Robust H-infinity Control for Cart-Pole Systems: A Multi-Scenario Approach to Swing-Up and Stabilization

The cart-pole (C-P) system remains a classic yet challenging benchmark for nonlinear and underactuated control. This paper proposes a general and comprehensive multi-scenario H-infinity (H∞) control framework that addresses swing-up and stabilization tasks without requiring explicit switching between controllers and is readily extendable to applications such as bipedal walking. The framework is evaluated through three complementary robust control designs: (i) Gain-scheduled H∞ control via interpolation of locally linearized models, (ii) Feedback linearization combined with robust optimal control, and (iii) Adaptive approximation using orthogonal basis functions for real-time estimation of unmodeled dynamics. Simulation results at upright (θ = 0) and inverted (θ = π) positions show that the adaptive H∞ controller outperforms all others, achieving a 1.5 s settling time, 5.2% overshoot, and steady-state error below 0.01 rad. It performs much better than PID and LQR controllers. These had a slower convergence rate and caused larger cart excursions. The feedback-linearized H∞ controller also achieved strong results with a favourable balance between performance and implementation complexity. The methods suggested are confirmed by comparative analyses to provide scenarios with faster convergence, more robust performance, less control effort, and greater accuracy. These findings endorse the framework’s worthiness for real-world use in robotic balance, rehabilitation systems, and dynamic locomotion under uncertain conditions.