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.