Stabilisation of nonlinear ODE and wave PDE cascaded systems with damping terms

Abstract

We investigate asymptotically stabilisation for the cascaded system of a nonlinear ODE and a wave PDE with damping terms by a predictor control. Based on the backstepping transformations, the cascaded system is transferred to a target system. Further, a predictor control is designed. It is proved that the target system is asymptotically stable by using a Lyapunov functional. Further the stability of the original system under the proposed control law is equivalent to that of the target system. An example is given to illustrate the validity of the proposed method.

Keywords:

• Cascaded system
• wave dynamics
• predictor control
• backstepping transformations
• damping terms

Acknowledgements

The authors thank the anonymous reviewers for their many helpful suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant numbers 61773350, 61471163], the Natural Science Foundation of Zhejiang Province [grant number LY17F030001], and outstanding young talents project of Natural Science Foundation of Hubei Province, China [Grant/Award Number: 2017CFA034].