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Optimal controllability in viscoelasticity of rate type
Author(s) -
Leugering G.,
Meister E.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080125
Subject(s) - controllability , mathematics , norm (philosophy) , viscoelasticity , reachability , optimal control , control theory (sociology) , subspace topology , observability , type (biology) , mathematical analysis , rank (graph theory) , control (management) , mathematical optimization , computer science , combinatorics , physics , artificial intelligence , political science , law , thermodynamics , ecology , biology
Recently, the control engineers interest turns upon material with structural damping, such as hysteretic effects in elastoplastic systems [27] and flexible space structures [30] and in particular with damping due to the viscoelastic nature of the material, in the sense of Kelvin, [7], [12]. The reason for this renewed interest is the possibility of constructing finite rank compensators with small spillover in the observation [1], [5], [11], [25]. However, a control theory for the infinite system does not seem to exist in the literature. It is shown that the trajectories, initially in a certain subspace, can be steered to rest in any time T > 0 using distributed load controls The reesults are partially contained in [19]. . Furthermore, and perhaps more interesting, the L 2 (0, T , H )‐norm of the control decreases as T increases. This gives rise to the problem of time‐optimal‐controllability and the correlation to the problem of minimum norm controllability. It is shown that the time‐optimal control is characterized by a weak “bang‐bang” principle.