{"authors":[{"id":null,"fullName":"Tucsnak, Marius","name":"Marius","surname":"Tucsnak","rank":1,"pid":null},{"id":null,"fullName":"Xu, Zhuo","name":"Zhuo","surname":"Xu","rank":2,"pid":null}],"openAccessColor":"gold","publiclyFunded":false,"eoscIfGuidelines":null,"type":"publication","language":{"code":"und","label":"Undetermined"},"countries":[{"code":"FR","label":"France","provenance":null}],"subjects":[{"subject":{"scheme":"keyword","value":"shallow water equations"},"provenance":null},{"subject":{"scheme":"keyword","value":"Control/observation systems governed by partial differential equations"},"provenance":null},{"subject":{"scheme":"keyword","value":"[MATH] Mathematics [math]"},"provenance":null},{"subject":{"scheme":"keyword","value":"analytic semigroup"},"provenance":null},{"subject":{"scheme":"keyword","value":"Feedback control"},"provenance":null},{"subject":{"scheme":"keyword","value":"93C20, 93B52, 35Q35, 49J21"},"provenance":null},{"subject":{"scheme":"keyword","value":"PDEs in connection with fluid mechanics"},"provenance":null},{"subject":{"scheme":"FOS","value":"01 natural sciences"},"provenance":null},{"subject":{"scheme":"keyword","value":"Riccati equation"},"provenance":null},{"subject":{"scheme":"keyword","value":"strong stability"},"provenance":null},{"subject":{"scheme":"keyword","value":"Optimization and Control (math.OC)"},"provenance":null},{"subject":{"scheme":"keyword","value":"Linear-quadratic optimal control problems"},"provenance":null},{"subject":{"scheme":"keyword","value":"FOS: Mathematics"},"provenance":null},{"subject":{"scheme":"FOS","value":"0101 mathematics"},"provenance":null},{"subject":{"scheme":"keyword","value":"Mathematics - Optimization and Control"},"provenance":null},{"subject":{"scheme":"keyword","value":"floating solid"},"provenance":null}],"mainTitle":"LQR control for a system describing the interaction between a floating solid and the surrounding fluid","subTitle":null,"descriptions":["This paper studies an infinite time horizon LQR optimal control problem for a system describing, within a linear approximation, the vertical oscillations of a floating solid, coupled to the motion of the free boundary fluid on which it floats. The fluid flow is described by a viscous version of the linearized Saint-Venant equations (shallow water regime). The major difficulty we are facing is that the domain occupied by the fluid is unbounded so that the system is not exponentially stable. This fact firstly raises challenges in proving the wellposedness, requiring the combined use of analytic semigroup theory and of an interpolation technique. 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