Adaptive Fixed-Time Control of Chaotic Systems Based on Dynamic Surface Technique

This article investigates the chaotic suppression problem of a chaotic system with uncertain parameters. To solve this problem, a dynamic surface constructed based on the adaptive backstepping control method is considered. First, a novel dynamic surface is introduced in the controller design process, which is utilized to alleviate the 'complexity explosion' problem of classical backstepping. Then, piecewise functions are used to avoid the singularity of virtual controllers and real controllers, and the proposed control scheme can achieve state stabilization of chaotic systems based on the fixed-time theory. The results indicate that the chaotic state can converge to a small neighborhood near the origin. Finally, simulations are used to verify the validity of the proposed approach, and the control scheme is applied to a permanent magnet synchronous motor (PMSM) and suppresses its chaotic behavior.