Stabilisation of unstable cascaded heat partial differential equation system subject to boundary disturbance

What is it about?

In this paper, we consider boundary stabilization for a cascade of unstable heat PDE systems with interconnection at one end and general external disturbance at the control end. An unknown input type observer is first designed by sliding mode control method to estimate the state, and its Filippov type solution is determined. To design an output feedback, we need to know a state feedback which could be realized by the backstepping transformation. The transformation transforms the system into an equivalent target system where the governing equations are stable. To deal with the disturbance, we apply the active disturbance rejection control to estimate the disturbance by output. Based on observer and disturbance estimator, an output feedback control is then designed. The existence of solution to the closed-loop system is proved and the stability is concluded. Finally, some numerical simulations are presented for illustration.

Featured Image