LQG Control and Sensing Co-Design

• 成果类型: Article
• 署名作者: Tzoumas, Vasileios; Carlone, Luca; Pappas, George J.; Jadbabaie, Ali
• 署名单位: Massachusetts Institute of Technology (MIT); University of Pennsylvania
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2997661
• 发表日期: 2021
• 页码: 1468-1483
• 关键词: Optimization; Approximation algorithms; Robot sensing systems; Sensor systems; estimation; Signal processing algorithms; Aerospace engineering; Autonomous systems; Algorithm design and analysis; computational complexity; multiagent systems; resource management

摘要

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.