Abstract
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 asymptoticallyO(T −(K+1/2) behavior for the norm of the control operator whereK is the order of the “least controllable” modes (the minimal exponent for the rank condition).
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References
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This research was partially supported under Grant AFOSR-82-0271. Portions of this were done while the author was visiting at the Systems Research Center (University of Maryland) with NSF support under CDR-85-00108 and at the Centre for Mathematical Analysis (Australian National University).
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Seidman, T.I. How violent are fast controls?. Math. Control Signal Systems 1, 89–95 (1988). https://doi.org/10.1007/BF02551238
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DOI: https://doi.org/10.1007/BF02551238