This paper is concerned with the problem of stabilizing one-dimensional parabolic systems related to formations by using finitedimensional controllers of a modal type. The parabolic system is described by a Sturm-Liouville operator, and the boundary condition is different from any of Dirichlet type, Neumann type, and Robin type, since it contains the time derivative of boundary values. In this paper, it is shown that the system is formulated as an evolution equation with unbounded output operator in a Hilbert space, and further that it is stabilized by using an RMF (residual mode filter)-based controller which is of finite-dimension. A numerical simulation result is also given to demonstrate the validity of the finite-dimensional controller.
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In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.
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In this paper, the time-optimal boundary control problem for a distributed parabolic system in which time lags appear in integral form in both the state equation and the boundary condition is presented. Some particular properties of optimal control are discussed.
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In this paper, the time-optimal control problem for a distributed parabolic system in which different multiple time-varying lags appear both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.
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