Optimal Pursuit Strategies in Discrete-State Probabilistic Systems
Optimal Pursuit Strategies in Discrete-State Probabilistic Systems
复制标题
离散状态概率系统中的最优追踪策略
DOI：
10.1115/1.3657260
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发表时间：
1962
期刊：
影响因子：
--
通讯作者：
L. Zadeh
中科院分区：
文献类型：
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作者：
J. H. Eaton;L. Zadeh
控制理论中的一个基本问题是寻找一个输入，使给定的系统在最短的时间内，或者更一般地说，以最小的代价，从一个指定的初始状态到一个指定的终端状态。这类特殊问题在大约10年前开始受到相当大的关注，Hopkin [1]、Feldbaum [2]、Lerner [3]、Bushmann [4]和Rose [5]等人做出了重要贡献。然而，直到1955年，Bellman、Glicksberg和Gross [6]才给出了n阶线性系统在限幅输入下的一般解。一年后LS庞特里亚金[7]提出了一些关于他的-现在庆祝-最大值原理的初步结果。这一事件标志着苏联和美国对最优控制问题的浓厚兴趣的开始，尽管庞特里亚金的工作直到他最近与Boltyanskii和Gamkrelidze的论文的出版和翻译才在美国广为人知[8，9]。在有些不同的路线中，在过去的三年里，卡尔曼和伯特伦[10，11]，克拉索夫斯基[12]，德索尔[13]和拉萨尔[14]对最优控制问题做出了重大贡献，尽管最大值原理及其变化构成了巨大的理论兴趣，它们在产生连续时间非线性系统的显式控制策略方面的实际用途是相当有限的。相比之下，最优控制问题可以在有限离散状态系统（即有限状态时序机）的上下文中更有效地处理。这类问题可以看作是Bellman [15，16，17]，Kalaba [18]，霍华德[19]等研究过的马氏决策过程的一个特例。在这方面特别相关的是贝尔曼关于马尔可夫决策过程的论文[16]以及霍华德书的附录[19]。
ONE OF THE basic problems in control theory is that of finding an input which would take a given system from a specified initial state to a specified terminal state in minimum time or, more generally, at minimum cost. Special problems of this type began to receive considerable attention about ten years ago, with Hopkin [l], s Feldbaum [2], Lerner [3], Bushaw [4], and Rose [5], among others, making significant contributions. It was not until 1955, however, that a general solution for the case of an nth order linear system subjected to amplitude-limited input was given by Bellman, Glicksberg, and Gross [6]. One year later LS Pontryagin [7] presented some preliminary results concerning his—by now celebrated—maximum principle. This event marks the beginning of intense interest in the problem of optimal control both in the Soviet Union and the United, States, although Pontryagin's work did not become widely known in the United States until the publication and translation of his recent papers with Boltyanskii and Gamkrelidze [8, 9]. Among somewhat different lines, significant contributions to the problem of optimal control were made during the past three years by, among others, Kalman and Bertram [10, 11], Krasovskii [12], Desoer [13], and LaSalle [14], Although the maximum principle and its variations constitute a contribution of great theoretical interest, their practical usefulness in yielding explicit control policies for continuous-time nonlinear systems is quite l'mited. By contrast, the problem of optimal control can be treated much more effectively in the context of finite discrete-state systems, that is, finite-state sequential machines. Such problems can be regarded as a special case of Markoffian decision processes which have been studied by Bellman [15, 16, 17], Kalaba [18], Howard [19], and others. Of particular relevance in this connection is Bellman's paper on Markoffian decision processes [16], and the Appendix of Howard's book [19].