Design of Linear Matrix Inequality-Based Adaptive Barrier Global Sliding Mode Fault Tolerant Control for Uncertain Systems with Faulty Actuators

Abstract

This paper proposes a linear matrix inequality (LMI)-based adaptive barrier global sliding mode control (ABGSMC) for uncertain systems with faulty actuators. The proposed approach is derived using a novel global nonlinear sliding surface to guarantee the global dynamic property and to ensure system stability and the occurrence of sliding in the presence of actuator faults. The optimal coefficients of the sliding surface are determined using the LMI method. The system’s asymptotic stability is proven using Lyapunov theory. Additionally, an adaptive barrier function is considered to ensure the convergence of the output variables to a predefined locality of zero in a limited time, even where external disturbances and actuator faults are present. In order to decrease the steepness of the control action and mitigate the chattering phenomenon, the hyperbolic tangent function is employed instead of the signum function in the sliding mode control. The proposed method is validated using a simulation study of the Genesio’s chaotic system.