Fuzzy Adaptive Fixed-time Sliding Mode Control with State Observer for A Class of High-order Mismatched Uncertain Systems

Using state observer has attracted a notable interest of researchers in control community to provide an on-line state estimator for control systems instead of measuring them physically by sensors which is costly, inaccurate, and easy to contaminate by noise. Some challenges ahead to design state observer in control systems are using estimated data by observer in the designed controller as well as the system stability analysis by using controller and observer simultaneously. This paper proposes Fuzzy Adaptive Fixed-time Sliding Mode Control (FAFSMC) technique for trajectory tracking of a class of high-order nonlinear systems with mismatched external disturbances and uncertainties. Meanwhile, the fixed-time state observer is proposed to incorporate with the controller for estimating the unmeasured even states (velocity) and providing on-line data in the controller. A proper candidate Lyapunov function is defined to verify the system global fixed-time stability by considering designed control law, state observer term, and adaptive law, simultaneously. The simulation results of three simulation examples, ship course system, two-link robotic manipulator, and three-link robotic manipulator, are carried out in Simulink/MATLAB to reveal the effectiveness of the proposed FAFSMC scheme compared with the other three conventional methods for solving trajectory tracking problem. Two performance criteria, Integral of the Square Value (ISV) and Integral of the Absolute value of the Error (IAE), are used to make a comprehensive comparison among the proposed FAFSMC method with state observer and the other three methods.