Optimal scheduling strategy for networked estimation with energy harvesting

Ashutosh Nayyar; Marcos M. Vasconcelos; Mukul Gagrani; Urbashi Mitra

REVIEW 1 major objections 6 minor 34 references

Optimal scheduling strategy for networked estimation with energy harvesting

T0 review · 1 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read For two symmetric unimodal sources, the globally optimal scheduling-estimation strategy is a threshold rule that transmits the observation farthest from its center only when its distance exceeds a threshold depending on time and battery…

desk verdict The two-sensor theorem is the real thing, but the missing finite-second-moment assumption and unproved Section IX extensions need to be addressed before this is taken as fully correct. read the letter →

arxiv 1908.06070 v1 pith:IYCSUZK7 submitted 2019-08-16 eess.SY cs.SY

Marcos M. Vasconcelos , Mukul Gagrani , Ashutosh Nayyar , Urbashi Mitra This is my paper · ORCID

classification eess.SYcs.SY

keywords networkedestimationenergyharvestingsensorschedulingremoteteamdecisioncommoninformationthresholdpolicysymmetricunimodaldistributions

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how a battery-powered scheduler should decide which of two sensors' measurements to send over a one-packet-per-slot network, while the estimators try to minimize mean-squared error plus transmission cost. The authors claim that, for independent sources with symmetric and unimodal distributions, this joint scheduling-estimation problem has an exact globally optimal solution, despite the non-convexity created by signaling. The optimal scheduler transmits the observation farthest from its distribution center only when that distance clears a threshold set by the remaining time and the battery level; the optimal estimators use the received sample when it arrives and the distribution center otherwise. The paper also gives a backwards recursion to compute the thresholds and extends the result to any number of sensors and to unequal weights and communication costs. If the claim is right, a team problem that is usually intractable becomes a simple offline threshold design.

What carries the argument

The central proof device is the combination of an information-structure expansion with the common information approach. Adding the scheduler's energy history and past transmission outcomes to each estimator's information creates common information among all decision makers, allowing the team problem to be re-expressed as a single coordinator POMDP whose state is $(X_t,E_t)$ and whose belief on $X_t$ is simply the product density $\pi_1\pi_2$. The coordinator's dynamic program reduces, for fixed estimation defaults, to a finite-dimensional optimization over those defaults. The Hardy-Littlewood rearrangement inequality then closes the argument: after centering, the error-minimization term is a symmetric decreasing function of the distance from the default, so the zero default—the source center—is a global minimizer. This rearrangement step is what converts an infinite-dimensional team problem into a scalar threshold rule.

What would settle it

Run a one-shot version with two independent scalar sources whose densities are not symmetric and unimodal (for example, one exponential and one bimodal mixture), and search numerically over estimation defaults and thresholds for the best achievable cost; if any nonzero default beats the center default when the other sensor's packet is transmitted, Lemma 5 collapses. A sharper test is to evaluate the auxiliary function $J_t^e(\tilde x_t)$ of Eq. (79) at $\tilde x_t=0$ and at small perturbations: under the paper's assumption the minimum must occur at zero, so any perturbation that lowers the cost is a counterexample.

Watch

Extended reading notes

Core claim

The paper claims that the sequential team problem—two sensors feeding two estimators over a shared network that carries one packet per time slot, with a scheduler whose finite battery harvests random energy—is exactly solvable. Provided each source density is symmetric and unimodal around its center $a_i$ in the radial sense of Definition 1, the strategy profile $(f^\star, g_1^\star, g_2^\star)$ of Theorem 1 is globally optimal for Problem 1. The scheduler's rule is a distance threshold: at time $t$ with energy $e$, it sends nothing if both $\|x_i-a_i\| \le \tau_t^\star(e)$, and otherwise it sends the sensor with the largest distance $\|x_i-a_i\|$. The estimators use $x_i$ when a packet arrives and $a_i$ when none does. The proof expands the estimators' information so that a coordinator with common information can solve a POMDP, then uses the Hardy-Littlewood rearrangement inequality to show the center default is globally optimal; because the optimal solution is adapted to the original information structure, it is also optimal there.

