Observer design for wave equation with a forcing term in the boundary

Abstract

This paper investigates the observer design problem for 1D wave equation with nonlinear boundary condition containing a forcing term, whose dynamics presents spatiotemporal chaotic behaviors. By introducing a linear error input on the left-end boundary, we construct an observer via the method of characteristics. Moreover, we present a sufficient and necessary condition for the stability of the error dynamics system. Numerical simulations are presented to illustrate the theoretical outcomes.

Keywords:

• Wave equation
• observer design
• method of characteristics

AMS Subject Classifications:

• 37N35
• 34C28

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

We gratefully acknowledge the support from Natural Science Foundation of China [grant number 11201504]; Fundamental Research Funds for the Central Universities [grant number 15lgpy14].