Modelling, Analysis and Co-Design of Wireless Control Networks

M1 (M2)

Alessandro D’Innocenzo

“Design of Embedded controllers, Wireless interconnect and System-on-chip”

DEWS IAB meeting, May 13, 2014

Group:

Prof. Maria D. Di Benedetto

Dr. Alessandro D’Innocenzo

Dr. Francesco Smarra (3rd year PhD student, just defended his PhD thesis)

Ing. Giovanni D. Di Girolamo (1st year PhD student)

Ing. Gabriella Fiore (1st year PhD student)

Scientific Collaborations:

KTH, Prof. Kalle Johansson

University of Pennsylvania, Prof. George Pappas

Université catholique de Louvain: Prof. Raphael Jungers

DEWS: Prof. Nicola Guglielmi

DEWS & Telecom Italia: Prof. Fortunato Santucci & Ing. Tiziano Ionta

Rensselaer Polytechnic Institute: Prof. Agung Julius

Running projects:

EU FP7 NoE Hycon2: Highly-complex and networked control systems, 2010-2014

Project proposals:

ICT-2013.3.4 CHORAL: Control of HeterOgenous systems with mixed cRiticALities. Coordinated by Luigi Palopoli, Università di Trento (new proposal for EU HORIZON2020 FoF-9)

ERC-2014-StG CHAMELEON: A platform for modelling, design, simulation and verifiCation of HierArchical distributed control systeMs over hEtErogeneous cOmmunication Networks

SIR-2014 FLASH: A platform for design of distributed automation systems over heterogeneous networks

Group, scientific collaborations and projects

Objective: control over wireless networks

Controller

Challenge: close the loop taking into account the

communication protocol

Challenge: close the loop taking into account the

communication protocol

Objective: control over wireless networks

Controller

WirelessHART MAC (scheduling) and Network (routing) layers

Time-triggered access to the channel

Time divided in periodic frames

Each frame divided in Π time slots of duration Δ

6

WirelessHART MAC (scheduling) and Network (routing) layers

Time-triggered access to the channel

Time divided in periodic frames

Each frame divided in Π time slots of duration Δ

7

WirelessHART MAC (scheduling) and Network (routing) layers

Time-triggered access to the channel

Time divided in periodic frames

Each frame divided in Π time slots of duration Δ

Enables redundancy in data routing

8

WirelessHART MAC (scheduling) and Network (routing) layers

Time-triggered access to the channel

Time divided in periodic frames

Each frame divided in Π time slots of duration Δ

Enables redundancy in data routing

Scheduling must guarantee relay via multiple paths

9

WirelessHART MAC (scheduling) and Network (routing) layers

Time-triggered access to the channel

Time divided in periodic frames

Each frame divided in Π time slots of duration Δ

Enables redundancy in data routing

Scheduling must guarantee relay via multiple paths

Redundancy in data routing…

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

Redundancy in data routing…

Close a control loop investigating two routing strategies:

1. Single-path dynamic routing: take into account switching behavior due to dynamic routing

2. Multi-path static routing: take into account algorithms to merge redundant data

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

Redundancy in data routing…

Close a control loop investigating two routing strategies:

1. Single-path dynamic routing: take into account switching behavior due to dynamic routing

2. Multi-path static routing: take into account algorithms to merge redundant data

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

Wireless control networks as switching systems

𝐾(𝑡)

Wireless control networks as switching systems

𝑡

𝐾(𝑡)

Wireless control networks as switching systems

𝑡+1

𝐾(𝑡)

Wireless control networks as switching systems

𝑡+…

𝐾(𝑡)

Different paths are associated with different delays.

Wireless control networks as switching systems

𝑡+…

𝐾(𝑡)

Different paths are associated with different delays.

Mathematical model: 𝑥 𝑡 + 1 = 𝐴𝑥 𝑡 + 𝐵 𝜎 𝑡 𝑣 𝑡 , 𝑡 ∈ ℕ, where 𝑥 𝑡 is the plant

and network state, 𝜎 𝑡 ∈ Σ depends on routing/scheduling. The switching signal is considered as a disturbance.

