Observer‐Based Coupling‐Coordinated Adaptive Hierarchical Sliding Mode Control for Underactuated Nonlinear Systems

ABSTRACT This paper proposes an observer‐based coupling‐coordinated adaptive hierarchical sliding mode control (CCAHSMC‐LSMO) framework for underactuated nonlinear systems. Addressing limitations in conventional methods, the design explicitly incorporates natural coupling between state variables in the first‐layer manifold. An adaptive moving sliding manifold adjusts slope values for faster convergence, while a variable switching gain balances robustness and chattering reduction. Furthermore, an LMI‐based Luenberger sliding mode observer ensures accurate state estimation under measurement noise. Stability is rigorously proven using Lyapunov theory. Simulations on a rotary inverted pendulum demonstrate the method's superiority over conventional aggregated hierarchical sliding mode control. Quantitative results indicate significant improvements, including 26% reduction in tracking errors, 50% faster settling time and 81% reduction in control effort under measurement noise. The framework effectively handles matched and unmatched disturbances, time‐varying parameters and multiplicative uncertainties. This integrated solution offers a practical and robust approach for complex underactuated systems, ensuring improved transient performance and reduced chattering without compromising stability.