Stochastic sensor scheduling via distributed convex optimization

Abstract

a b s t r a c tIn this paper, we propose a stochastic scheduling strategy for estimating the states of N discrete-time linear time invariant (DTLTI) dynamic systems, where only one system can be observed by the sensor at each time instant due to practical resource constraints. The idea of our stochastic strategy is that a system is randomly selected for observation at each time instant according to a pre-assigned probability distribution. We aim to find the optimal pre-assigned probability in order to minimize the maximal estimate error covariance among dynamic systems. We first show that under mild conditions, the stochastic scheduling problem gives an upper bound on the performance of the optimal sensor selection problem, notoriously difficult to solve. We next relax the stochastic scheduling problem into a tractable suboptimal quasi-convex form. We then show that the new problem can be decomposed into coupled small convex optimization problems, and it can be solved in a distributed fashion. Finally, for scheduling implementation, we propose centralized and distributed deterministic scheduling strategies based on the optimal stochastic solution and provide simulation examples.

Distributed zero‐gradient‐sum algorithm for convex optimization with time‐varying communication delays and switching networks

“…In this paper, we focus on a class of distributed convex optimization problem with the following optimization objective: where f i : R n → R is a local cost function and is assumed to be strongly convex; x ∗ ∈ R n is the optimal value of . This optimal problem widely exists in real‐world applications such as sensor scheduling, source localization, distributed active power optimal control in power systems, and so on. For the distributed optimization problem , a large number of work have been carried out.…”

“…The main idea is to estimate the optimal point by a consensus term plus a negative gradient term with deterministic or randomized iteration. 3,7 To date, many researchers apply the consensus-based distributed optimization algorithm to solve the problem (1) and present a lot of results. [8][9][10][11] However, the basis consensus-based subgradient algorithms need to select the diminishing step sizes, which lead to the slow convergence rate.…”

“…Thus far, there exist many works about the consensus problem in the presence of time delays 25 and switching networks, [26][27][28] where the average consensus or leader-follower consensus are extensively investigated. However, few works [29][30][31][32][33] have discussed the effects of communication delays and switching topologies on the optimization consensus problem (1).…”

Kalman Filtering with Optimally Scheduled Measurements in Bandwidth Limited Communication Media

“…Moreover, this work differs from [11] and [13] because they assume a distributed computation model, in which all or some sensors/processors can determine whether to transmit data (which is suited to contention-based networks). In this paper, on the other hand, it is assumed that network access is determined in a centralized manner, such as in field bus networks.…”

“…Note that, in contrast to the sensor selection problem [10], [11], which selects a number of sensors and discards the rest, sensor scheduling involves determining the order and frequency of sensors to be granted medium access; that is, none of the sensors is discarded.…”