一类准有色控制相关乘性噪声线性系统的最优输出反馈控制
Optimal output feedback control of a class of linear systems with quasi-colored control-dependent multiplicative noise
摘要：
研究了一类带有准有色控制相关乘性噪声的\a离散线性系统的均方最优输出反馈控制问题。所研究的噪声是新颖的，并表现出建模一类网络现象，如随机传输延迟的优势。最优输出反馈控制器的设计使用一个最优均方状态反馈增益和两个观测器增益，这是由均方稳定的解决方案的修改代数Riccati方程（MARE），假设对象是最小相位和左可逆的。一个必要和充分条件的存在性稳定解的MARE明确提出。结果表明，分离原理对该工作的最优控制设计具有一定的意义。结果也分别应用于具有随机传输时延和模拟擦除信道的网络系统的最优控制问题。
英文摘要：
This paper addresses the mean-square optimal control problem for \a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have advantage on modeling a class of network phenomena such as random transmission delays. The optimal output feedback controller is designed using an optimal mean-square state feedback gain and two observer gains, which are determined by the mean-square stabilizing solution to a modified algebraic Riccati equation (MARE), provided that the plant is minimum-phase and left-invertible. A necessary and sufficient condition for the existence of the stabilizing solution to the MARE is explicitly presented. It shows that the separation principle holds in a certain sense for the optimal control design of the work. The result is also applied to the optimal control problems in networked systems with random transmission delays and analog erasure channels, respectively.
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