Rate of prefix-free codes in LQG control systems
Rate of prefix-free codes in LQG control systems
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LQG 控制系统中无前缀代码的比率
DOI：
10.1109/isit.2016.7541729
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
M. Skoglund
中科院分区：
文献类型：
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作者：
Takashi Tanaka;K. Johansson;T. Oechtering;H. Sandberg;M. Skoglund
在本文中，我们考虑了离散时间线性二次高斯（LQG）控制问题，其中的状态信息的植物被编码在一个可变长度的二进制码字在每一个时间步，和控制输入确定的基础上产生的码字在过去。我们推导出一个下界的速率达到所需的LQG控制性能的无前缀码的类。这个下界与某个有向信息表达式的下确界一致，并且可以用半定规划（SDP）计算。基于Silva等人的技术，我们还通过构造配备有具有减法抖动和Shannon-Fano编码的均匀量化器的控制器来提供最佳可实现速率的上界。所获得的下限和上限之间的差距小于0：754 r + 1比特/时间步长，而不管所需的LQG控制性能如何，其中r是通过SDP获得的信噪比矩阵的秩，其不大于状态的维数。
In this paper, we consider a discrete time linear quadratic Gaussian (LQG) control problem in which state information of the plant is encoded in a variable-length binary codeword at every time step, and a control input is determined based on the codewords generated in the past. We derive a lower bound of the rate achievable by the class of prefix-free codes attaining the required LQG control performance. This lower bound coincides with the infimum of a certain directed information expression, and is computable by semidefinite programming (SDP). Based on a technique by Silva et al., we also provide an upper bound of the best achievable rate by constructing a controller equipped with a uniform quantizer with subtractive dither and Shannon-Fano coding. The gap between the obtained lower and upper bounds is less than 0:754r + 1 bits per time step regardless of the required LQG control performance, where r is the rank of a signal-to-noise ratio matrix obtained by SDP, which is no greater than the dimension of the state.