic systems, A-SLS reduces reachable-tube conservativeness, maintains real-time performance, and scales to whole-body control for a quadruped with 61 states, 8 uncertain parameters, and 12 control inputs. We further demonstrate the approach on hardware, where a physical Crazyflie drone learns an uncertain dynamics parameter online to stabilize on the fly.

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