Optimal linear quadratic Gaussian control for discrete time-varying system with simultaneous input delay and state/control-dependent noises
Optimal linear quadratic Gaussian control for discrete time-varying system with simultaneous input delay and state/control-dependent noises
复制标题
具有同步输入延迟和状态/控制相关噪声的离散时变系统的最优线性二次高斯控制
DOI：
10.1002/oca.2576
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发表时间：
2020
影响因子：
1.8
通讯作者：
Cui Wei
中科院分区：
文献类型：
--
作者：
Lu Xiao;Zhang Qiyan;Liang Xiao;Wang Haixia;Sheng Chunyang;Zhang Zhiguo;Cui Wei
研究了具有输入时滞和状态/控制相关噪声的离散时变系统的线性二次高斯（LQG）控制问题。当状态变量可精确观测时，首先利用变分法得到最大值原理。其次，借助所得到的最大值原理和数学归纳法，建立了系统状态与协状态之间的非齐次关系。指出非齐次关系是正、倒向随机差分方程的解。最后，基于FBSDES的解，以耦合Riccati方程的形式给出了最优LQG控制的充分必要条件。并给出了最优控制器的解析表达式。将所得结果应用于具有丢包的网络控制系统。数值例子说明了所提出的算法的有效性。
This article focuses on the problem of linear quadratic Gaussian (LQG) control for discrete time-varying system with input delay and state/control-dependent noises. When the state variables can be exactly observed, first, we obtain the maximum principle by applying the method of variation. Second, a nonhomogeneous relationship between the state and the costate is developed in virtue of the obtained maximum principle and the mathematical induction. It is noted that the nonhomogeneous relationship is the solution to the forward and backward stochastic difference equations (FBSDEs). Finally, based on the solution to the FBSDEs, a necessary and sufficient condition for the optimal LQG control is derived in terms of coupled Riccati equations. Moreover, the analytical expression of the optimal controller is presented. The derived results are applied in networked control systems with packet dropout. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.