Load-bearing premise

The entire result depends on each source distribution being symmetric and unimodal in the strong sense that points closer to the center always have density at least as high as points farther away, together with each source having a finite second moment; if those fail, the threshold policy may stop being globally optimal.

Editorial extensions

If this is right

The optimal thresholds can be computed offline by backward recursion, so the scheduler only needs to compare current distances with a precomputed table indexed by time and battery level.
When the remaining battery energy exceeds the remaining time slots, the optimal threshold is zero and the scheduler always transmits the observation farthest from its center; as the battery depletes, it waits for observations of increasingly large magnitude.
The optimal estimators are memoryless defaults: use the received sample if it arrives, otherwise use the known center; no signaling benefit changes the default estimate.
The same threshold structure holds for any number of sensors: transmit the argmax over all distances if the maximum exceeds the threshold.
With unequal sensor weights and communication costs, the no-transmission region becomes a rectangle defined by two thresholds and the boundary between transmitting sensor 1 and sensor 2 becomes a hyperbola-like curve.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Editorial inference: for correlated or Markov sources, the paper's rearrangement step fails, but the threshold rule remains a natural heuristic, and its suboptimality gap could be quantified against a dynamic-programming lower bound.
Editorial inference: because the value-of-information curves in the examples are nonmonotone in battery capacity, the threshold recursion could be repurposed as a battery-sizing tool that selects the capacity maximizing the benefit of closed-loop scheduling.
Editorial inference: the information-expansion-plus-common-information argument is not tied to the squared-error cost, so similar threshold policies are plausible for other symmetric performance measures, such as $p$-norm errors, with the threshold recursion adjusted accordingly.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: the two-sensor theorem is the real thing, provided you add the unstated finite-second-moment assumption. The extensions in Section IX are asserted, not proved, and should be downgraded or completed.

What's new: this is the first finite-horizon jointly optimal scheduling/estimation policy for two non-collocated estimators with an energy-harvesting scheduler and i.i.d. symmetric unimodal sources. It moves past the one-shot result and the single-sensor battery result by coupling the scheduling decision to both observations and the battery state. The proof is a clean combination of information-structure expansion and common-information POMDP, with a rearrangement inequality to pin the estimator prescription to zero. I checked Lemmas 4 and 5: the pointwise minimization gives the threshold, and the Hardy–Littlewood step is executed correctly for sources with finite second moments. The threshold recursion is well-defined and the numerics illustrate the policy.

Soft spots. First, Theorem 1 states only symmetry and unimodality, but the MSE objective and Lemma 5 need finite second moments. A Cauchy source satisfies the stated assumptions and gives infinite cost under every policy; the theorem becomes vacuous and the rearrangement argument lacks integrability. This is a minor fix—add one line to Theorem 1 and the extensions—but it is a real gap. Second, Section IX-A asserts the N-sensor case without proof, and IX-B gives a formula for unequal weights/costs without derivation. These may be true, but as written they are unsupported claims and should be either proved or explicitly labeled as conjectures. Third, the monotonicity of V_t in e is asserted with an intuitive argument; acceptable, but the proof leans on it.

Overall: the central result holds up under the right assumptions. The paper deserves a serious referee. I'd send it out with a request to add the moment condition and to rewrite Section IX as conjectures if no proofs are provided.

Referee Report

1 major / 6 minor

Summary. The paper studies a finite-horizon remote estimation problem with two sensor-estimator pairs sharing a communication channel managed by an energy-harvesting scheduler. The scheduler observes both source realizations and decides, at each time, which (if any) measurement is transmitted, subject to a battery state. The goal is to jointly minimize the sum of mean-squared estimation errors and a transmission cost. The main contribution is a structural result: when the source densities are symmetric and unimodal around their means, the optimal policy is a threshold policy that transmits the source with the largest deviation from its mean only if that deviation exceeds a threshold depending on time and energy; estimators use the received value or the source mean otherwise. The proof uses an expansion of the estimators' information, a common-information-based POMDP formulation, and a rearrangement inequality to show that the optimal estimator prescriptions are the source means. A recursive algorithm computes the thresholds, and numerical examples compare the policy with a blind scheduling benchmark.

