SIAM Journal on Control and Optimization · 2000 · 27 citations · 6 references
Natural SciencesMathematicsOcean EngineeringDynamical SystemsFluid DynamicsOcean WavesControl Of Dynamical SystemsControl SystemsControl TheoryFeedback ControlStabilityStability TheoryControllabilityFeedbackFinite TimeFinite-time StabilityOperatorsSurface Wave StabilitySystem StabilityWave Equation Models
This paper deals with a physical system that can be represented by an abstract wave equation: a canal with wave generators. We first study the various degrees of controllability that this system can enjoy, with two kinds of input operators and associated control spaces, corresponding to "flexible" and "rigid" generators. A counterexample to the exact controllability and a positive result for the approximate controllability are given for the flexible generator case. In the rigid case, we show that approximate controllability in finite time does not hold. We also study the stability of the system when the elevation of the surface is measured at x=0, and a static feedback is used to control a rigid generator. We show that strong stability holds (but with a nonuniform decay), although the perturbation caused by the feedback on the system operator is not dissipative in the natural topology.
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