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Many modern controllers are composed of different components that communicatein real-time over some network with limited resources. In this work, we areinterested in designing a controller that can be implemented with a minimumnumber of sensor-to-actuator messages, while satisfying safety constraints overa finite horizon. For finite horizon problems, a linear time-varying controllerwith memory can be represented as a block-lower-triangular matrix. We show thatthe rank of this matrix exactly captures the minimum number of messages neededto be sent from the sensors to actuators to implement such a controller.Moreover, we introduce a novel matrix factorization called causal factorizationthat gives the required implementation. Finally, we show that the rank of thecontroller is the same as the rank of the Youla parameter, enabling the Youlaparametrization (or analogous parametrizations) to be used to design thecontroller, which reduces the overall design problem into a rank minimizationone over a convex set. Finally, convex relaxations for rank are used todemonstrate that our approach leads to 20-50% less messages on a simulationthan a benchmark method.

A Low Rank Approach to Minimize Sensor-to-Actuator Communication in Finite Horizon Output Feedback