Hausdorff moment problem and nonlinear time optimality

Sklyar, G. M.; Ignatovich, S. Yu.

ESAIM: Control, Optimisation and Calculus of Variations, Tome 28 (2022), article no. 15

A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form ẋ₁ = u, {\dot{x}}_j=x_1^{j-1}, j = 2, …, n, is obtained for arbitrary n. In the paper we present the following surprising observation: this nonlinear optimality problem leads to a truncated Hausdorff moment problem, which gives analytic tools for finding the optimal time and optimal controls. Being homogeneous, the mentioned system approximates affine systems from a certain class in the sense of time optimality. Therefore, the obtained results can be used for solving the time-optimal control problem for systems from this class.

Classification : 49K15, 44A60, 93C10
Keywords: Nonlinear control system, time-optimal control problem, truncated Hausdorff moment problem

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