Significance. If established, this is a notable exact solution to a non-convex team decision problem with non-classical information structure and energy constraints. The result extends prior one-shot and single-sensor analyses. The proof is largely coherent: Lemma 4's pointwise minimization and Lemma 5's rearrangement argument are valid under the stated assumptions, and the threshold computation is explicit. The paper would be strengthened by stating the necessary finite-second-moment condition, which is currently implicit. The techniques (information structure expansion, common information) are of interest to the networked estimation community.

major comments (1)

[Theorem 1, Eq. (8)] The theorem assumes only that π1 and π2 are symmetric and unimodal in the sense of Definition 1. This does not guarantee that the cost functional J in Eq. (8) is finite: if a source has infinite second moment (e.g., a Cauchy distribution), then at every time the untransmitted source contributes E[||X_i - a_i||^2] = ∞, making J infinite for every admissible strategy. Under those conditions the global optimality statement is vacuous and the minimization in Eq. (8) is not well-posed as a finite-valued problem. The proof of Lemma 5 in Appendix B, specifically the Hardy-Littlewood step in Eq. (86) and the subsequent integration over the other source, presumes finite second moments. Please add the explicit assumption E[||X_i - a_i||^2] < ∞ for i=1,2 to Theorem 1, and note that Section IX inherits this requirement.

minor comments (6)

[Section IX-B, Eqs. (68)-(69)] The claimed global optimality for the unequal-weights and unequal-communication-cost extension is asserted without proof; the paper should either provide a proof or explicitly label this as a conjecture.
[Section IX-A] The statement that Theorem 1 extends to an arbitrary number of sensors is given without proof; a brief indication of how the proof in Lemmas 4-5 generalizes would be helpful.
[Section VI, Lemma 4] The definition of the threshold τ*_t(e) in Lemma 4 contains a stray '1' after the square root, and the tie-breaking rule for arg max in Section II-D should be explicitly invoked in Theorem 1 to make (11) well-defined when ‖x1-a1‖ = ‖x2-a2‖.
[Section VIII, Eq. (60)] The displayed equation for the blind scheduling strategy is missing a closing brace, and the text 'the is given by' should be corrected.
[Section I] There are typographical errors, including 'transmismitted' and 'accross,' that should be corrected in a revision.
[Appendix B, proof of Lemma 5] The monotonicity of Vπ_t(e) in e is used but not proved; a brief sentence justifying that more energy cannot increase the optimal cost would be useful.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the threshold policy is derived from the dynamic program and the estimation structure is proven self-contained.

full rationale

Theorem 1's scheduling strategy is not assumed or fitted: Lemma 4 derives the threshold policy from a pointwise minimization of the coordinator's dynamic-programming instantaneous cost, and the threshold tau*_t(e) is defined as sqrt(C^1_{t+1}(e)-C^0_{t+1}(e)) in terms of the value functions C^0 and C^1, which are computed recursively by Algorithm 1 rather than chosen to force the result. Lemma 5 proves that the zero estimate prescription is a global minimizer of Eq. (43) using the Hardy-Littlewood rearrangement inequality; this proof does not presuppose the form of f* or g*. The information-structure expansion and coordinator POMDP are used to convert the team problem into a single-agent dynamic program, after which the optimal solution is shown to be adapted to the original information structure, so the relaxed problem does not smuggle in the conclusion. Citations to the authors' prior works [10], [20], and [30] describe related techniques or prior one-shot results, but the proof in the paper reproduces the needed arguments and does not rely on those citations as load-bearing. The only concern identified is a correctness/assumption gap, not circularity: Theorem 1 states only symmetry and unimodality with no finite-second-moment assumption, so sources such as Cauchy distributions make the MSE objective in Eq. (8) infinite and the Hardy-Littlewood step in Eq. (86) non-integrable. That is a matter of missing hypotheses or proof validity, not an equivalence between inputs and outputs. Consequently, no circular step is present and the paper's derivation chain is self-contained with respect to its stated model assumptions.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the radially monotone source model, the independence assumptions that make the belief state constant, finite second moments for a well-posed MSE objective, and two standard mathematical tools (POMDP dynamic programming and Hardy-Littlewood rearrangement). The coordinator in Section V is a proof device, not a claimed new physical or mathematical entity; no new forces, particles, dimensions, or conserved quantities are introduced.

