| Abstract: | The performance of estimation and control algorithms depend on the available sensors, actuators and their precisions. While instruments with higher precisions provide better performance, it may lead to unnecessarily expensive designs due to higher costs of high precision components. Moreover, the combinatorial problem of selecting an optimal set of sensors and/or actuators becomes nontrivial for large-scale systems. Most engineering system designs, with stringent accuracy requirements, specify an error budget for subsystem accuracy. In control system design, such an error budget needs to be met by state or output estimation algorithms. In such a case, the designer may select unnecessarily precise sensors to meet the accuracy goal, resulting in unnecessarily expensive designs. Also, higher precision can cause interference for other sensors in the environment, such as RADARS, resulting in degradation in the overall system's performance. This work presents a framework for co-designing a sparse sensing network with the least precise sensors and the estimator (observer or filter) that guarantees the prescribed H₂ or H∞ estimation accuracy for linear time-invariant systems. Convex optimization problems for minimizing sensor precisions are formulated for continuous and discrete-time linear time-invariant systems, with and without model uncertainties. This work also presents new scalable procedures, based on the alternating direction method of multipliers (ADMM), to solve the proposed optimization problems, which can be quite large for realistic engineering problems. Different heuristics for determining a sparse sensor set with the least precise sensors are discussed, and their performances are compared using numerical simulations. The problem formulation addressing the design of sparse actuation architecture is also presented. However, the co-design of sparse actuation with optimal precision suffers from theoretical challenges such as non-convexity of optimization problems. The ₂application of the proposed framework is demonstrated using numerical examples |
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