标题： 半线性动态规划：分析、算法和确定性等价性质 显示英文标题

标题： Semilinear Dynamic Programming: Analysis, Algorithms, and Certainty Equivalence Properties

摘要： 我们考虑一类涉及部分线性结构以及系统方程和代价函数的一些正性性质的动态规划（DP）问题。 我们处理确定性和随机问题，可能具有马尔可夫跳跃参数。 我们主要关注无限时间范围的问题，并证明在我们的假设下，最优代价函数是线性的，并且可以使用标准DP算法高效地计算出一个最优策略。 此外，我们表明，我们的随机问题中存在类似于经典线性二次最优控制问题的确定性等价形式。 显示英文摘要

摘要： We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly with Markov jump parameters. We focus primarily on infinite horizon problems and prove that under our assumptions, the optimal cost function is linear, and that an optimal policy can be computed efficiently with standard DP algorithms. Moreover, we show that forms of certainty equivalence hold for our stochastic problems, in analogy with the classical linear quadratic optimal control problems.