Optimal event-triggered sliding mode control for discrete-time non-linear systems against actuator saturation

This study investigates the optimal event-triggered sliding mode control (SMC) problem for discrete-time non-linear systems with actuator saturation. A differential-type sliding surface function outperforming the traditional linear version is constructed for the considered system. In order to save the communication resource, a state-dependent event-triggered scheme is designed to determine whether the current state should be transmitted or not automatically. An optimal version is designed to further decrease the computational cost. A Jacobian matrix is introduced to handle the non-linear function error resulting from the implementation of the event-triggered scheme. Combining the above techniques and the Lyapunov stable theory, time-dependent sufficient conditions are developed to guarantee that the sliding mode dynamics are stable and satisfy the desired disturbance attenuation performance. Moreover, time-independent sufficient criteria are presented to obtain the desired performance of the sliding mode dynamics by employing some inequalities. Based on the derived time-independent conditions, sufficient conditions are provided to compute the gain for the sliding surface. A sliding mode controller with adaptive law is designed to guarantee that the trajectories of the saturated control system can be driven onto the predefined sliding manifold. Finally, simulation results are given to illustrate the effectiveness of the proposed control strategy.