Abdon E. Choque‐RiveroEfrain Cruz MullisacaGraciela A. Gonzalez2026-03-222026-03-22202210.1109/ropec55836.2022.10018689https://doi.org/10.1109/ropec55836.2022.10018689https://andeanlibrary.org/handle/123456789/72917For the Brunovsky system, given an initial point <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x^{0}$</tex> in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbb{R}^{2}$</tex>, we consider the problem of finding a set of bounded controls that allows to return to the state <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x^{0}$</tex> in finite time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$T(x^{0})$</tex>. We use the Korobov's controllability function method <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta(x)$</tex>, in particular, the case where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Theta(x^{0})$</tex> represents the motion time from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$x^{0}$</tex> to the same point. We present the solution of the aforementioned problem with the additional condition that the objective is achieved in the optimal time.enBounded functionPoint (geometry)Set (abstract data type)Computer scienceFunction (biology)AlgorithmArtificial intelligenceMathematicsarticle