Optimal capacity allocation for sampled networked systems

Abstract

We consider the problem of estimating the states of weakly coupled linear systems from sampled measurements.We assume that the total capacity available to the sensors to transmit their samples to a network manager in charge of the estimation is bounded above, and that each sample requires the same amount of communication. Our goal is then to find an optimal allocation of the capacity to the sensors so that the average estimation error is minimized.We show that when the total available channel capacity is large, this resource allocation problem can be recast as a strictly convex optimization problem, and hence there exists a unique optimal allocation of the capacity. We further investigate how this optimal allocation varies as the available capacity increases. In particular, we show that if the coupling among the subsystems is weak, then the sampling rate allocated to each sensor is nondecreasing in the total sampling rate, and is strictly increasing if and only if the total sampling rate exceeds a certain threshold.the same for all pair (i, j), for i = j, are made to simplify the notations of the paper, but are not necessary for the results to hold. The Brownian motions w i are pairwise independent and the ν i (kτ 0 ) are pairwise independent normal random variables. The w i and ν i are also assumed to be independent.We refer to the system described in (1) as subsystem S i . The samples y i (kτ 0 ), k ∈ N, are sent over a common channel to a network manager whose objective is to estimate the states x i of the subsystems S i , for all i = 1, . . . , N , from these samples. The network manager needs to decide the schedule with which it receives the samples in order to minimize the estimation error. Note that since the systems are coupled, the knowledge of y i can help with the estimation of x j , for i = j.

Joint Actuator-Sensor Design for Stochastic Linear Systems

“…We refer to [18] or Prop. 3 of [6] for a prove of the above inequalities. We also gave in [6] generic conditions on when the inequalities are strict.…”

“…3 of [6] for a prove of the above inequalities. We also gave in [6] generic conditions on when the inequalities are strict. If we let Φ(r, s) be defined as in (5), with K and Σ replace by K(r) and Σ(s), then we have the following fact: (A, c) detectable, we have…”

“…When the system is networked, comprised of several physical entities (such as a swarm of robots or unmanned aerial vehicles), allocation of communication resource can be also considered as an intrinsic parameter. Optimal resource allocation/communication scheduling has also been addressed widely in the literature (see, for example, [1]- [6]).…”

Optimal Sensor Precision for Multi-Rate Sensing for Bounded Estimation Error

“…K k and F are the design variables with tr (F ) ≤ γ d , M n and system parameter C k is defined in (18) and (10). The variable W is a diagonal matrix, which is user defined and serves as a normalizing weight on S k := R −1 k , where R k is defined in (12).…”

“…The proposed framework also impacts other important problems in sensing, such as sensor scheduling and selection. Existing algorithms for sensor scheduling [1]- [10] and selection [11]- [15] assume that the sensor's noise variance is given. The framework in this paper can be used to determine them optimally.…”