Periodic Event-Triggered Sub-Optimal LQR Control of Disturbed System with a Dynamic Threshold Algorithm

This paper develops a periodic dynamic event-triggered suboptimal control method for continuous-time linear disturbed systems. Contrary to the continuous monitoring of trigger conditions in optimal event trigger control, this method can adjust the trigger difficulty at fixed intervals to improve information utilization, thereby reducing the relative error between the optimal cost and the sub-optimal cost. Firstly, the control gain is determined by employing the algebraic Riccati equation based on the disturbed system. Subsequently, a periodic dynamic event triggered mechanism is proposed to achieve sub-optimization, which is only evaluated at a fixed sampling period. Then, the selected interval of the sampling period is established based on the continuous form of the trigger mechanism. Furthermore, while ensuring the stability of the closed-loop system, the mathematical relationship between the suboptimal cost and the optimal cost is analyzed. Finally, the effectiveness of this approach is validated through simulations conducted on an electric vehicle charging system.