A high gain free extended state observer to output feedback stabilization of one-dimensional unstable wave equation

The most key component toward an emerging control technology known as active disturbance rejection control is the extended state observer (ESO) which is a systematic design to realize total disturbance estimation via observable measured output. There are, however, two limitations in design of ESO: a) the high gain must be resorted, and closely with b) the derivative of total disturbance is necessarily supposed to be bounded. Since high gain is highly critical to engineers and we can find sporadically estimation/cancellation strategy in other control method like adaptive control and internal model principle, there exists space to relax these two limitations in ESO. In this paper, we demonstrate for the first time an online disturbance estimation by designing a completely different infinite-dimensional disturbance estimator for an unstable wave equation. This disturbance estimator is completely different from the existing ones and as a result, we are able to design a new extended state observer (ESO) where the two limitations aforementioned are released. An ESO based stabilizing output feedback is then designed. It is shown that the closed-loop system is asymptotically stable and all subsystems involved are guaranteed to be bounded. The numerical simulations are presented to illustrate the effective of the proposed scheme.