LQG制御とセンシングの協調設計
LQG Control and Sensing Co-Design
限られたセンサ候補からコストを考慮してセンシングと制御を同時設計する問題を扱い、分離原理と近似優モジュラ集合関数最適化に基づく多項式時間アルゴリズムを提案した論文。
著者: Vasileios Tzoumas, Luca Carlone, George J. Pappas, Ali Jadbabaie
分類: math.OC, cs.MA, cs.RO, cs.SY, eess.SY, math.DS
原文アブストラクト
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.
