کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
695089 1460645 2016 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
The stochastic reach-avoid problem and set characterization for diffusions
ترجمه فارسی عنوان
مسئله تصادفی دسترس ـ اجتناب و خصوصیات تعیین شده برای اشاعه
کلمات کلیدی
قابل دسترسی؛ کنترل تصادفی؛ برنامه نویسی پویا؛ معادلات دیفرانسیل با مشتقات جزئی. راه حل ویسکوزیته ناپیوسته
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
چکیده انگلیسی

In this article we approach a class of stochastic reachability problems with state constraints from an optimal control perspective. Preceding approaches to solving these reachability problems are either confined to the deterministic setting or address almost-sure stochastic requirements. In contrast, we propose a methodology to tackle problems with less stringent requirements than almost sure. To this end, we first establish a connection between two distinct stochastic reach-avoid problems and three classes of stochastic optimal control problems involving discontinuous payoff functions. Subsequently, we focus on solutions of one of the classes of stochastic optimal control problems—the exit-time problem, which solves both the two reach-avoid problems mentioned above. We then derive a weak version of a dynamic programming principle (DPP) for the corresponding value function; in this direction our contribution compared to the existing literature is to develop techniques that admit discontinuous payoff functions. Moreover, based on our DPP, we provide an alternative characterization of the value function as a solution of a partial differential equation (PDE) in the sense of discontinuous viscosity solutions, along with boundary conditions both in Dirichlet and viscosity senses. Theoretical justifications are also discussed to pave the way for deployment of off-the-shelf PDE solvers for numerical computations. Finally, we validate the performance of the proposed framework on the stochastic Zermelo navigation problem.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Automatica - Volume 70, August 2016, Pages 43–56
نویسندگان
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