A general comparison principle for Hamilton Jacobi Bellman equations on stratified domains 1

IF 1.3 3区数学 Q4 AUTOMATION & CONTROL SYSTEMS

Esaim-Control Optimisation and Calculus of Variations Pub Date : 2022-12-22 DOI:10.1051/cocv/2022089

H. Zidani, O. Jerhaoui

引用次数: 2

Abstract

This manuscript aims to study finite horizon, first order Hamilton Jacobi Bellman (HJB) equations on stratified domains. This problem is related to optimal control problems with discontinuous dynamics. We use nonsmooth analysis techniques to derive a strong comparison principle as in the classical theory and deduce that the value function is the unique viscosity solution. Furthermore, we prove some stability results of the Hamilton Jacobi Bellman equation. Finally, we establish a general convergence result for monotone numerical schemes in the stratified case.

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分层域上Hamilton - Jacobi - Bellman方程的一般比较原理

本文旨在研究分层域上的有限视界，一阶Hamilton Jacobi Bellman (HJB)方程。这个问题涉及到具有不连续动力学的最优控制问题。我们利用非光滑分析技术推导出经典理论中的强比较原理，并推导出值函数是唯一的粘度解。进一步证明了Hamilton Jacobi Bellman方程的一些稳定性结果。最后，我们建立了在分层情况下单调数值格式的一般收敛结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Esaim-Control Optimisation and Calculus of Variations Mathematics-Computational Mathematics

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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.