Time optimality and the power moment problem

A solution of the problem of exact determination of a time optimal control for the equation $x^{(n)}=u$, $|u|\le1$, in the open loop form as well as in the closed loop form is presented in this paper. A system of special polynomials, called canonical variables, is introduced. The solution is obtained in terms of Hankel determinants and a sequence of Markov determinants in the canonical variables. A connection between the solution obtained and the power moment problem is investigated.
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