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Controllability of evolution differential inclusions in Banach spaces. (English) Zbl 1128.93005
The authors study the controllability of distributed systems modeled by the evolution differential inclusion $$ \frac{d}{dt}[y(t) - g(t,y(t))] \in A(t) y(t) + F(t,y(t)) + (Bu)(t), \; t \in [0,b].\tag1$$ In this equation, $y(t) \in X$, $u(t) \in U$, where $X$ and $U$ are Banach spaces, $A(t)$ generates an evolution operator $U(t,s)$ on $X$, and $F$ is a multivalued map. Assuming some appropriate boundedness conditions, and that the operator $W: L^{2}([0,b],U) \to X$ defined by $$ W(u) = \int_{0}^{b} U(b,s) (Bu)(s) \, d s $$ admits a bounded inverse modulo $\ker W$, they establish that the system (1) is exactly controllable on $[0,b]$.

MSC:
93B05Controllability
93C25Control systems in abstract spaces
34G25Evolution inclusions
34H05ODE in connection with control problems
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References:
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