Intelligent robust control of inverted pendulum using hierarchical sliding mode and ELM-based estimator

Abstract

The Inverted Pendulum Cart (IPC) system is a significant challenge in control theory, is used as a benchmark for evaluating advanced actuator control techniques, and has critical applications in robotics and autonomous systems. This paper proposes a new control strategy based on a Hierarchical Non-Singular Fast Terminal Sliding Mode (HNFTSM) controller technique enhanced by an Extreme Learning Machine (ELM) neural network to achieve system stability. HNFTSM provides finite time convergence and resistance to disturbances and uncertainty, while the ELM contributes to estimating these disturbances to improve performance. The stability of this strategy is proven using the Lyapunov stability theory, which ensures that all system states reach the desired equilibrium in finite time. Furthermore, the proposed hierarchical control scheme guarantees finite-time convergence of all closed loop IPC states under bounded uncertainties. A comprehensive comparative analysis is conducted against other advanced control techniques, including HSMC, HNTSM, ELM-HNTSM, and conventional NFTSM controllers. Simulation results show that the proposed approach outperforms other methods in tracking accuracy, convergence speed, singularity avoidance, and chattering reduction, which enhances the effectiveness of system control and makes it promising for practical applications.