Optimal control of processes governed by partial differential equations part II: Vibrations
Tóm tắt
This paper is concerned with damping of vibrations of one-dimensional media by distributed or boundary control. Given an initial state of vibration at the timet=0, the problem is considered to find a control along the medium or on its boundary by which the initial state is transferred to the position of rest at some given timeT>0. At first the problem of null-controllability is studied where the control functions are taken fromL
2 [0,T]. Then the problem of timeminimal null-controllability is investigated where null-controllability is tried to be achieved by norm-bounded controls inL
2 [0,T] forT being as small as possible. The main result here is that time-minimal norm-bounded controls are controls with least norm on the minimum time interval which in addition equals the prescribed bound on the norm. The main tool for the treatment of these control problems is the theory of trigonometric moment problems.
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