In this paper, we study the Integrated Communication and Control (ICAC) problem. Specifically, we investigate how messages can be transmitted from the controller/encoder to the observer/decoder through the control signal in Multiple-Input Multiple-Output (MIMO) vector-state Linear Quadratic Gaussian (LQG) systems under control constraints. We provide a computable capacity expression using semidefinite programming. We further show that it is possible to transmit data at a nonzero rate over an LQG system while maintaining the same optimal control cost as in the case where no information message are transmitted. Finally, we discuss how this framework generalizes communication over MIMO Gaussian channels with feedback, both with and without InterSymbol Interference (ISI).

翻译：本文研究了集成通信与控制问题。具体而言，我们探讨了在控制约束条件下，多输入多输出向量状态线性二次高斯系统中如何通过控制信号将消息从控制器/编码器传输至观测器/解码器。我们利用半定规划方法给出了可计算的容量表达式。进一步证明，在保持与无信息传输情形相同最优控制成本的前提下，通过LQG系统仍能以非零速率传输数据。最后，我们讨论了该框架如何推广到具有反馈的多输入多输出高斯信道通信场景，包括存在与不存在符号间干扰两种情况。