Caputo Derivative-Based FTC Design and Sensor Fault Estimation for Lipschitz Fractional Nonlinear Systems

Abstract

Sensor fault estimation and active fault-tolerant control (FTC) are still important problems for guaranteeing the fractional-order nonlinear systems' (FONS) stability under sensor faults. To deal with this problem, this work uses the Caputo fractional derivative framework to construct a unified strategy for simultaneous sensor fault estimation and active (FTC). Sufficient conditions obtained are in the form of linear matrix inequalities (LMIs) from a stability study based on Lyapunov theory. The proposed  approach is applied to a two-state system with a biased sensor fault to demonstrate its performance. The simulation results indicate that the adaptive observer can accurately estimate the fault magnitude and has robust tracking ability with large initial estimation errors. Moreover, the fault tolerant controller is capable of stabilizing the system successfully with zero steady state error and without any overshoot.