On the Attainable Sets of Control Systems with p-Integrable Controls

H. W. Lou
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H. W. Lou: Fudan University

Journal of Optimization Theory and Applications, 2004, vol. 123, issue 1, No 6, 123-147

Abstract: Abstract It is well known that, for a control system, under suitable assumptions, the closure of the attainable set does not change if we consider p-integrable controls for different p. This is an interesting problem and has not been studied in depth, whether or not the attainable set changes when p changes. We show that, for a linear system, the attainable sets may be different for different p. In the two-dimensional case, we prove that the number of indices for which the attainable sets change is finite. Moreover, we show that, for a class of systems, the attainable sets are the same, when the time duration is large enough.

Keywords: Attainable sets; control systems; p-integrable controls (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTA.0000043994.99474.ff

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