Abstract
Let f 1,…, f k, k ≥ 2, be real-analytic vector fields defined on a neighborhood of the origin in R n, and t > 0. The point x ∈ R n is called attainable from the origin for a time less than t and with no more than N switchings, if there exists a subdivision 0 = to < t 1 < … < T N +1 < t of the segment [0,t] and solutions ξ j (t), t ∈ [t j , t j +1] of the differential equations ẋ = f ij (x), for some i j ∈ {1,…,k}, such that ξ0(0) = 0, ξ j −1(t j ) = ξ j (t j ) for j = 1,…, N, ξ N (t N +1) = x. Let A t (N) be the set of all such points x; the set \( {A_t} = \bigcup\limits_{N > 0} {At} (N) \) is called the attainable set for a time no greater than t.
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Agrachev, A.A. (1999). Is it possible to recognize local controllability in a finite number of differentiations?. In: Blondel, V., Sontag, E.D., Vidyasagar, M., Willems, J.C. (eds) Open Problems in Mathematical Systems and Control Theory. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-0807-8_4
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DOI: https://doi.org/10.1007/978-1-4471-0807-8_4
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