Wireless control networks as switching systems

𝑡+…

𝐾(𝑡)

Problem: Design a controller 𝐾(𝑡) s.t. the closed loop system is asymptotically stable.

Given a state-feedback static controller 𝐾(𝑡), the closed loop systems is asymptotically

stable iff the Joint Spectral Radius of 𝐴 + 𝐵 𝜎 𝑡 𝐾 𝑡𝜎 𝑡 ∈Σ

is smaller than 1.

Different paths are associated with different delays.

Mathematical model: 𝑥 𝑡 + 1 = 𝐴𝑥 𝑡 + 𝐵 𝜎 𝑡 𝑣 𝑡 , 𝑡 ∈ ℕ, where 𝑥 𝑡 is the plant

and network state, 𝜎 𝑡 ∈ Σ depends on routing/scheduling. The switching signal is considered as a disturbance.

Wireless control networks as switching systems

𝑡+…

Problem: Design a controller 𝐾(𝑡) s.t. the closed loop system is asymptotically stable.

Given a state-feedback static controller 𝐾(𝑡), the closed loop systems is asymptotically

stable iff the Joint Spectral Radius of 𝐴 + 𝐵 𝜎 𝑡 𝐾 𝑡𝜎 𝑡 ∈Σ

is smaller than 1.

Insights: Switching systems analysis and design is a crowded research area:

• Leverage special structure of matrices 𝐴 and 𝐵 𝜎 𝑡 to provide tailored results

that outperform classical results on general switching systems

𝐾(𝑡)

Different paths are associated with different delays.

Mathematical model: 𝑥 𝑡 + 1 = 𝐴𝑥 𝑡 + 𝐵 𝜎 𝑡 𝑣 𝑡 , 𝑡 ∈ ℕ, where 𝑥 𝑡 is the plant

and network state, 𝜎 𝑡 ∈ Σ depends on routing/scheduling. The switching signal is considered as a disturbance.

Wireless control networks as switching systems

Collaboration with Raphael Jungers (Université catholique de Louvain) • R.M. Jungers, A. D'Innocenzo, M.D. Di Benedetto. Modeling, analysis and design of linear

systems with switching delays. Submitted for publication • R.M. Jungers, A. D'Innocenzo, M. D. Di Benedetto. Further results on controllability of

linear systems with switching delays. 9th IFAC World Congress, 2014 • R.M. Jungers, A. D'Innocenzo, M. D. Di Benedetto. How to control Linear Systems with

switching delays. 13th ECC, 2014 • R.M. Jungers, A. D'Innocenzo, M.D. Di Benedetto. Feedback stabilization of dynamical

systems with switched delays. 51st IEEE CDC, 2012

𝐾(𝑡)

Wireless control networks as switching systems

𝐾(𝑡)

Stabilizability depends on our knowledge of the (routing) switching signal 𝜎(𝑡):

Wireless control networks as switching systems

𝐾(𝑡)

Stabilizability depends on our knowledge of the (routing) switching signal 𝜎(𝑡):

• No knowledge of routing signal, i.e. we cannot measure 𝝈 𝒕 : then 𝑲 𝒕 = 𝑲, ∀𝒕 ∈ ℕ

– Existence of non-linear controllers that outperform any linear controller

– Approximation methods for the design of 𝐾 𝑡 , in collaboration with N. Guglielmi (DEWS)

Wireless control networks as switching systems

𝐾(𝑡)

Stabilizability depends on our knowledge of the (routing) switching signal 𝜎(𝑡):

• No knowledge of routing signal, i.e. we cannot measure 𝝈 𝒕 : then 𝑲 𝒕 = 𝑲, ∀𝒕 ∈ ℕ

– Existence of non-linear controllers that outperform any linear controller

– Approximation methods for the design of 𝐾 𝑡 , in collaboration with N. Guglielmi (DEWS)

