随机线性双曲系统最优边界控制问题的收费公路性质

IF 1.3 3区 数学 Q4 AUTOMATION & CONTROL SYSTEMS Esaim-Control Optimisation and Calculus of Variations Pub Date : 2023-07-10 DOI:10.1051/cocv/2023051
M. Gugat, M. Herty
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引用次数: 1

摘要

在许多应用中,在由线性双曲型偏微分方程控制的系统中,一些问题参数是不确定的。如果参数不确定分布的概率分布信息可用,则系统的不确定状态可以通过多项式混沌展开用一个固有公式来描述。这允许得到具有随机参数的最优边界控制问题的解。我们表明,与确定性情况类似,收费公路结果在很大的时间范围内,动态最优控制问题的最优状态在相当大的时间间隔上接近于相应的不确定静态最优控制问题的最优状态。对于完全不确定系统和广义多项式混沌近似,我们给出了积分收费公路的结果。
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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.
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来源期刊
Esaim-Control Optimisation and Calculus of Variations
Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics
自引率
7.10%
发文量
77
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.
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