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This study addresses the challenge of selecting sensors for linear time-varying (LTV) systems dynamically. We present a framework that designs an online sparse sensor schedule with performance guarantees using randomized algorithms for large-scale LTV systems. Our approach calculates each sensor’s contribution at each time in real-time and immediately decides whether to keep or discard the sensor in the schedule, with no possibility of reversal. Additionally, we provide new performance guarantees that approximate the fully-sensed LTV system with a multiplicative approximation factor and an additive one by using a constant average number of active sensors at each time. We demonstrate the validity of our findings through several numerical examples. 

In this paper, we consider the problem of sensor selection for discrete-time linear dynamical networks. We develop a framework to design a sparse sensor schedule for a given large-scale linear system with guaranteed performance bounds using a learning-based algorithm. To sparsify the sensors in both time and space, we build our combinatorial optimization problems based on the notion of systemic controllability/observability metrics for linear dynamical networks with three properties: monotonicity, convexity, and homogeneity with respect to the controllability/observability Gramian matrix of the network. These combinatorial optimizations are inherently intractable and NP-hard. However, solving a continuous relaxation for each optimization is considered best practice. This is achievable since we constructed the objective based on the systemic metrics, which are convex. Furthermore, by leveraging recent advances in sparsification literature and regret minimization, we then round the fractional solution obtained by the continuous optimization to achieve a (1+epsilon) approximation sparse schedule that chooses on average a constant number of sensors at each time, to approximate all types of systemic metrics.