Many problems in economics and management science can be formulated as optimal control problems.Generally,we could use the Pontryagin maximum principle to analyze these problems.This approach often involves solving the two-point-boundary-value problem (TPBVP) which seldom admits the closed-form expression for the optimal solution.In addition,its analysis would become much more difficult if the uncertainty is introduced.Active disturbances rejection controller (ADRC) is a model-independent controller.It has good robustness and adaptability for the controlled systems with nonlinearity,large time delay,and high uncertainty.We notice that although the previous work has focused mainly on its application in industrial engineering,the basic idea of ADRC also reflects naturally the rational behavior of a decision maker in the face of dynamic optimization problems in economics and management science.This paper investigates a classical stochastic inventory control model under the framework of ADRC.First,we give a brief introduction of ADRC and the traditional approach used in the analysis of inventory control problems.We further demonstrate how an ADRC can be used to analyze a specific inventory control problem.In this model,ADRC is composed of three parts,including tracking differentiator,extended state observer,and nonlinear state feedback.Given a target inventory level,the tracking differentiator is used as an arrangement for the transition process.The extended state observer is used to obtain the actual output of the controlled system and to estimate its on-line derivatives of different orders.The nonlinear feedback control is constructed by the information obtained from the tracking differentiator and the extended state observer.Two typical cases,including constant demand and demand with seasonal change,are discussed in detail.The optimal production rates and the corresponding optimal inventory trajectories are obtained by ADRC.Moreover,they are compared to those obtained by the traditional method.Our findings show that if the demand function is a constant,the total cost of production and inventory by the approach of ADRC would be lower with a probability of about 45％ than the one obtained from the standard method of stochastic optimal control.This indicates that ADRC is highly effective in dealing with the controlled systems whose structures are completely known.On the other hand,if the demand function allows for an unknown seasonal element,the traditional method of dynamic optimization will no longer be valid for this case,but the approach of ADRC can still work very well to obtain satisfactory results.From the viewpoint of application,ADRC should be a powerful tool for solving a large class of control problems with or without uncertainties.%自抗扰控制(ADRC)是一种独立于模型的控制思想,尽管人们过去主要关注的是ADRC在工业控制领域中的应用,但其设计思路也比较自然地反映了决策者在动态优化问题中的理性分析过程.本文基于随机动态优化理论和ADRC两种不同方法,对比研究经典的随机生产库存模型.研究表明:当需求函数为常数时,ADRC给出的生产策略有近45％的概率比随机动态优化理论求解的生产策略带来的总成本更低;当需求函数含未知的季节性周期变动时,此时再利用随机最优控制理论无法求得最优生产策略的解析解,而ADRC仍然能够消除不确定环境带来的冲击,通过实时反馈获得满意的生产策略.因此,融入经济与管理科学问题的相关特点,合理地利用ADRC可能大大简化问题的分析难度,为随机动态优化问题提供一种新的分析思路.
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