LQG Control and Sensing Co-Design

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...

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Bibliographic Details
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
Online Access:Get full text
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Summary: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 .
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2020.2997661