On Homogeneous Finite-Time Control for Linear Evolution Equation in Hilbert Space

Abstract : Based on the notion of generalized homogeneity, a new algorithm of feedback control design is developed for a plant modeled by a linear evolution equation in a Hilbert space with a possibly unbounded operator. The designed control law steers any solution of the closed-loop system to zero in a finite time. Method of homogeneous extension is presented in order to make the developed control design principles to be applicable for evolution systems with non-homogeneous operators. The design scheme is demonstrated for heat equation with the control input distributed on the segment [0, 1].
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Andrey Polyakov, Jean-Michel Coron, Lionel Rosier. On Homogeneous Finite-Time Control for Linear Evolution Equation in Hilbert Space. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2018, 63 (9), pp.3143 - 3150. ⟨10.1109/TAC.2018.2797838⟩. ⟨hal-01695475⟩

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