• We can measure and keep memory of 𝝈 𝒕 : then 𝑲 𝒕 = 𝑲 𝝈 𝒕 − 𝒅 : 𝝈 𝒕

– Pathologic switching sequences that invalidate stabilizability

– Configure network nodes to avoid such sequences

Wireless control networks as switching systems

Stabilizability depends on our knowledge of the (routing) switching signal 𝜎(𝑡):

• No knowledge of routing signal, i.e. we cannot measure 𝝈 𝒕 : then 𝑲 𝒕 = 𝑲, ∀𝒕 ∈ ℕ

– Existence of non-linear controllers that outperform any linear controller

– Approximation methods for the design of 𝐾 𝑡 , in collaboration with N. Guglielmi (DEWS)

• We can measure and keep memory of 𝝈 𝒕 : then 𝑲 𝒕 = 𝑲 𝝈 𝒕 − 𝒅 : 𝝈 𝒕

– Pathologic switching sequences that invalidate stabilizability

– Configure network nodes to avoid such sequences

• We can measure and keep memory of 𝝈 𝒕 and have a finite horizon knowledge of future 𝑵

switching signals: then 𝑲 𝒕 = 𝑲 𝝈 𝒕 − 𝒅 : 𝝈 𝒕 + 𝑵

– If 𝑁 ≥𝑛 + 2 𝐷2 𝐷

stabilizability is guaranteed (𝑛 plant state-space dimension, 𝐷 maximum delay)

– Configure network nodes to design routing policies for appropriate time-windows

𝐾(𝑡)

Redundancy in data routing…

Close a control loop investigating two routing strategies:

1. Single-path dynamic routing: take into account switching behavior due to dynamic routing

2. Multi-path static routing: take into account algorithms to merge redundant data

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

Multi-path static routing

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

Investigate algorithms to merge redundant data:

• Objective: stabilize the closed-loop system

Multi-path static routing

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

0.1

0.9

Investigate algorithms to merge redundant data:

• Objective: stabilize the closed-loop system

• Best strategy: keep most recent packet vs. compute linear combination?

Multi-path static routing

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

0.1

0.9

Investigate algorithms to merge redundant data:

• Objective: stabilize the closed-loop system

• Best strategy: keep most recent packet vs. compute linear combination?

• Different paths are associated with different delays

Multi-path static routing

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

0.1

0.9

Investigate algorithms to merge redundant data:

• Objective: stabilize the closed-loop system

• Best strategy: keep most recent packet vs. compute linear combination?

• Different paths are associated with different delays

• Not a trivial question, best strategy from the point of view of stability strongly depends on plant and network: need for a control-theoretic approach

Multi-path static routing

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

0.1

0.9

Investigate algorithms to merge redundant data:

• Objective: stabilize the closed-loop system

• Best strategy: keep most recent packet vs. compute linear combination?

• Different paths are associated with different delays

• Not a trivial question, best strategy from the point of view of stability strongly depends on plant and network: need for a control-theoretic approach

Fault tolerant control

Mf

𝐹 set of all configurations of links subject to a failure or a malicious intrusion

Do not reconfigure the whole network (i.e. scheduling and routing) when a failure occurs: instead, only reconfigure neighbors of faulty nodes

Do not add complexity to local communication to detect faulty or malicious nodes: instead, use plant dynamics and path redundancy

Fault tolerant control

Problem 1: N&S Conditions on network to guarantee the existence of a stabilizing controller for the MCN dynamics 𝑀𝑓 associated to any 𝑓 ∈ 𝐹

Problem 2: N&S Conditions on network to design a dynamical system (FDI) able to detect and isolate any 𝑓 ∈ 𝐹

A. D'Innocenzo, M.D. Di Benedetto, E. Serra. Fault Tolerant Control of Multi-Hop Control Networks. IEEE T ransactions on Automatic Control, 58(6):1377-1389, 2013.

