Stochastic Control With Affine Dynamics and Extended Quadratic Costs

• 成果类型: Article
• 署名作者: Barratt, Shane; Boyd, Stephen
• 署名单位: Stanford University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3064535
• 发表日期: 2022
• 页码: 320-335
• 关键词: Dynamic Programming; minimization; indexes; Symmetric matrices; pathology; Integrated circuits; finance; Convex Optimization; Dynamic programming (DP); stochastic control

摘要

An extended quadratic function is a quadratic function plus the indicator function of an affine set, i.e., a quadratic function with embedded linear equality constraints. In this article, we show that, under some technical conditions, random convex extended quadratic functions are closed under addition, composition with an affine function, expectation, and partial minimization, i.e., minimizing over some of its arguments. These properties imply that dynamic programming can be tractably carried out for stochastic control problems with random affine dynamics and extended quadratic cost functions. While the equations for the dynamic programming iterations are much more complicated than for traditional linear quadratic control, they are well suited to an object-oriented implementation, which we describe. We also describe a number of known and new applications.