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首页> 外文期刊>IEEE Transactions on Automatic Control >Embedding adaptive JLQG into LQ martingale control with a completely observable stochastic control matrix
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Embedding adaptive JLQG into LQ martingale control with a completely observable stochastic control matrix

机译：利用完全可观察的随机控制矩阵将自适应JLQG嵌入LQ ting控制

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摘要

With jump linear quadratic Gaussian (JLQG) control, one refers to the control under a quadratic performance criterion of a linear Gaussian system, the coefficients of which are completely observable, while they are jumping according to a finite-state Markov process. With adaptive JLQG, one refers to the more complicated situation that the finite-state process is only partially observable. Although many practically applicable results have been developed, JLQG and adaptive JLQG control are lagging behind those for linear quadratic Gaussian (LQG) and adaptive LQG. The aim of this paper is to help improve the situation by introducing an exact transformation which embeds adaptive JLQG control into LQM (linear quadratic Martingale) control with a completely observable stochastic control matrix. By LQM control, the authors mean the control of a martingale driven linear system under a quadratic performance criterion. With the LQM transformation, the adaptive JLQG control can be studied within the framework of robust or minimax control without the need for the usual approach of averaging or approximating the adaptive JLQG dynamics. To show the effectiveness of the authors' transformation, it is used to characterize the open-loop-optimal feedback (OLOF) policy for adaptive JLQG control.
机译：对于跳跃线性二次高斯（JLQG）控制，是指根据线性高斯系统的二次性能准则进行的控制，该线性高斯系统的系数是完全可观察到的，而它们是根据有限状态Markov过程跳跃的。对于自适应JLQG，人们指的是更为复杂的情况，即有限状态过程只能部分观察到。尽管已开发出许多实际可应用的结果，但是JLQG和自适应JLQG控制仍落后于线性二次高斯（LQG）和自适应LQG的控制。本文的目的是通过引入精确的变换来帮助改善这种情况，该变换将具有完全可观察的随机控制矩阵的自适应JLQG控制嵌入到LQM（线性二次Mar）控制中。通过LQM控制，作者的意思是在二次性能标准下控制mar驱动的线性系统。通过LQM变换，可以在鲁棒或最小极大值控制的框架内研究自适应JLQG控制，而无需平均或逼近自适应JLQG动态的常规方法。为了显示作者转换的有效性，该方法用于表征自适应JLQG控制的开环最佳反馈（OLOF）策略。

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