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

Abstract
Many modern controllers are composed of different components that communicate in real-time over some network with limited resources. In this talk, we are interested in designing a controller that can be implemented with a minimum number of sensor-to-actuator messages, while satisfying safety constraints over a finite horizon. For finite horizon problems, a linear time-varying controller with memory can be represented as a block-lower-triangular matrix. We show that the rank of this matrix exactly captures the minimum number of messages needed to be sent from the sensors to actuators to implement such a controller. Moreover, we introduce a novel matrix factorization called causal factorization that gives the required implementation. Finally, we show that the rank of the controller is the same as the rank of the Youla parameter, enabling the Youla parametrization (or analogous parametrizations such as system level synthesis) to be used to design the controller, which reduces the overall design problem into a rank minimization one over a convex set. Finally, convex relaxations for rank are used to demonstrate that our approach leads to 20-50% less messages on a simulation than a benchmark method.

Bio
Jakob Nylof received a BSc in Engineering Physics from KTH Royal Institute of Technology and is currently completing a MSc in Mathematics from the same institution, graduating in June 2024. His master thesis is about Q-learning in continuous time, supervised by Prof. Boualem Djehiche. During his studies, he has completed two research internships: one at KTH under supervision of Prof. Karl H. Johansson on quantized average consensus algorithms and one at the University of Michigan supervised by Prof. Necmiye Ozay on minimizing sensor-actuator messages in finite-horizon output feedback, which each led to publications. He has also completed an exchange semester at ETH Zürich while studying physics, where his courses were centered around quantum computation.