信噪比约束信道上的最优线性控制
Optimal Linear Control over Channels with Signal-to-Noise Ratio Constraints
AI总结：
针对有色噪声和信噪比约束的信道，通过Youla参数化和谱分解求解凸优化问题，得到最优LTI控制器，并给出稳定化的充要条件。
摘要：
我们考虑一个网络控制系统，其中受随机扰动的线性时不变（LTI）被控对象通过具有有色噪声和信噪比（SNR）约束的通信信道进行控制。控制器基于输出反馈，由测量被控对象输出并通过信道传输的编码器，以及接收信道输出并发出控制信号的解码器组成。目标是在满足SNR约束的条件下稳定被控对象并最小化二次代价函数。研究表明，最优LTI控制器可以通过在Youla参数中求解凸优化问题并进行谱分解得到。待最小化的泛函由两项之和组成：第一项是经典线性二次控制问题中的代价，第二项是由信道噪声引起的新项。LTI控制器稳定化的SNR充要条件直接来自优化问题的约束。文中展示了如何通过半定规划近似该最小化问题。最后通过数值例子说明该解。
英文摘要：
We consider a networked control system where a linear time-invariant (LTI) plant, subject to a stochastic disturbance, is controlled over a communication channel with colored noise and a signal-to-noise ratio (SNR) constraint. The controller is based on output feedback and consists of an encoder that measures the plant output and transmits over the channel, and a decoder that receives the channel output and issues the control signal. The objective is to stabilize the plant and minimize a quadratic cost function, subject to the SNR constraint. It is shown that optimal LTI controllers can be obtained by solving a convex optimization problem in the Youla parameter and performing a spectral factorization. The functional to minimize is a sum of two terms: the first is the cost in the classical linear quadratic control problem and the second is a new term that is induced by the channel noise. %todo ta bort meningen? A necessary and sufficient condition on the SNR for stabilization by an LTI controller follows directly from a constraint of the optimization problem. It is shown how the minimization can be approximated by a semidefinite program. The solution is finally illustrated by a numerical example.
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