Abstract
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 increases as the available control time shrinks. This paper gives the asymptotics of minimalL p-norm controls as the time duration goes to zero; there are also some further remarks for other related norms.
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References
F. H. Clarke,Optimization and Nonsmooth Analysis, SIAM, Philadelphia, PA, 1990.
T. I. Seidman, How violent are fast controls?,Math. Control Signals Systems,1 (1988), 89–95.
W. H. Wonham,Linear Multivariable Control: A Geometric Approach, Springer-Verlag, Berlin, 1985.
K. Yosida,Functional Analysis, Springer-Verlag, Berlin, 1980.
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This author was supported in part by the NNSF of China and the Trans-Century Training Programme Foundation for the Talents of the State Education Commission of China. Part of the work was done while this author was visiting the Department of Mathematics, University of Tennessee. He would like to thank Professor S. M. Lenhart for her hospitality.
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Seidman, T.I., Yong, J. How violent are fast controls?, II. Math. Control Signal Systems 9, 327–340 (1996). https://doi.org/10.1007/BF01211854
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DOI: https://doi.org/10.1007/BF01211854