Temat: exact solution - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Controllability of semilinear systems with fixed delay in control
Autorzy:: Kumar, S.
Sukavanam, N.
Powiązania:: https://bibliotekanauki.pl/articles/952777.pdf
Data publikacji:: 2015
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: first order delay system
mild solution
fixed point
exact controllability
Opis:: In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.
Źródło:: Opuscula Mathematica; 2015, 35, 1; 71-83
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Exact controllability of a string to rest with a moving boundary
Autorzy:: Gugat, Martin
Powiązania:: https://bibliotekanauki.pl/articles/970107.pdf
Data publikacji:: 2019
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:: pde constrained optimization
optimal control of pdes
optimal boundary control
wave equation
analytic solution
exact controllability
moving boundaries
mining elevator
Opis:: We consider the problem of steering a ﬁnite string to the zero state in ﬁnite time from a given initial state by controlling the state at one boundary point while the other boundary point moves. As a possible application we have in mind the optimal control of a mining elevator, where the length of the string changes during the transportation process. During the transportation process, oscillations of the elevator-cable can occur that can be damped in this way. We present an exact controllability result for Dirichlet boundary control at the ﬁxed end of the string that states that there exist exact controls for which the oscillations vanish after ﬁnite time. For the result we assume that the movements are Lipschitz continuous with a Lipschitz constant, whose absolute value is smaller than the wave speed. In the result, we present the minimal time, for which exact controllability holds, this time depending on the movement of the boundary point. Our results are based upon travelling wave solutions. We present a representation of the set of successful controls that steer the system to rest after ﬁnite time as the solution set of two point-wise equalities. This allows for a transformation of the optimal control problem to a form where no partial diﬀerential equation appears. This representation enables interesting insights into the structure of the successful controls. For example, exact bang-bang controls can only exist if the initial state is a simple function and the initial velocity is zero.
Źródło:: Control and Cybernetics; 2019, 48, 1; 69-87
0324-8569
Pojawia się w:: Control and Cybernetics
Dostawca treści:: Biblioteka Nauki

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