assumptions (6)

domain assumption Source densities π1,π2 are symmetric and unimodal around their centers (radial monotonicity).
Invoked in Definition 1 and used in Lemma 5/Appendix B to apply Hardy-Littlewood; without it the zero estimate need not be optimal.
domain assumption Sources are independent across sensors and i.i.d. in time, and the harvest process is independent of sources.
Section II-A; this makes the belief state a fixed product density in Eq. (36) and the state process Markov.
domain assumption Each source has finite second moment.
The MSE objective in Eq. (8) is only finite under this condition; the paper does not state it explicitly.
standard math Standard dynamic programming and POMDP optimality results.
Lemmas 1 and 3 rely on standard MDP/POMDP results [31].
standard math Hardy-Littlewood rearrangement inequality.
Theorem 2 in Appendix A is the key inequality behind Lemma 5.
domain assumption Noiseless unicast channel model with erasure value ∅.
Section II-A defines Y_i^t as X_i^t when transmitted and ∅ otherwise; this deterministic noiseless model underpins the estimator rule in Eq. (12).

how reviews work

0 comments

Cite this review

Pith. "Pith review of Optimal scheduling strategy for networked estimation with energy harvesting." pith.science (2026). https://pith.science/paper/IYCSUZK7

@misc{pith2026190806070,
  author       = {Pith},
  title        = {Pith review of: Optimal scheduling strategy for networked estimation with energy harvesting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IYCSUZK7}},
  note         = {Machine review of arXiv:1908.06070}
}

read the original abstract

Joint optimization of scheduling and estimation policies is considered for a system with two sensors and two non-collocated estimators. Each sensor produces an independent and identically distributed sequence of random variables, and each estimator forms estimates of the corresponding sequence with respect to the mean-squared error sense. The data generated by the sensors is transmitted to the corresponding estimators, over a bandwidth-constrained wireless network that can support a single packet per time slot. The access to the limited communication resources is determined by a scheduler who decides which sensor measurement to transmit based on both observations. The scheduler has an energy-harvesting battery of limited capacity, which couples the decision-making problem in time. Despite the overall lack of convexity of the team decision problem, it is shown that this system admits globally optimal scheduling and estimation strategies under the assumption that the distributions of the random variables at the sensors are symmetric and unimodal. Additionally, the optimal scheduling policy has a structure characterized by a threshold function that depends on the time index and energy level. A recursive algorithm for threshold computation is provided.

Figures

Figures reproduced from arXiv: 1908.06070 by the authors.

**Figure 1.** Schematic diagram for the remote sensing system two sensor-estimator pairs with an energy harvesting scheduler. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗

**Figure 2.** Partition of the observation space used to illustrate the issue of signaling in problems of networked estimation. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Pictorial representation of the optimal scheduling [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Optimal threshold function for the scheduling of two i.i.d. standard Gaussian sources. The threshold is a function of the energy level [PITH_FULL_IMAGE:figures/full_fig_p017_4.png]

**Figure 5.** Figure 5: Optimal threshold function for the scheduling of two i.i.d. standard Gaussian sources with energy harvesting. The threshold is a function [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

**Figure 6.** Figure 6: Comparison between the performances of the optimal open-loop and closed-loop strategies as a function of the battery capacity, [PITH_FULL_IMAGE:figures/full_fig_p018_6.png]

**Figure 7.** Figure 7: Value of Information in the numerical example as a function of the battery capacity. [PITH_FULL_IMAGE:figures/full_fig_p019_7.png]

**Figure 8.** Figure 8: Optimal scheduling decision region for a cost function with unequal weights and communication costs. Notice that the boundaries [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]

