# LQG Control and Sensing Co-Design

arXiv: https://arxiv.org/abs/1802.08376 · HTML: https://mlsanity.com/paper/1802.08376/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Feb 2018.

## Built on by (most cited first, 5 of 5)

- [Beyond Robustness: A Taxonomy of Approaches towards Resilient Multi-Robot Systems](https://mlsanity.com/paper/2109.12343/) (2021)
- [A Reinforcement Learning Approach to Sensing Design in Resource-Constrained Wireless Networked Control Systems](https://mlsanity.com/paper/2204.00703/) (2022)
- [To Compute or not to Compute? Adaptive Smart Sensing in Resource-Constrained Edge Computing](https://mlsanity.com/paper/2209.02166/) (2022)
- [CODEI: Resource-Efficient Task-Driven Co-Design of Perception and Decision Making for Mobile Robots Applied to Autonomous Vehicles](https://mlsanity.com/paper/2503.10296/) (2025)
- [Communication-Control Codesign for Large-Scale Wireless Networked Control Systems](https://mlsanity.com/paper/2410.11316/) (2024)

## Abstract (arXiv)

We investigate a Linear-Quadratic-Gaussian (LQG) control and sensing co-design problem, where one jointly designs sensing and control policies. We focus on the realistic case where the sensing design is selected among a finite set of available sensors, where each sensor is associated with a different cost (e.g., power consumption). We consider two dual problem instances: sensing-constrained LQG control, where one maximizes control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes sensor cost subject to performance constraints. We prove no polynomial time algorithm guarantees across all problem instances a constant approximation factor from the optimal. Nonetheless, we present the first polynomial time algorithms with per-instance suboptimality guarantees. To this end, we leverage a separation principle, that partially decouples the design of sensing and control. Then, we frame LQG co-design as the optimization of approximately supermodular set functions; we develop novel algorithms to solve the problems; and we prove original results on the performance of the algorithms, and establish connections between their suboptimality and control-theoretic quantities. We conclude the paper by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation.