Minimal L2-Consistent Data-Transmission

TL;DR

This paper proposes a novel approach to minimize sensor-to-actuator transmissions in control systems while maintaining L2 gain constraints, using approximate causal factorization to improve solution feasibility.

Contribution

It introduces approximate causal factorization for rank minimization in control design, addressing limitations of nuclear norm heuristics and ensuring system stability.

Findings

Effective reduction in sensor-actuator transmissions demonstrated on a benchmark

Bounded degradation of L2 gain due to factorization error

Method improves feasibility over traditional nuclear norm approaches

Abstract

In this work, we consider non-collocated sensors and actuators, and we address the problem of minimizing the number of sensor-to-actuator transmissions while ensuring that the L2 gain of the system remains under a threshold. By using causal factorization and system level synthesis, we reformulate this problem as a rank minimization problem over a convex set. When heuristics like nuclear norm minimization are used for rank minimization, the resulting matrix is only numerically low rank and must be truncated, which can lead to an infeasible solution. To address this issue, we introduce approximate causal factorization to control the factorization error and provide a bound on the degradation of the L2 gain in terms of the factorization error. The effectiveness of our method is demonstrated using a benchmark.