**Figure 9.** Figure 9: Conceptual plot of G e t (x˜t; xt) as a function of x 1 t while keeping its remaining arguments fixed. This figure illustrates that when the norm of x˜ 1 t tends to infinity the function remains bounded. Using the fact that X1 t and X2 t are independent, and the functi…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

34 extracted references · 34 canonical work pages

[1]

Cyber–physical systems: A perspective at the centennial,

K.-D. Kim and P. R. Kumar, “Cyber–physical systems: A perspective at the centennial,” Proceedings of the IEEE, vol. 100, pp. 1287–1308, May 2012

work page 2012
[2]

Bemporad, M

A. Bemporad, M. Heemels, and M. Johansson, Networked control systems . Hidelberg: Springer, 2010, vol. 406

work page 2010
[3]

Optimal estimation over the collision channel,

M. M. Vasconcelos and N. C. Martins, “Optimal estimation over the collision channel,” IEEE Transactions on Automatic Control , vol. 62, no. 1, pp. 321–336, January 2017

work page 2017
[4]

Optimal remote estimation of discrete random variables over the collision channel,

——, “Optimal remote estimation of discrete random variables over the collision channel,” IEEE Transactions on Automatic Control , vol. 64, no. 4, pp. 1519 – 1534, April 2019

work page 2019
[5]

Yuksel and T

S. Yuksel and T. Basar, Stochastic Networked Control Systems . Springer, 2013

work page 2013
[6]

KNOW-ME: a case study in wireless body area sensor network design,

U. Mitra, A. Emken, S. Lee, M. Li, V . Rozgic, G. Thatte, H. Vathsangam, D.-S. Zois, M. Annavaram, S. Narayanan, M. Levorato, D. Spruijt-Metz, and G. S. Sukhatme, “KNOW-ME: a case study in wireless body area sensor network design,” IEEE Communications Magazine, vol. 50, no. 5, pp. 116–125, May 2012

work page 2012
[7]

Energy-efﬁcient, heterogeneous sensor selection for physical activity detection in wireless body area networks,

D.-S. Zois, M. Levorato, and U. Mitra, “Energy-efﬁcient, heterogeneous sensor selection for physical activity detection in wireless body area networks,” IEEE Transactions on Signal Processing , vol. 61, no. 7, pp. 1581–1594, April 2013

work page 2013
[8]

Sequential decision-making in healthcare iot: Real-time health monitoring, treatments and interventions,

D.-S. Zois, “Sequential decision-making in healthcare iot: Real-time health monitoring, treatments and interventions,” in IEEE 3rd World Forum on Internet of Things , 2016

work page 2016

Show all 34 references

[9]

Remote state estimation with communication costs for ﬁrst-order LTI systems,

G. M. Lipsa and N. C. Martins, “Remote state estimation with communication costs for ﬁrst-order LTI systems,” IEEE Transactions on Automatic Control, vol. 56, no. 9, pp. 2013–2025, September 2011

2013
[10]

Optimal strategies for communication and remote estimation with an energy harvesting sensor,

A. Nayyar, T. Basar, D. Teneketzis, and V . Veeravalli, “Optimal strategies for communication and remote estimation with an energy harvesting sensor,” IEEE Transactions on Automatic Control , vol. 58, no. 9, pp. 2246–2260, September 2013

2013
[11]

Transmission scheduling for remote state estimation and control with an energy harvesting sensor,

A. S. Leong, S. Dey, and D. E. Quevedo, “Transmission scheduling for remote state estimation and control with an energy harvesting sensor,” Automatica, vol. 91, pp. 54–60, May 2018

2018
[12]

Stability analysis of networked control systems,

G. C. Walsh, H. Ye, and L. G. Bushnell, “Stability analysis of networked control systems,”IEEE Transaction on Control Systems Technology, vol. 10, no. 3, pp. 438–446, May 2002

2002
[13]

