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On the ”bang-bang” principle for nonlinear evolution inclusions. (English) Zbl 0780.34045

This paper appears to be (verbatim) the same as [Dyn. Syst. Appl. 2, No. 1, 61-74 (1993; see the review below)]. The results are on extremal solutions of control systems (solutions corresponding to extreme values of the orientor field). The author establishes existence of these extremal solutions for nonlinear evolution inclusions in Hilbert space and shows that these extremal solutions are dense in the solutions of the original system. This density result is used to derive versions of the “bang-bang” principle for certain nonlinear infinite dimensional control systems. An example involving a nonlinear parabolic distributed parameter system is worked out in detail.

MSC:

34G20 Nonlinear differential equations in abstract spaces
93C20 Control/observation systems governed by partial differential equations
93C25 Control/observation systems in abstract spaces
34A60 Ordinary differential inclusions

Citations:

Zbl 0780.34046
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References:

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