<p>This paper proposes a novel robust optimal control strategy for a two-wheeled inverted pendulum (TWIP) system to achieve accurate tracking of both longitudinal and yaw velocities while significantly enhancing robustness and reducing energy consumption. The core innovation of this study lies in overcoming the inherent limitations of hierarchical sliding mode control (HSMC), off-policy adaptive dynamic programming (ADP) within a zero-sum game, and a high-order disturbance observer (HODO). This is achieved through a synergistic combination of these three methodologies, leveraging their mutual compensation to formulate a consistent and robust control strategy. Specifically, rather than relying on a traditional switching control law, the proposed approach utilizes the ADP framework to derive robust optimal reaching and yaw control laws. Furthermore, to ensure strict robustness against model uncertainties and external disturbances, the HODO—designed based on the linearized TWIP dynamics—is incorporated for active disturbance compensation. This novel combination not only enhances overall system stability but also significantly reduces energy consumption. The practical feasibility and effectiveness of the proposed strategy are validated through real-time experiments on a physical TWIP platform. Experimental results demonstrate that the proposed method significantly outperforms traditional HSMC and linear quadratic regulator (LQR) approaches in terms of dual-motion velocity tracking accuracy, chattering suppression, and energy efficiency.</p>