Event-based model predictive control of discrete-time non-linear systems with external disturbances

The event-based model predictive control (MPC) problem for discrete-time non-linear control systems with external disturbances is studied. Two triggering conditions are designed based on whether the system state is within the terminal region or not. The first one is triggered outside the terminal region when the difference between the actual system state trajectory and the corresponding optimal state trajectory violates a relative threshold, while the second one is triggered inside the terminal region if the difference between the actual system state trajectory and the predicted nominal state trajectory violates a desired relative threshold. The feasibility analysis and stability analysis are given in detail. Sufficient conditions for feasibility relating to the triggering threshold and disturbance bound are obtained. Sufficient conditions for stability of the event-based control system referring to system parameters, triggering threshold and disturbance bound are given. Besides, the upper bound of the state trajectory is obtained and a robust invariant set that the system state will enter in finite time is given. Finally, simulation examples are given to validate the effectiveness of the proposed method.