Switching dynamic event-triggered disturbance rejection control for uncertain Lipschitz nonlinear system using recursive observers

This paper investigates the event-triggered disturbance rejection control problem for a class of uncertain Lipschitz nonlinear systems with time-varying disturbances. The design process to address this problem involves the construction of a state and disturbance joint observer, along with the design of an event-triggered controller that incorporates a designable minimum inter-event time. To design the joint observer, time-varying disturbances are initially transformed into multiple intermediate variables by employing a linear combination of system states and disturbance derivatives. Subsequently, the recursive observers are constructed to obtain intermediate variable estimations, while the recursive mechanism is utilized to compensate for the extra derivative term arising from disturbance transformation. Then, states and disturbance estimations are used to develop the event-triggered disturbance rejection controller. The event-triggered protocol includes a mandatory resting interval and a dynamic trigger variable that monotonically increases during the resting interval, ensuring a guaranteed minimum inter-event time while also decreasing the trigger frequency. Finally, we provide numerical examples to showcase the effectiveness of the proposed method. Simulation results show that the proposed method is able to reduce the steady-state error by 59.6% and extend the minimum trigger interval by at least 2.44 times compared to existing methods.