Almost global practical exponential stabilisation of a floating rigid body

References

• Adams, R. A., & Fournier, J. J. F. (2003). Sobolev spaces (2nd ed.). Academic Press.
   Google Scholar
• Badra, M., & Takahashi, T. (2014a). Feedback stabilization of a fluid-rigid body interaction system. Advances in Differential Equations, 19(11/12), 1137–1184.
   Web of Science ®Google Scholar
• Badra, M., & Takahashi, T. (2014b). Feedback stabilization of a simplified 1D fluid-particle system. Annales de l'Institut Henri Poincaré, Analyse Non Linéaire, 31(2), 369–389. https://doi.org/10.4171/aihpc
   Web of Science ®Google Scholar
• Badra, M., & Takahashi, T. (2017). Feedback boundary stabilization of 2D fluid-structure interaction systems. Discrete and Continuous Dynamical Systems, 37(5), 2315–2373. https://doi.org/10.3934/dcds.2017102
   Web of Science ®Google Scholar
• Bai, Y., & Jin, W. L. (2015). Marine structural design (2nd ed.). Elsevier.
   Google Scholar
• Bello, J. A. (1996). Lr regularity for the Stokes and Navier–Stokes problems. Annali di Matematica Pura ed Applicata, 170(1), 187–206. https://doi.org/10.1007/BF01758988
   Google Scholar
• Bocchi, E. (2020). Floating structures in shallow water: Local well-posedness in the axisymmetric case. SIAM Journal on Mathematical Analysis, 52(1), 306–339. https://doi.org/10.1137/18M1174180
   Web of Science ®Google Scholar
• Bost, C., Cottet, G. H., & Maitre, E. 2010. Convergence analysis of a penalization method for the three-dimensional motion of a rigid body in an incompressible viscous fluid. SIAM Journal on Numerical Analysis 48(4), 1313–1337. https://doi.org/10.1137/090767856
   Web of Science ®Google Scholar
• Conca, C., Martin, J. H. S., & Marius, T. 2000. Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid. Communications in Partial Differential Equations 25(5), 1019–1042. https://doi.org/10.1080/03605300008821540
   Web of Science ®Google Scholar
• Desjardins, B., & Esteban, M. J. (1999). Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Archive for Rational Mechanics and Analysis, 146(1), 59–71. https://doi.org/10.1007/s002050050136
   Web of Science ®Google Scholar
• Desjardins, B., & Esteban, M. J. (2000). On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models. Communications in Partial Differential Equations, 25(7–8), 1399–1413. https://doi.org/10.1080/03605300008821553
   Web of Science ®Google Scholar
• Desjardins, B., Esteban, M. J., Grandmont, C., & Tallec, P. L. 2001. Weak solutions for a fluid-structure interaction model. Revista Matemática Complutense 14(2), 523–538. https://doi.org/10.5209/rev_REMA.2001.v14.n2.17030
   Google Scholar
• DiPerna, R. J., & Lions, P. L. (1989). Ordinary differential equations, transport theory and Sobolev spaces. Inventiones Mathematicae, 98(3), 511–547. https://doi.org/10.1007/BF01393835
   Web of Science ®Google Scholar
• Do, K. D. (2015). Coordination control of quadrotor VTOL aircraft in three-dimensional space. International Journal of Control, 88(3), 543–558. https://doi.org/10.1080/00207179.2014.966324
   Web of Science ®Google Scholar
• Do, K. D. (2019a). Forwarding control design for strict-feedforward systems. Journal of Dynamic Systems, Measurement, and Control, 141(8), 081010:1–081010:12. https://doi.org/10.1115/1.4042881
   Web of Science ®Google Scholar
• Do, K. D. (2019b). Inverse optimal gain assignment control of evolution systems and its application to boundary control of marine risers. Automatica, 106(189), 242–256. https://doi.org/10.1016/j.automatica.2019.05.020
   Google Scholar
• Do, K. D. (2020). Nonlinear control with wave observer to maximize harvested power for point absorber wave energy converters. Asian Journal of Control, 24(1), 1–30. https://doi.org/10.1002/asjc.2461.
   Google Scholar
• Do, K. D., & Pan, J. (2009). Control of ships and underwater vehicles. Springer.
   Google Scholar
• Evans, L. (2000). Partial differential equations. American Mathematical Society.
   Google Scholar
• Falcao, A. (2010). Wave energy utilization: A review of the technologies. Renewable and Sustainable Energy Reviews, 14(3), 899–918. https://doi.org/10.1016/j.rser.2009.11.003
   Web of Science ®Google Scholar
• Faltinsen, O. (1993). Sea loads on ships and offshore structures. Cambridge University Press.