Scheduling of event-triggered controllers on a shared network,

A. Cervin and T. Henningsson, “Scheduling of event-triggered controllers on a shared network,” in Proceedings of the 47th IEEE Conference on Decision and Control , 2008, pp. 3601–3606

2008
[14]

Networked estimation under contention-based medium access,

M. Rabi, L. Stabellini, A. Proutiere, and M. Johansson, “Networked estimation under contention-based medium access,” International Journal of Robust and Nonlinear Control , vol. 20, no. 2, pp. 140–155, January 2010

2010
[15]

Random access design for wireless control systems,

K. Gatsis, A. Ribeiro, and G. J. Pappas, “Random access design for wireless control systems,” Automatica, vol. 91, pp. 1–9, May 2018

2018
[16]

Multiple loop self-triggered model predictive control for network scheduling and control,

E. Henriksson, D. E. Quevedo, E. G. W. Peters, H. Sandberg, and K. H. Johansson, “Multiple loop self-triggered model predictive control for network scheduling and control,” IEEE Transaction on Control Systems Technology , vol. 23, no. 6, pp. 2167–2181, 2015

2015
[17]

Price-based adaptive scheduling in multi-loop control systems with resource constraints,

A. Molin and S. Hirche, “Price-based adaptive scheduling in multi-loop control systems with resource constraints,” IEEE Transactions on Automatic Control, vol. 59, no. 12, pp. 3282–3295, December 2014. August 19, 2019 DRAFT 25

2014
[18]

Observation-driven scheduling for remote estimation of two Gaussian random variables,

M. M. Vasconcelos and U. Mitra, “Observation-driven scheduling for remote estimation of two Gaussian random variables,” IEEE Transactions on Control of Network Systems , to appear
[19]

Networked state estimation over a shared communication medium,

M. Xia, V . Gupta, and P. J. Antsaklis, “Networked state estimation over a shared communication medium,” IEEE Transactions on Automatic Control, 2017

2017
[20]

Optimal sensor scheduling strategies in networked estimation,

M. M. Vasconcelos, A. Nayyar, and U. Mitra, “Optimal sensor scheduling strategies in networked estimation,” in Proceedings of the 56th IEEE Conference on Decision and Control , 2017

2017
[21]

Information-theoretic analysis of an energy harvesting communication system,

O. Ozel and S. Ulukus, “Information-theoretic analysis of an energy harvesting communication system,” in IEEE 21st International Symposium on Personal, Indoor and Mobile Radio Communications Workshops , October 2010

2010
[22]

State estimation in energy harvesting systems,

O. Ozel and V . Anantharam, “State estimation in energy harvesting systems,” in Proceedings of the Information Theory and Applications Workshop, La Jolla, CA, 2016

2016
[23]

Optimal packet scheduling in an energy harvesting communication system,

J. Yang and S. Ulukus, “Optimal packet scheduling in an energy harvesting communication system,” IEEE Transactions on Communications, vol. 60, no. 1, pp. 220–230, January 2012

2012
[24]

Transmission policies for energy harvesting sensors with time-correlated energy supply,

N. Michelusi, K. Stamatiou, and M. Zorzi, “Transmission policies for energy harvesting sensors with time-correlated energy supply,” IEEE Transactions on Communications , vol. 61, no. 7, pp. 2988–3001, July 2013

2013
[25]

Energy management policies for harvesting-based wireless sensor devices with battery degradation,

N. Michelusi, L. Badia, R. Carli, L. Corradini, and M. Zorzi, “Energy management policies for harvesting-based wireless sensor devices with battery degradation,” IEEE Transactions on Communications , vol. 61, no. 12, pp. 4934–4947, December 2013

2013
[26]

Optimal adaptive random multiaccess in energy harvesting wireless sensor networks,

N. Michelusi and M. Zorzi, “Optimal adaptive random multiaccess in energy harvesting wireless sensor networks,” IEEE Transactions on Communications, vol. 63, no. 4, pp. 1355–1372, April 2015

2015
[27]

Channels, learning, queueing and remote estimation systems with a utilization-dependent component,

V . Jog, R. J. La, and N. C. Martins, “Channels, learning, queueing and remote estimation systems with a utilization-dependent component,” arXiv:1905.04362v1, 2019

