Abstract
A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form ẋ1 = u, ẋj = ẋ1j−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.
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
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