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First-order differentiability of the flow of a system withL p controls (1996)

Bianchini, R. M. ; Margheri, A.

Springer

Journal of optimization theory and applications 89 (1996), S. 293-310

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ISSN: 1573-2878

Keywords: Nonlinear control systems ; flow differentiability ; L p -controls

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract This paper considers the study of the regularity of the flow of a nonautonomous nonlinear control process when the set of control maps is endowed with theL p -topology. Roughly speaking, it is proved that, if the norm of the mapf(t, x, u) defining the process together with its first derivatives goes to infinity, with the norm ofu not faster than⊥u⊥ p ,p〉1, then the flow isC 1 in theL p -topology. This property implies that, if the control maps are bounded, then the flow is differentiable in anyL p ,p〉1. Moreover, it is proved that the only systems for which the flow is differentiable inL 1 are the affine ones.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02192531

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