Previous results on SISO LTI systems

Mf

Fault tolerant control

A. D'Innocenzo, F. Smarra, M.D. Di Benedetto. Fault Tolerant Control of MIMO Multi-Hop Control Networks. Submitted for publication

M.D. Di Benedetto, A. D'Innocenzo, F. Smarra. Fault-tolerant control of a wireless HVAC control system. ISCCSP2014, 2014

A. D'Innocenzo, M.D. Di Benedetto, F. Smarra. Fault detection and isolation of malicious nodes in MIMO Multi-hop Control Networks. 52nd IEEE CDC, 2013

F. Smarra, A. D'Innocenzo, M.D. Di Benedetto. Fault Tolerant Stabilizability of MIMO Multi-Hop Control Networks. 3rd IFAC NecSys 2012

Mf

Extension to MIMO LTI systems

Multi-path static routing

…makes system tolerant to long-term link failures

…enables detection and isolation of failures and malicious attacks

…makes system robust to short-term link failures (e.g. packet losses)

0.1

0.9

Investigate algorithms to merge redundant data:

• Objective: stabilize the closed-loop system

• Best strategy: keep most recent packet vs. compute linear combination?

• Different paths are associated with different delays

• Not a trivial question, best strategy from the point of view of stability strongly depends on plant and network: need for a control-theoretic approach

Robustness to packet losses via routing redundancy

𝛾1

𝛾3

Robustness to packet losses via routing redundancy

𝑢 𝑘 = 𝛾1𝑣 𝑘 − 1 ,⋯ , 𝛾𝐷𝑣 𝑘 − 𝐷 ′, 𝛾 = 𝛾1, ⋯ , 𝛾𝐷

𝛾1

𝛾3

Robustness to packet losses via routing redundancy

𝑢 𝑘 = 𝛾1𝑣 𝑘 − 1 ,⋯ , 𝛾𝐷𝑣 𝑘 − 𝐷 ′, 𝛾 = 𝛾1, ⋯ , 𝛾𝐷

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝛾 𝑣 𝑘 , 𝑣 𝑘 = 𝐾(𝛾)𝑥(𝑘)

𝛾1

𝛾3 𝐾(𝛾)

Robustness to packet losses via routing redundancy

𝑢 𝑘 = 𝛾1𝑣 𝑘 − 1 ,⋯ , 𝛾𝐷𝑣 𝑘 − 𝐷 ′, 𝛾 = 𝛾1, ⋯ , 𝛾𝐷

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝛾 𝑣 𝑘 , 𝑣 𝑘 = 𝐾(𝛾)𝑥(𝑘)

𝑥 𝑘 + 1 = 𝐴 + 𝐵(𝛾)𝐾(𝛾) 𝑥 𝑘

Closed-loop dynamics, no packet losses

𝛾1

𝛾3 𝐾(𝛾)

Robustness to packet losses via routing redundancy

𝑥 𝑘 + 1 = 𝐴 + 𝐵(𝛾)𝐾(𝛾) − 𝐵𝜎 𝑘 (𝛾)𝐾(𝛾) 𝑥 𝑘

Closed-loop dynamics, packet losses

𝑢 𝑘 = 𝛾1𝑣 𝑘 − 1 ,⋯ , 𝛾𝐷𝑣 𝑘 − 𝐷 ′, 𝛾 = 𝛾1, ⋯ , 𝛾𝐷

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝛾 𝑣 𝑘 , 𝑣 𝑘 = 𝐾(𝛾)𝑥(𝑘)

𝛾1

𝛾3 𝐾(𝛾)

Robustness to packet losses via routing redundancy

Markov Chain

Closed-loop dynamics, packet losses

𝑢 𝑘 = 𝛾1𝑣 𝑘 − 1 ,⋯ , 𝛾𝐷𝑣 𝑘 − 𝐷 ′, 𝛾 = 𝛾1, ⋯ , 𝛾𝐷

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝛾 𝑣 𝑘 , 𝑣 𝑘 = 𝐾(𝛾)𝑥(𝑘)

𝑥 𝑘 + 1 = 𝐴 + 𝐵(𝛾)𝐾(𝛾) − 𝐵𝜎 𝑘 (𝛾)𝐾(𝛾) 𝑥 𝑘

𝛾1

𝛾3 𝐾(𝛾)

