Adaptive control of uncertain nonlinear time delay systems in the presence of actuator failures and applications to chemical reactor systems

Abstract

This paper presents an adaptive actuator failure compensation scheme for a class of uncertain nonlinear systems with unknown nonlinearities, unknown time varying delays and in the presence of time varying actuator failures. The considered actuator failure is modeled to cover both loss of effectiveness and stuck at some time varying values where the values, times and patterns of the failures are unknown. With the help of Neural Networks to approximate the unknown nonlinear functions, a novel adaptive actuator failure compensation controller is developed based on the backstepping design method. The appropriate Lyapunov–Krasovskii functionals are introduced to design new adaptive laws to compensate the unknown time varying actuator failures as well as uncertainties from unknown nonlinearities and time varying delays. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighborhood of the origin. Finally, the developed approach is applied to the control design of a chemical reactor with delayed recycle streams. The simulation results are provided to show the effectiveness of the proposed approach.