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Invariance of the reachable set under nonlinear perturbations. (English) Zbl 0626.49018

The author considers a linear control system governed by an integral equation of the form \[ x(t)=\bar x(t)+\int^{t}_{0}\psi (t,s)[\Phi (s,x(s))+B(s)v(s)]ds \] on [0,T], under suitable conditions to ensure the existence of solutions \(x=x_{\Phi}(.,v)\) for \(v\in V\). The principal result of this paper is that the reachable set is invariant for \(\Phi\) in a suitable class F of nonlinear perturbations.
Reviewer: M.Megan

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
45D05 Volterra integral equations
49K40 Sensitivity, stability, well-posedness
93B05 Controllability
93C10 Nonlinear systems in control theory
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C25 Control/observation systems in abstract spaces
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