论文标题
部分可观测时空混沌系统的无模型预测
Optimal control for production inventory system with various cost criterion
论文作者
论文摘要
储层计算是预测湍流的有力工具，其简单的架构具有处理大型系统的计算效率。然而，其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间，然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用，该系统模拟了湍流的若干特征。我们表明，使用径向基函数作为非线性投影器，即使只有部分观测并且不知道控制方程，也能稳健地捕捉复杂的系统非线性。最后，我们表明，当测量稀疏、不完整且带有噪声，甚至控制方程变得不准确时，我们的网络仍然可以产生相当准确的预测，从而为实际湍流系统的无模型预测铺平了道路。
In this article, we investigate a dynamic control problem of a production-inventory system. Here, demands arrive at the production unit according to a Poisson process and are processed in an FCFS manner. The processing time of the customers' demand is the exponential distribution. The production manufacturers produce the items on a make-to-order basis to meet customer demands. The production is run until the inventory level becomes sufficiently large. We assume that an item's production time follows exponential distribution and the amount of time for the produced item to reach the retail shop is negligible. Also, we assume that no new customer joins the queue when there is a void inventory. This yields an explicit product-form solution for the steady-state probability vector of the system. The optimal policy that minimizes the discounted/average/pathwise average total cost per production is derived using a Markov decision process approach. We find optimal policy using value/policy iteration algorithms. Numerical examples are discussed to verify the proposed algorithms.
