{"title":"Hausdorff moment problem and nonlinear time optimality","authors":"G. Sklyar, S. Ignatovich","doi":"10.1051/cocv/2022007","DOIUrl":null,"url":null,"abstract":"A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form $\\dot x_1=u$, $\\dot x_j=x_1^{j-1}$, $j=2,\\ldots,n$, 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 a certain class of affine systems 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.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":"42 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Control Optimisation and Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/cocv/2022007","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form $\dot x_1=u$, $\dot x_j=x_1^{j-1}$, $j=2,\ldots,n$, 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 a certain class of affine systems 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.
期刊介绍：
ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations.
Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines.
Targeted topics include:
in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory;
in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis;
in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