Robustness to packet losses via routing redundancy

Closed-loop dynamics, packet losses

i.i.d. 𝑝0, 𝑝1, … , 𝑝𝑁

𝑢 𝑘 = 𝛾1𝑣 𝑘 − 1 ,⋯ , 𝛾𝐷𝑣 𝑘 − 𝐷 ′, 𝛾 = 𝛾1, ⋯ , 𝛾𝐷

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + 𝐵 𝛾 𝑣 𝑘 , 𝑣 𝑘 = 𝐾(𝛾)𝑥(𝑘)

𝑥 𝑘 + 1 = 𝐴 + 𝐵(𝛾)𝐾(𝛾) − 𝐵𝜎 𝑘 (𝛾)𝐾(𝛾) 𝑥 𝑘

𝛾1

𝛾3 𝐾(𝛾)

Robustness to packet losses via routing redundancy

𝐴𝑖 = (𝐴 + 𝐵 − 𝐵𝑖 𝐾)⊗ (𝐴 + 𝐵 − 𝐵𝑖 𝐾)

Theorem [Costa et al.]: the system is asymptotically mean square stable

(MSS) if and only if 𝑆 = 𝑝0𝐴 0 + 𝑝1𝐴 1 +…+ 𝑝𝑁𝐴 𝑁 is Schur stable: 𝑟 𝑆 < 1.

Robustness to packet losses via routing redundancy

𝐴𝑖 = (𝐴 + 𝐵 − 𝐵𝑖 𝐾)⊗ (𝐴 + 𝐵 − 𝐵𝑖 𝐾)

Optmization: min𝜸 𝑟 𝑆

Constraint: 𝑟 𝑆 < 1

Theorem [Costa et al.]: the system is asymptotically mean square stable

(MSS) if and only if 𝑆 = 𝑝0𝐴 0 + 𝑝1𝐴 1 +…+ 𝑝𝑁𝐴 𝑁 is Schur stable: 𝑟 𝑆 < 1.

Non linear w.r.t. 𝛾

Robustness to packet losses via routing redundancy

𝐴𝑖 = (𝐴 + 𝐵 − 𝐵𝑖 𝐾)⊗ (𝐴 + 𝐵 − 𝐵𝑖 𝐾)

Optmization: min𝜸 𝑟 𝑆

Constraint: 𝑟 𝑆 < 1

Theorem [Costa et al.]: the system is asymptotically mean square stable

(MSS) if and only if 𝑆 = 𝑝0𝐴 0 + 𝑝1𝐴 1 +…+ 𝑝𝑁𝐴 𝑁 is Schur stable: 𝑟 𝑆 < 1.

Non linear w.r.t. 𝛾

Robustness to packet losses via routing redundancy

Provide computationally efficient approximations leveraging the fact that packet loss probability is much smaller than correct tx probability

𝐴𝑖 = (𝐴 + 𝐵 − 𝐵𝑖 𝐾)⊗ (𝐴 + 𝐵 − 𝐵𝑖 𝐾)

Optmization: min𝜸 𝑟 𝑆

Constraint: 𝑟 𝑆 < 1

Theorem [Costa et al.]: the system is asymptotically mean square stable

(MSS) if and only if 𝑆 = 𝑝0𝐴 0 + 𝑝1𝐴 1 +…+ 𝑝𝑁𝐴 𝑁 is Schur stable: 𝑟 𝑆 < 1.

Optmization: min𝜸 𝑟 𝑆

Constraint: 𝑟 𝑆 < 1 Non linear w.r.t. 𝛾

Gerschgorin disks

(polynomial)

Robustness to packet losses via routing redundancy

Provide computationally efficient approximations leveraging the fact that packet loss probability is much smaller than correct tx probability

F. Smarra, A. D'Innocenzo, M.D. Di Benedetto. Optimal co-design of control, scheduling and routing in multi-hop control networks. 51st IEEE CDC, 2012

F. Smarra, A. D'Innocenzo and M.D. Di Benedetto. Approximation methods for optimal network coding in a multi-hop control network with packet losses. Submitted for publication

Theorem [Costa et al.]: the system is asymptotically mean square stable

(MSS) if and only if 𝑆 = 𝑝0𝐴 0 + 𝑝1𝐴 1 +…+ 𝑝𝑁𝐴 𝑁 is Schur stable: 𝑟 𝑆 < 1.

