Optimal Control Method for Sliding Self‐Balancing Biased Inverted Pendulum Based on Integral Sliding Mode

ABSTRACT This study presents a novel control strategy that integrates Integral Sliding Mode Control (ISM) with the Q‐learning algorithm to address the optimal control problem of a sliding self‐balancing biased inverted pendulum system. This system is a class of continuous‐time systems characterized by external disturbances and uncertain internal dynamics. The proposed optimal control framework combines the benefits of offline reinforcement learning techniques with the high robustness inherent in integral sliding mode control. The primary objective is to design a discontinuous integral sliding mode controller that ensures the system state reaches the sliding surface within a finite time. The Q‐learning algorithm leverages offline reinforcement learning to determine the optimal gain matrix, thereby ensuring the asymptotic stability of the closed‐loop system. Furthermore, based on the Lyapunov stability theorem, a rigorous proof of the system state's ultimate boundedness is provided.