Minimax Control of Discrete Time Stochastic Systems
Minimax Control of Discrete Time Stochastic Systems
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DOI：
10.1137/0302034
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发表时间：
1964
期刊：
影响因子：
--
通讯作者：
D. Sworder
中科院分区：
文献类型：
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作者：
D. Sworder
1.导论.在本文中，一个对象的控制策略与随机元素的合成将进行研究。与要控制的对象相关联的随机性可以通过几种不同的方式来实现。例如，要使用的控制规则可以明确地依赖于被加性随机噪声污染的系统的输出测量。另一方面，也可能是描述过程的方程中包含的某些参数是随机变量。如果性能标准是系统状态和控制策略的非负泛函，那么人们可能希望以使该泛函的期望值最小化的方式选择控制。在过程的某些参数不完全指定的情况下，这导致了最优控制规则可能是这些未确定参数的函数的概念问题。由于性能指标现在只提供了控制策略的部分排序，因此必须选择一个辅助标准来为设计者提供“最佳”控制。在下文中，我们将广泛使用Blackwell和Girshick [1]提出的博弈论的定义和结果。它将表明，控制问题的基本结构特性，可以制定由这个理论提供的框架内。
1. Introduction. In this paper the synthesis of a control policy for an object with stochastic elements will be investigated. The randomness associated with the object to be controlled can come about in several different ways. For example, the control rule to be used may depend explicitly on output measurements from the system whichare contaminated with additive random noise. On the other hand, it might be that some ofthe parameters which are contained in the equations describing the process are random variables. If the criterion of performance is a nonnegative functional of the system state and of the control policy, one might hope to choose the control in such a way that the expected value of this functional is minimized. In the case where certain parameters of the processare incompletely specified, this leads to the conceptual problem that an optimal control rule may be a function of these undetermined parameters. Since the performance index now provides only a partial ordering of control policies, an auxiliary criterion must be chosen to provide the designer with a" best" control. In what follows we will make extensive use of the definitions and results from thetheory ofgames as presented by Blackwell and Girshick [1]. It will be shown that the basic structural properties of the control problem can be formulated within the framework provided by this theory.