How violent are fast controls, III∗
نویسنده
چکیده
For (coupled systems of) partial differential equations for which nullcontrol is possible in arbitrarily short time, the typical blowup rate for the control cost is exponential in 1/T . It is shown how to derive this rate for a variety of systems, including the thermoelastic system with control restricted to a small patch in the domain and to a single component (thermal, displacement, or velocity).
منابع مشابه
How violent are fast controls?, II
For a linear autonomous system, if a state is reachable from zero in some time duration, then it is reachable within any positive time duration. However, the norm of the control that steers the zero state to the given reachable state will be increasing as the available control time shrinks. This paper gives the asymptotics of minimal L-norm controls as the time duration goes to zero; there are ...
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For any controllable linear system it is clear that the minimum control energy must increase unboundedly as the available time for exact control decreases to 0. This is made precise, obtaining asymptotically O(T−(K+1/2) behavior for the norm of the control operator where K is the order of the ‘least controllable’ modes (the minimal exponent for the rank condition).
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