Towards Cyber Physical Networks: Joint Design of Network ......2016/06/10 · Mikhail Vilgelm (TUM) | [email protected] | ITG Workshop: 5G Mobile Networks - Towards the Tactile

Towards Cyber Physical Networks: Joint Design ofNetwork and Control

Chair of Communication NetworksDepartment of Electrical and Computer EngineeringTechnical University of Munich

Mikhail Vilgelm∗, Mohammad H. Mamduhi†, Wolfgang Kellerer∗, Sandra Hirche†

∗Chair of Communication Networks, †Chair of Information-oriented ControlTechnical University of Munich

Dresden, 10 June 2016

Overview• Motivation & Framework

• Problem statement

• Stability Analysis

• Numerical Evaluation

• Adaptive Scheduler

Mikhail Vilgelm (TUM) | [email protected] | ITG Workshop: 5G Mobile Networks - Towards the Tactile Internet 2

Chair of Communication Networks,Department of Electrical and Computer Engineering,Technical University of Munich,

Networked Control Systems• Tactile Internet applications: healthcare, robotics, manufacturing, smart grid, etc., rely on Control

Systems [Fet14]

• Distributed, large scale systems must be interconnected: Networked Control Systems [WTJ+11]

• Separate treatment of application and network - inefficient

• Event-triggered control paradigm [MAB+03, BHP09]→ Non-deterministic transmission patterns→ no static resource allocation / reservation

Idea: Exploit Control System properties for Efficient Medium Access Design



Framework of cross-layer design

SensorController Plant

Medium Access Control Unit –

Scheduler

wireless channel

channel quality,

collision feedback

available

resources

transmission

urgency, amount

of data

transmission,

back-off



Problem Statement: scenario• NCS of N heterogeneous LTI control loops

with the plant process:

xik+1 = Aixi

k +Biuik +wi

k

• Local scheduler Si deciding:

δik =

{1, xi

k sent through the channel0, xi

k blocked.

• Shared network→ sub-systems can collide:

γik =

{1, xi

k successfully received0, xi

k collided.

SharedCommunication Network

PlantƤi

Sensor with Scheduler Si

ControllerCi

Ƥ

S

C

Ƥ

S

CƤ S

C

uki

xki

zki

From this slide on: [VMKH16]



Network Model• Homogeneous sampling period k• Network state – available channels (TX

opportunities) Mk per sampling period k• Multichannel Slotted ALOHA [Yue91]• Thus, received signal at the controller side is:

zik =

{xi

k, θ ik = 1

∅, otherwise,

where, θ ik = δ i

kγ ik.

• Control law:

uik = ϑ

ik(Z

ik) =−LiE

[xi

k|Zik],

• If a transmission fails, use model-basedestimator:

E[xi

k|Zik]= (Ai−BiLi)E

[xi

k−1|Zik−1]

1 2 3 Mk. . . .

kth sampling period (k+1)th sampling period

uniform choice

control loop

scheduler

channelMk

From: [VMKH16]Mikhail Vilgelm (TUM) | [email protected] | ITG Workshop: 5G Mobile Networks - Towards the Tactile Internet 6


Threshold-based Scheduler• Network-induced estimation error ei

k:

eik :=xi

k−E[xi

k|Zik]

• Estimation error follows the dynamics:

eik+1 = (1−θ

ik)Aiei

k +wik

control loop

scheduler

channelMk

• Local threshold-based scheduler with the policy:

P[δ ik+1 = 1|ei

k] =

{0, if ‖ei

k‖ ≤ Λi

1, otherwise.

• At time step k, local schedulers let gk sub-systems transmit:

P[γ ik+1 = 1|‖ei

k‖> Λi] =

(Mk−1

Mk

)gk

From: [VMKH16]Mikhail Vilgelm (TUM) | [email protected] | ITG Workshop: 5G Mobile Networks - Towards the Tactile Internet 7


Stability Analysis• Noise with unsupported distribution→

stochastic stability notions LSP:

given ξ , ξ ′ > 0: limk→∞ supP[eT

k ek ≥ ξ ′]≤ ξ

Proof outline

• Aggregated error state: ek = [e1k

T, ...,eN

kT]T

• Stability condition: at least one successful transmission

• Probability of all sub-systems to collide:

Pkfail ≤

MN +min(N,M)

∑j=1

(−1)j · j!(M

j

)(Nj

)(M− j)N−j

MN

• Adjust M according to N to guarantee stability

From: [VMKH16]



Performance Evaluation: Metrics

• NCS performance: average error variance

Σ =1N

N

∑i=1

var[eik]

• Network performance:− Average channel utilization (throughput):

T = E[

nsp

M

]− Average collision ratio:

rcoll = E

[nc

p

ncp+ns

p

]• For the following: global transmission threshold: Λi := Λ′, ∀i ∈ N• Evaluation performed using numerical simulation∗

From: [VMKH16]

