SCIENCE CHINA Information Sciences, Volume 63 , Issue 12 : 222201(2020) https://doi.org/10.1007/s11432-019-2631-6

## Estimation of velocity potential of water waves using a Luenberger-like observer

• AcceptedAug 5, 2019
• PublishedOct 27, 2020
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### Acknowledgment

This work was supported by Scientific Instruments Development Program of National Natural Science Foundation of China (Grant No. 615278010) and Science and Technology Planning Project of Guangdong (Grant No. 2017B010116005).

### References

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• Figure 1

(Color online) Schematic of water waves. The red lines delineate the water domain $\Omega$.

• Figure 2

(Color online) Mesh grid of the water domain $(x,y)~\in~[0,\lambda]~\times~[-h,0]$. The step sizes are $\Delta_x$ and $\Delta_y$.

• Table 1

Table 1$t_1$: time required for the estimated velocity potential to reach the velocitypotential of the system at $x=1.5$ m with a precision of $5%$; $t_2$: time required for the estimated surface elevation to reach the surface elevation of the system at$x=1.5$ m with a precision of $5%$.

 Gain 1 2 3 4 5 6 7 8 9 10 11 $t_1$ (s) 7.31 3.35 2.39 1.74 1.11 1.16 1.14 1.01 0.26 0.38 0.8 $t_2$ (s) 5.24 2.66 1.72 1.17 1.06 0.81 0.35 0.34 0.32 0.32 0.29
• Table 2

Table 2Relation between $M$ and $F^*$. The third row denotes the shortest time required for the estimated states $(\hat~\xi,~\hat~\eta)$ to reach the actual states of the dynamical system $(\xi,~\eta)$ at $x=1.5$ m with a precision of $5%$.

 $M$ 1 2 3 4 5 6 7 8 9 10 11 12 $F^*$ 9.5 8.7 8.6 8.4 8.8 8.6 8.7 8.6 8.7 8.7 8.5 8.7 Time 0.3 0.52 0.48 0.43 0.46 0.46 0.47 0.44 0.47 0.47 0.44 0.47

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