Event-Triggered Integral Sliding Mode Optimal Control of the Linear Systems with Uncertainties Based on LQR Control

This paper presents an event-triggered integral sliding mode control (EISMC) scheme aimed at solving the optimal control problem in linear systems. Initially, a linear quadratic regulator (LQR) controller is developed to achieve optimal control. Subsequently, we propose the EISM controller, which effectively addresses disturbances and system uncertainties while ensuring that the system remains in an optimal control state at all times. The EISM controller enhances both control accuracy and the frequency of updates, significantly reducing energy consumption. Additionally, we establish a lower bound for the event-triggered time interval to prevent zero behavior. Finally, we illustrate the effectiveness of our approach through simulation examples.