1905 arXiv
[28]

Teams, signaling, and information theory,

Y .-C. Ho, M. Kastner, and E. Wong, “Teams, signaling, and information theory,” IEEE Transactions on Automatic Control , vol. 23, no. 2, pp. 305–312, April 1978

1978
[29]

A counter-example in stochastic optimum control,

H. S. Witsenhausen, “A counter-example in stochastic optimum control,” SIAM Journal on Control , vol. 6, no. 1, pp. 131–147, 1968

1968
[30]

Decentralized stochastic control with partial history sharing: A common information approach,

A. Nayyar, A. Mahajan, and D. Teneketzis, “Decentralized stochastic control with partial history sharing: A common information approach,” IEEE Transactions on Automatic Control , vol. 58, no. 7, pp. 1644 – 1658, July 2013

2013
[31]

Kumar and P

P. Kumar and P. Varaiya, Stochastic systems: Estimation, Identiﬁcation and Adaptive Control . Englewood Cliffs, NJ: Prentice-Hall, 1986

1986
[32]

Scheduling and estimation strategies in a sequential networked estimation problem,

M. Gagrani, M. M. Vasconcelos, and A. Nayyar, “Scheduling and estimation strategies in a sequential networked estimation problem,” in 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton) , 2018, pp. 871–878

2018
[33]

A short course on rearrangement inequalities,

A. Burchard, “A short course on rearrangement inequalities,” in Lecture notes of the IMDEA Winter School , 2009

2009
[34]

G. H. Hardy, J. E. Littlewood, and G. P ´olya, Inequalities. Cambridge University Press, 1952. August 19, 2019 DRAFT

1952

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Cyber–physical systems: A perspective at the centennial,

K.-D. Kim and P. R. Kumar, “Cyber–physical systems: A perspective at the centennial,” Proceedings of the IEEE, vol. 100, pp. 1287–1308, May 2012

work page 2012

[2] [2]

Bemporad, M

A. Bemporad, M. Heemels, and M. Johansson, Networked control systems . Hidelberg: Springer, 2010, vol. 406

work page 2010

[3] [3]

Optimal estimation over the collision channel,

M. M. Vasconcelos and N. C. Martins, “Optimal estimation over the collision channel,” IEEE Transactions on Automatic Control , vol. 62, no. 1, pp. 321–336, January 2017

work page 2017

[4] [4]

Optimal remote estimation of discrete random variables over the collision channel,

——, “Optimal remote estimation of discrete random variables over the collision channel,” IEEE Transactions on Automatic Control , vol. 64, no. 4, pp. 1519 – 1534, April 2019

work page 2019

[5] [5]

Yuksel and T

S. Yuksel and T. Basar, Stochastic Networked Control Systems . Springer, 2013

work page 2013

[6] [6]

KNOW-ME: a case study in wireless body area sensor network design,

U. Mitra, A. Emken, S. Lee, M. Li, V . Rozgic, G. Thatte, H. Vathsangam, D.-S. Zois, M. Annavaram, S. Narayanan, M. Levorato, D. Spruijt-Metz, and G. S. Sukhatme, “KNOW-ME: a case study in wireless body area sensor network design,” IEEE Communications Magazine, vol. 50, no. 5, pp. 116–125, May 2012

work page 2012

[7] [7]

Energy-efﬁcient, heterogeneous sensor selection for physical activity detection in wireless body area networks,

D.-S. Zois, M. Levorato, and U. Mitra, “Energy-efﬁcient, heterogeneous sensor selection for physical activity detection in wireless body area networks,” IEEE Transactions on Signal Processing , vol. 61, no. 7, pp. 1581–1594, April 2013

work page 2013

[8] [8]

Sequential decision-making in healthcare iot: Real-time health monitoring, treatments and interventions,

D.-S. Zois, “Sequential decision-making in healthcare iot: Real-time health monitoring, treatments and interventions,” in IEEE 3rd World Forum on Internet of Things , 2016

work page 2016