𝐴𝑖 = (𝐴 + 𝐵 − 𝐵𝑖 𝐾)⊗ (𝐴 + 𝐵 − 𝐵𝑖 𝐾)

Optmization: min𝜸 𝑟 𝑆

Constraint: 𝑟 𝑆 < 1 Non linear w.r.t. 𝛾

Gerschgorin disks

(polynomial)

Transmission mean square error

minimization (convex)

Robustness to packet losses via routing redundancy

Provide computationally efficient approximations leveraging the fact that packet loss probability is much smaller than correct tx probability

F. Smarra, A. D'Innocenzo, M.D. Di Benedetto. Optimal co-design of control, scheduling and routing in multi-hop control networks. 51st IEEE CDC, 2012

F. Smarra, A. D'Innocenzo and M.D. Di Benedetto. Approximation methods for optimal network coding in a multi-hop control network with packet losses. Submitted for publication

Theorem [Costa et al.]: the system is asymptotically mean square stable

(MSS) if and only if 𝑆 = 𝑝0𝐴 0 + 𝑝1𝐴 1 +…+ 𝑝𝑁𝐴 𝑁 is Schur stable: 𝑟 𝑆 < 1.

𝐴𝑖 = (𝐴 + 𝐵 − 𝐵𝑖 𝐾)⊗ (𝐴 + 𝐵 − 𝐵𝑖 𝐾)

Collaboration with Telecom Italia

Router 2

Router 3

Router 4 Router 1

How to measure service-specific QoS? Streaming

service YouTube

server Router 2

Router 3

Router 4 Router 1

Streaming service

YouTube server Router 2

Router 3

Router 4 Router 1

Objective: End-to-end QoS, performance and QoE model-based analysis

Network model E2e service

(e.g. http, streaming, ftp…)

QoE & QoS

assessment/prediction

Routers local feedback (e.g. delay, PLR, buffer…)

and feedforward (e.g. traffic statistics)

Streaming service

YouTube server Router 2

Router 3

Router 4 Router 1

Network model

Effect of failure

on service-specific QoE & QoS

E2e service (e.g. http,

streaming, ftp…)

Routers local feedback (e.g. delay, PLR, buffer…)

and feedforward (e.g. traffic statistics)

Objective: End-to-end QoS, performance and QoE model-based analysis

Modeling problem

• Service (http, ftp, mailing, video streaming, …)

• UDP-IP or TCP-IP (TCP-SAK; Cubic, Reno, …)

• Routing (OSPFv2 on Ipv4, …)

• Network topology

Choose appropriate level of abstraction

Streaming service

YouTube server Router 2

Router 3

Router 4 Router 1

Modeling problem

• Service (http, ftp, mailing, video streaming, …)

• UDP-IP or TCP-IP (TCP-SAK; Cubic, Reno, …)

• Routing (OSPFv2 on Ipv4, …)

• Network topology

Choose appropriate level of abstraction

Streaming service

YouTube server Router 2

Router 3

Router 4 Router 1

– Packet-level models [e.g. Omnet++]

Extremely accurate vs. large computational requirements for large-scale simulations

– Aggregate fluid-like models [Floyd et Al. SIGCOMM2000, Misra et al. SIGCOMM2000]

Complexity reduction vs. mostly capture steady-state behavior

– Hybrid systems models [Bohacek et al., SIGMETRICS’03]

Complexity reduction & abstraction level of traffic flow and packet losses accurate up to round-trip-time

Results & future work

Results

• Preliminary investigation towards QoE assessment and prediction in Service Provider Networks

• Relax model complexity guaranteeing accuracy up to rund-trip-time

• Derive explicit trajectory of bandwidth, packet drops and buffer differentiated for each TCP flow (e.g. service) and router

• Enable use of performance and QoE metrics based not only on average variables:

– e.g. packet loss average rate vs. packets per burst loss rate, [Kühlewind et al. PAM'13]

• M.D. Di Benedetto, A. Di Loreto, A. D'Innocenzo, T. Ionta. Modeling of traffic congestion and re-routing in a service provider network. IEEE ICC, 2014.