∗Source code & repeatability instructions available: https://github.com/mvilgelm/AdaptiveMAC



https://github.com/mvilgelm/AdaptiveMAC

Performance Evaluation: General• Network performance: “classical” slotted

ALOHA plot

• Exists a peak throughput

• Number of collisions grows with the number ofsub-systems

• Average error variance grows with the numberof sub-systems N

• After the peak throughput is reached – growsexponentially due to a very high collision rate

0 5 10 15 20 25 30 35 40Number of sub-systems N

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

Thro

ughp

ut

0.0

0.2

0.4

0.6

0.8

1.0

Ratio

of c

ollid

ed p

acke

ts

2 4 6 8 10 12 14 16 18 20 22 24Number of subsystems N

100

101

102

103

Aver

age

var[ei k]

From: [VMKH16]



Performance Evaluation: Threshold

• Network and control performance are coupledvia the threshold

• If the threshold is set too low, performancedegrades drastic due to collision

• If the threshold is set too high, performancedegrades slowly due to underutilized network

• Always exists a threshold (global), for whichcontrol and network performance are optimal

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Threshold Λ′

0

5

10

15

20

25

30

35

40

45

Aver

age

var[ei k]

N=10N=16N=20

→ to optimally use the network, adaptive scheduling policy is required

From: [VMKH16]



Scheduler with Threshold Adaptation• Scenario: varying number of channels

Mk ∈ {M1,M2}, M1 < M2:

P[Mk = M1] = 1−P[Mk = M2]

• Might occur in a case of dynamic resourceallocation [LKY11, 3GP11]

• Adaptive scheduling policy:

Λ′k = f (Mk)

• Optimal threshold for given N, M:Optimal Λ′

N 4 6 8 10 12 14 16M = 5 1.0 1.5 2.0 2.4 3.5 5.2 8.1M = 10 0.6 0.8 1.0 1.2 1.4 1.6 1.8

M1 M2

1 - P[M=M2]P[M=M2]

P[M=M2]

1-P[M=M2]

control loop

scheduler

channelMk

From: [VMKH16]



Scheduler with Threshold Adaptation (2)

• Comparison with non-adaptive: (A) chosen forM1 and (B) chosen for M2

• Gain from the adaptation depends on thenumber of sub-systems

• Gain is larger for non-adaptive targetingworse network state – scheduler (A) risksunderutilization, while scheduler (B) risks highcollision ratio

4 6 8 10 12 14 16Number of sub-systems N

101

102

Aver

age

var[ei k]

Non-Adapt. (B)Non-Adapt. (A)Adaptive

From: [VMKH16]



Conclusions

Contributions summary:

• Threshold-based scheduler & multi-channel slotted aloha

• Proved stochastic stability

• Numerically evaluated control and network performance

• Illustrated coupling of control & network via Λ′

• Proposed adaptive scheduling policy

Outlook

• Traffic Analysis of NCS

• Centralized Network- and Control-aware scheduler

• Design of control law based on the network knowledge



References[3GP11] 3GPP, Technical Report 37.868: Study on RAN Improvements for Machine-type Communications (Release

11), Tech. report, 3GPP Technical Specification Group Radio Access Network, 2011.

[BHP09] J. S. Baras, P. Hovareshti, and S. Perumal, Event Triggered Distributed Collaborative Control, Proc. EuropeanControl Conf. (ECC) (Budapest, Hungary), Aug. 2009.

[Fet14] Gerhard P Fettweis, The tactile internet: applications and challenges, Vehicular Technology Magazine, IEEE 9(2014), no. 1, 64–70.

[LKY11] Ki-Dong Lee, Sang Kim, and Byung Yi, Throughput comparison of random access methods for M2M serviceover LTE networks, GLOBECOM Workshops (GC Wkshps), 2011 IEEE, Dec 2011, pp. 373–377.

[MAB+03] R.M. Murray, K.J. Astrom, S.P. Boyd, R.W. Brockett, and G. Stein, Future directions in control in aninformation-rich world, Control Systems, IEEE 23 (2003), no. 2, 20–33.

[VMKH16] Mikhail Vilgelm, Mohammad H Mamduhi, Wolfgang Kellerer, and Sandra Hirche, Adaptive decentralized macfor event-triggered networked control systems, Proc. 19th ACM Conference on Hybrid Systems: Computationand Control (HSCC’16), 2016.

[WTJ+11] Geng Wu, S. Talwar, K. Johnsson, N. Himayat, and K.D. Johnson, M2M: From mobile to embedded Internet,IEEE Commun. Mag. 49 (2011), no. 4, 36–43.

[Yue91] Wuyi Yue, The effect of capture on performance of multichannel slotted aloha systems, Communications, IEEETransactions on 39 (1991), no. 6, 818–822.



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Towards Cyber Physical Networks: Joint Design of Network ......2016/06/10 · Mikhail Vilgelm (TUM) | [email protected] | ITG Workshop: 5G Mobile Networks - Towards the Tactile