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Is it possible to recognize local controllability in a finite number of differentiations?

  • Andrei A. Agrachev
Part of the Communications and Control Engineering book series (CCE)

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 xR 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 = 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.

Keywords

Vector Field Local Controllability Steklov Mathematical Institute Taylor Polynomial Scalar Input 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Andrei A. Agrachev
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

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