Stabilization of ODE with hyperbolic equation actuator subject to boundarycontrol matched disturbance

Abstract

In this paper, we consider stabilisation for a cascade of ODE and first-order hyperbolic equation withexternal disturbance flowing to the control end. The active disturbance rejection control (ADRC) andsliding mode control (SMC) approaches are adopted in investigation. By ADRC approach, the distur-bance is estimated through a disturbance estimator with both time-varying high gain and constanthigh gain, and the disturbance is canceled online in the feedback loop. It is shown that the resultingclosed-loop system with time-varying high gain is asymptotically stable and is practically stable withconstant high gain. By SMC approach, the existence and uniqueness of the solution for the closedloop via SMC are proved, and the monotonicity of the ‘reaching condition’ is presented. The resultingclosed-loop system is shown to be exponentially stable. The numerical experiments are carried outto illustrate effectiveness of the proposed control law.