初始状态不确定性下H-infinity控制中的速率-代价权衡
Rate-cost Trade-offs in H-infinity Control with Initial State Uncertainty
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中文总结 AI 辅助
本文研究数字通信信道下H-infinity控制中数据速率与性能的权衡，针对标量系统建立速率下界并证明对数量化的自然性，提出可达方案且在高速率极限下渐近最优。
中文摘要 AI 辅助
我们考虑了在观测器与控制器之间存在数字通信信道时的H-infinity控制问题，并研究了所需通信数据速率与H-infinity性能之间的基本权衡。系统遵循线性动力学且没有加性内部噪声，因此不确定性仅限于初始状态。对于标量系统，利用确定性零时刻覆盖论证，我们建立了在给定H-infinity代价下所需数据速率的下界，并论证了对数量化（Elia, 2000）为何是自然选择。我们进一步提出了一种可达性方案，并表明对于标量系统，在高数据速率极限下，其速率渐近地匹配逆命题。
英文摘要
We consider the problem of H-infinity control in the presence of a digital communication channel between the observer and the controller and investigate the fundamental trade-off between the required communication data rate and H-infinity performance. The system follows linear dynamics and has no additive internal noise, so that the uncertainty is confined to the initial state. For the scalar system, using a deterministic time-zero covering argument, we establish a lower bound on the required data rate for a given H-infinity cost and demonstrate why logarithmic quantization (Elia, 2000) is a natural choice. We further develop an achievability scheme and show that, for the scalar system, its rate matches the converse asymptotically in the high-data-rate limit.
发表机构
- California Institute of Technology（加州理工学院）
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