Future work

• Model priority-based QoS routing protocols

• Investigate formal relation among QoE, performance and QoS metrics

• Apply to a realistic application scenario: negotiate with a new “big” customer

• Create model of a sub-network of the TI network

Scenario: negotiate with a new “big” customer

• Create model of a sub-network of the TI network

• Feed network model with traffic load using Telecom routers’ statistics

Scenario: negotiate with a new “big” customer

• Create model of a sub-network of the TI network

• Feed network model with traffic load using Telecom routers’ statistics

• Perturb network with model of customer required services

Scenario: negotiate with a new “big” customer

• Create model of a sub-network of the TI network

• Feed network model with traffic load using Telecom routers’ statistics

• Perturb network with model of customer required services

• Estimate QoE and performance and better negotiate…

Scenario: negotiate with a new “big” customer

Application Area A2

• Model predictive control for energy saving in energy efficient buildings – PhD student Francesco Smarra visited Model Predictive Control Lab @ UCB

• Supervision, control and protection systems for novel nuclear plants – Prof. Stefano Di Gennaro

• Photovoltaic Systems Management (work in progress) – PhD student Alessio Iovine is visiting Laboratoire des Signaux et Systèmes

(L2S) at Supélec, École Supérieure d'Électricité

Appendix

Optimal control

𝐶 𝑧 = 𝑀 𝑧 𝑧𝐷𝑅𝑧𝐷𝑂𝑑𝑠𝑧𝑠 + 𝑑𝑠−1𝑧

𝑠−1 +⋯+ 𝑑0(𝑧 − 1)(𝑧𝑚 + 𝑐𝑚−1𝑧

𝑚−1 +⋯+ 𝑐0)

𝑐 = 𝑐𝑚−1, 𝑐𝑚−2, … , 𝑐0 ; 𝑑 = 𝑑𝑠, 𝑑𝑠−1, … , 𝑑0 ;

𝑤𝑂= 𝑊𝑂 𝑒 , ∀𝑒 ∈ 𝐸𝑂

𝑤𝑅 = 𝑊𝑅 𝑒 , ∀𝑒 ∈ 𝐸𝑅 𝑃 𝑧 =

1

𝑀(𝑧)𝑃′(𝑧) =

𝑏𝑛−1𝑧𝑛−1 + 𝑏𝑛−2𝑧

𝑛−2 +⋯+ 𝑏0𝑀(𝑧) 𝑧𝑟 + 𝑎𝑟−1𝑧

𝑟−1 +⋯+ 𝑎0

Optimal control

min𝒄,𝒅,𝒘𝑹,𝒘𝑶

𝑒(𝑘)𝐿2

2

subject to:

1) 𝐷𝐶𝐷𝑃′ + 𝑁𝐶′𝑁𝐺𝑅𝑁𝑃𝑁𝐺𝑂 = 𝑧𝑙;

2) 𝑂𝑢 ≤ 𝑂 𝑢, 𝑂𝑦 ≤ 𝑂 𝑦;

3) 𝑅𝑒 ≤ 𝑅 𝑒, ∀𝑒 ∈ 𝐸𝑅 ∪ 𝐸𝑂.

Deadbeat stability

No wind-up phenomena

Limited bandwidth

Minimize error energy

Optimal control

min𝒄,𝒅,𝒘𝑹,𝒘𝑶

𝑒(𝑘)𝐿2

2

subject to:

1) 𝐷𝐶𝐷𝑃′ + 𝑁𝐶′𝑁𝐺𝑅𝑁𝑃𝑁𝐺𝑂 = 𝑧𝑙;

2) 𝑂𝑢 ≤ 𝑂 𝑢, 𝑂𝑦 ≤ 𝑂 𝑦;

3) 𝑅𝑒 ≤ 𝑅 𝑒, ∀𝑒 ∈ 𝐸𝑅 ∪ 𝐸𝑂.

