Disturbance rejection approaches of Korteweg–de Vries-Burgers equation under event-triggering mechanism

• Published in: Automatica (Oxford) Vol. 169; p. 111844
• Main Authors: Kang, Wen, Zhang, Jing, Wang, Jun-Min
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2024
• Subjects: ADRC; DOBC; Event-triggering mechanism; Korteweg–de Vries-Burgers equation; Korteweg–de Vries-Burgers equation; ADRC; DOBC; Event-triggering mechanism
• ISSN: 0005-1098
• DOI: 10.1016/j.automatica.2024.111844

In this paper, disturbance rejection approaches are suggested to stabilize Korteweg–de Vries–Burgers (KdVB) equation under the averaged measurements. Here two approaches—active disturbance rejection control (ADRC) and disturbance observer-based control (DOBC), are introduced to reject the external unknown disturbance actively. The main challenging issue is to design the effective extended state observer (ESO)/disturbance observer (DO) for KdVB equation respectively. As for ADRC strategy, the disturbance is rejected on the basis of an ESO. As for DOBC strategy, a DO is constructed to estimate the disturbance formulated by an exogenous system. Continuous-time and event-triggered anti-disturbance controllers are further presented for distributed stabilization of KdVB system. To significantly reduce the amount of control updates, an event-triggering mechanism is utilized and the Zeno behaviour is avoided. Sufficient stability conditions are established via Lyapunov functional method. The effectiveness of proposed approaches is verified by simulation results.