ISSN:
1573-8698
Keywords:
93C25
;
Differential inclusion
;
approximate weak and strong invariance
;
viability
;
∈-trajectory
;
lower and upper Hamiltonians
;
proximal normal cone
;
proximal aiming
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Consider a mappingF from a Hilbert spaceH to the subsets ofH, which is upper semicontinuous/Lipschitz, has nonconvex, noncompact values, and satisfies a linear growth condition. We give the first necessary and sufficient conditions in this general setting for a subsetS ofH to be approximately weakly/strongly invariant with respect to approximate solutions of the differential inclusion $$\dot x(t) \in F(x)$$ . The conditions are given in terms of the lower/upper Hamiltonians corresponding toF and involve nonsmooth analysis elements and techniques. The concept of approximate invariance generalizes the well-known concept of invariance and in turn relies on the notion of an ∈-trajectory corresponding to a differential inclusion.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02463280
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