   Google Scholar
• Feireisl, E. (2003). On the motion of rigid bodies in a viscous incompressible fluid. Journal of Evolution Equations, 3(3), 419–441. https://doi.org/10.1007/s00028-003-0110-1
   Web of Science ®Google Scholar
• Fossen, T. I. (2002). Marine control systems. Marine Cybernetics.
   Google Scholar
• Galdi, G. P. (1989). An introduction to the mathematical theory of the Navier-Stokes equations: Steady-state problems. Springer.
   Google Scholar
• Grandmont, C., & Maday, Y. (2000). Existence for an unsteady fluid-structure interaction problem. ESAIM: Mathematical Modelling and Numerical Analysis, 34(3), 609–636. https://doi.org/10.1051/m2an:2000159
   Web of Science ®Google Scholar
• Gunzburger, M. D., Lee, H. C., & Seregin, G. A. 2000. Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. Journal of Mathematical Fluid Mechanics 2(3), 219–266. https://doi.org/10.1007/PL00000954
   Web of Science ®Google Scholar
• Koo, W. C., & Kim, M. H. (2007a). Current effects on nonlinear wave-body interactions by a 2D fully nonlinear numerical wave tank. Journal of Waterway, Port, Coastal, and Ocean Engineering, 133(2), 136–146. https://doi.org/10.1061/(ASCE)0733-950X(2007)133:2(136)
   Web of Science ®Google Scholar
• Koo, W. C., & Kim, M. H. (2007b). Fully nonlinear wave-body interactions with surface-piercing bodies. Ocean Engineering, 34(7), 1000–1012. https://doi.org/10.1016/j.oceaneng.2006.04.009
   Web of Science ®Google Scholar
• Lackner, M. A., & M. A. Rotea (2011). Structural control of floating wind turbines. Mechatronics, 21(4), 704–719. https://doi.org/10.1016/j.mechatronics.2010.11.007
   Web of Science ®Google Scholar
• Lannes, D. (2017). On the dynamics of floating structures. Annals of PDE, 3, Article number: 11.
   Google Scholar
• Li, Y., & Lin, M. (2010). Wave-body interactions for a surface-piercing body in water of finite depth. Journal of Hydrodynamics, 22(6), 745–752. https://doi.org/10.1016/S1001-6058(09)60112-8
   Web of Science ®Google Scholar
• Li, Y., & Lin, M. (2012). Regular and irregular wave impacts on floating body. Ocean Engineering, 42(1), 93–101. https://doi.org/10.1016/j.oceaneng.2012.01.019
   Google Scholar
• Maity, D., Martin, J. S., Takahashi, T., & Tucsnak, M. 2019. Analysis of a simplified model of rigid structure floating in a viscous fluid. Journal of Nonlinear Science 29(5), 1975–2020. https://doi.org/10.1007/s00332-019-09536-5
   Web of Science ®Google Scholar
• Nouri, A., & Poupaud, F. (1995). An Existence theorem for the multifluid Navier–Stokes problem. Journal of Differential Equations, 122(1), 71–88. https://doi.org/10.1006/jdeq.1995.1139
   Web of Science ®Google Scholar
• Paidoussis, M. P. (1998). Fluid-structure interactions (Vol. 1). Academic Press.
   Google Scholar
• Robinson, J. C., Rodrigo, J. L., & Sadowski, W. 2016. The three-dimensional Navier–Stokes equations. Cambridge University Press.
   Google Scholar
• San Martin, J. A., Starovoitov, V., & Tucsnak, M. 2002. Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid. Archive for Rational Mechanics and Analysis 161(2), 113–147. https://doi.org/10.1007/s002050100172
   Web of Science ®Google Scholar
• Takahashi, T. (2003). Existence of strong solutions for the equations modelling the rigid motion of a rigid-fluid system in a bounded domain. Advances in Difference Equations, 8(12), 1499–1532.
   Google Scholar
• Takahashi, T., & Tucsnak, M. (2004). Global strong solutions for the two dimensional motion of a rigid body in a viscous fluid. Journal of Mathematical Fluid Mechanics, 6(1), 53–77. https://doi.org/10.1007/s00021-003-0083-4
   Web of Science ®Google Scholar
• Takahashi, T., Tucsnak, M., & Weiss, G. 2015. Stabilization of a fluid-rigid body system. Journal of Differential Equations 259(11), 6459–6493. https://doi.org/10.1016/j.jde.2015.07.024
   Web of Science ®Google Scholar
• Temam, R. (1995). Navier–Stokes equations and nonlinear functional analysis (2nd ed.). SIAM.
   Google Scholar
• Tsiotras, P. (1996). Stabilization and optimality results for the attitude control problem. Journal of Guidance, Control, and Dynamics, 19(4), 772–779. https://doi.org/10.2514/3.21698
   Web of Science ®Google Scholar