Uniform synchronization for chaotic systems via event‐triggered aperiodic intermittent control

Abstract

AbstractThis paper studies the uniform synchronization for chaotic systems via event‐triggered aperiodic intermittent control (E‐APIC). A synchronization scheme via E‐APIC is proposed for master‐slave chaotic systems. Based on the error state and three indices of threshold‐value, check‐period, and control‐free index, E‐APIC is designed and the synchronization is achieved by such an E‐APIC. Also, a simplified E‐APIC is derived by letting the control‐free index trend to zero. With respect to the uncertainties, the simplified E‐APIC is strengthened to be robust for the uniform synchronization. Moreover, in order to compare with the synchronization schemes via periodic intermittent control (PIC), time‐based aperiodic intermittent control (T‐APIC), and event‐triggered impulsive control (ETIC), criteria of synchronization via PIC and T‐APIC and the scheme of ETIC are given respectively. And by using the same control width, the theoretical results on rate of control (RoC) and number of control (NoC) are derived respectively and show that E‐APIC has less RoC and NoC than both PIC and T‐APIC. The chaotic Chua's system is used to test the uniform synchronization via PIC, T‐APIC, E‐APIC, and ETIC. The numerical simulations show that E‐APIC has better performances on aspects of NoC, RoC, cost, and average non‐control width than PIC, T‐APIC, and ETIC.