{"title":"随机线性双曲系统最优边界控制问题的收费公路性质","authors":"M. Gugat, M. Herty","doi":"10.1051/cocv/2023051","DOIUrl":null,"url":null,"abstract":"In many applications, in systems that are governed by a linear hyperbolic partial differential equations some of the problem parameters are uncertain. If information about the probability distribution of the parametric uncertainty distribution is available, the uncertain state of the system can be described using an intrinsic formulation through a polynomial chaos expansion. \n This allows to obtain solutions for optimal boundary control problems with random parameters. \nWe show that similar to the deterministic case, a turnpike result holds in the sense that for large time horizons the optimal states for dynamic optimal control problems on a substantial part of the time interval approach the optimal states for the corresponding uncertain static optimal control problem. We show integral turnpike results both for the full uncertain system as well as for a generalized polynomial chaos approximation.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Turnpike properties of optimal boundary control problems with random linear hyperbolic systems\",\"authors\":\"M. Gugat, M. Herty\",\"doi\":\"10.1051/cocv/2023051\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In many applications, in systems that are governed by a linear hyperbolic partial differential equations some of the problem parameters are uncertain. If information about the probability distribution of the parametric uncertainty distribution is available, the uncertain state of the system can be described using an intrinsic formulation through a polynomial chaos expansion. \\n This allows to obtain solutions for optimal boundary control problems with random parameters. \\nWe show that similar to the deterministic case, a turnpike result holds in the sense that for large time horizons the optimal states for dynamic optimal control problems on a substantial part of the time interval approach the optimal states for the corresponding uncertain static optimal control problem. We show integral turnpike results both for the full uncertain system as well as for a generalized polynomial chaos approximation.\",\"PeriodicalId\":50500,\"journal\":{\"name\":\"Esaim-Control Optimisation and Calculus of Variations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2023-07-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Control Optimisation and Calculus of Variations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/cocv/2023051\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Control Optimisation and Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/cocv/2023051","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Turnpike properties of optimal boundary control problems with random linear hyperbolic systems
In many applications, in systems that are governed by a linear hyperbolic partial differential equations some of the problem parameters are uncertain. If information about the probability distribution of the parametric uncertainty distribution is available, the uncertain state of the system can be described using an intrinsic formulation through a polynomial chaos expansion.
This allows to obtain solutions for optimal boundary control problems with random parameters.
We show that similar to the deterministic case, a turnpike result holds in the sense that for large time horizons the optimal states for dynamic optimal control problems on a substantial part of the time interval approach the optimal states for the corresponding uncertain static optimal control problem. We show integral turnpike results both for the full uncertain system as well as for a generalized polynomial chaos approximation.
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.