LQG Control and Sensing Co-Design

• Published in: IEEE transactions on automatic control Vol. 66; no. 4; pp. 1468 - 1483
• Main Authors: Tzoumas, Vasileios, Carlone, Luca, Pappas, George J., Jadbabaie, Ali
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Aerospace engineering; algorithm design and analysis; Algorithms; Approximation algorithms; autonomous systems; Co-design; computational complexity; Constraints; Estimation; Linear quadratic Gaussian control; Mathematical analysis; multiagent systems; Optimization; Polynomials; Power consumption; resource management; Robot control; Robot sensing systems; Sensor systems; Sensors; Signal processing algorithms
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2020.2997661

We investigate a linear-quadratic-Gaussian (LQG) control and sensing codesign 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 a control performance subject to a sensor cost budget, and minimum-sensing LQG control, where one minimizes a sensor cost subject to performance constraints. We prove that 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, which partially decouples the design of sensing and control. Then, we frame LQG codesign 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 article by discussing two applications, namely, sensing-constrained formation control and resource-constrained robot navigation .