Truncated Hausdorff Moment Problem and Analytic Solution of the Time-Optimal Problem for One Class of Nonlinear Control Systems

2020/07/05 by Grigory M. Sklyar, Sklyar, Grigory M., S. Yu. Ignatovich +1
Computer Science · Engineering · #44A60 (Secondary) #49K15 (Primary) #93C10 #Aerospace Engineering and Control Systems #FOS: Mathematics #Guidance and Control Systems #Mathematical Control Systems and Analysis #Optimization and Control (math.OC)

paper · pdf · doi:10.48550/arxiv.2007.02398

openalex publication_date 2020/07/05 · openalex created_date 2020/07/10 · openalex updated_date 2026/07/28

Abstract

A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form x₁=u, x_j=x₁^j-1, j=2,…,n, is obtained for arbitrary n. The main goal of the paper is to present the following surprising observation: this nonlinear optimality problem leads to a truncated Hausdorff moment problem, which is applied essentially for finding the optimal time and optimal controls.

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