Stabilization of serially connected hybrid PDE–ODE system with unknown external disturbances

ABSTRACT

The anti-disturbance stabilization problem of a kind of serially connected hybrid PDE–ODE system is considered. The system is constituted by n wave equations with n point masses at joint nodes and the free end, where the unknown disturbances exist. We stabilize the system by designing the nonlinear pointwise feedback control laws, in which the technique of sliding-mode control is employed to reject those disturbances. The well-posedness of the corresponding nonlinear closed-loop system is proved based on the theory of nonlinear maximal monotone operators. The exponential stability of the closed-loop system is further obtained. Finally, some numerical simulations are given to show the effectiveness of the control design proposed in this paper.

KEYWORDS:

• Hybrid PDE–ODE system
• stabilization
• point mass
• feedback control
• disturbance rejection

AMS SUBJECT CLASSIFICATIONS:

• 34H15
• 93B52
• 93D15
• 93C20

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Natural Science Foundation of China [grant number 61573252], [grant number 61174080].