Polynomial function of 𝒄, 𝒅,𝒘𝑹, 𝒘𝑶

Polynomial function of 𝒅,𝒘𝑹

Polynomial function of 𝒘𝑹, 𝒘𝑶

Polynomial function of 𝒅,𝒘𝑹

NP-Hard problem

Optimal control

min𝒄,𝒅,𝒘𝑹,𝒘𝑶

𝑒(𝑘)𝐿2

2

subject to:

1) 𝐷𝐶𝐷𝑃′ + 𝑁𝐶′𝑁𝐺𝑅𝑁𝑃𝑁𝐺𝑂 = 𝑧𝑙;

2) 𝑂𝑢 ≤ 𝑂 𝑢, 𝑂𝑦 ≤ 𝑂 𝑦;

3) 𝑅𝑒 ≤ 𝑅 𝑒, ∀𝑒 ∈ 𝐸𝑅 ∪ 𝐸𝑂.

Polynomial function of 𝒄, 𝒅,𝒘𝑹, 𝒘𝑶

Polynomial function of 𝒅,𝒘𝑹

Polynomial function of 𝒘𝑹, 𝒘𝑶

Polynomial function of 𝒅,𝒘𝑹

NP-Hard problem

Conditions on the network parameters such that the problem is convex F. Smarra, A. D'Innocenzo, M.D. Di Benedetto. Optimal co-design of control, scheduling and

routing in multi-hop control networks. 51st IEEE CDC, 2012.

Optimal control, packet losses

min𝒄,𝒅,𝒘𝑹,𝒘𝑶

𝑒(𝑘)𝐿2

2

subject to:

1) max 𝑒𝑖𝑔 𝑆 < 1;

2) 𝑂𝑢 ≤ 𝑂 𝑢, 𝑂𝑦 ≤ 𝑂 𝑦;

3) 𝑅𝑒 ≤ 𝑅 𝑒, ∀𝑒 ∈ 𝐸𝑅 ∪ 𝐸𝑂.

Mean Square Stability

No wind-up phenomena

Limited bandwidth

Minimize error energy

|λ𝒊| + 𝑹𝒊

𝑇𝑆𝑇−1 = 𝑝0𝑇𝐴 0𝑇−1 + 𝑇(𝑝1𝐴 1+…+𝑝𝑁𝐴 𝑁)𝑇

−1

𝐷 = 𝑑𝑖𝑎𝑔(λ1, … , λ𝑛) 𝐸 = [𝑒𝑖𝑗]

𝑅𝑖 = |𝑒𝑖𝑗|

𝑗

1 -1 λ2 λ1 λ𝑛

(𝑝0≫ 𝑝1, … , 𝑝𝑁!)

Robustness to packet losses via routing redundancy

𝑑𝑒𝑔

Problem 2: min𝜸 |||λ𝒊| + 𝑹𝒊||∞

𝑇𝑆𝑇−1 = 𝑝0𝑇𝐴 0𝑇−1 + 𝑇(𝑝1𝐴 1+…+𝑝𝑁𝐴 𝑁)𝑇

−1

𝐷 = 𝑑𝑖𝑎𝑔(λ1, … , λ𝑛) 𝐸 = [𝑒𝑖𝑗]

𝑅𝑖 = |𝑒𝑖𝑗|

𝑗

𝑝𝑜𝑙𝑦𝑛𝑜𝑚𝑖𝑎𝑙

𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠 𝑜𝑓 𝛾 1

1 -1 λ2 λ1 λ𝑛

(𝑝0≫ 𝑝1, … , 𝑝𝑁!)

𝜗(𝛾)6𝑝

3−11𝑝2+2𝑝

𝜗(𝛾)4𝑝(𝑝−1)2

Robustness to packet losses via routing redundancy

Problem 3:

min𝜸 𝐸( 𝐵 (𝛾) 2) Quadratic optimization problem

0

𝛾1 = 0.15 𝛾2 = 0.85

𝑥 𝑘 + 1 = 𝐴𝑥 𝑘 + (𝐵(𝛾) − 𝐵𝜎 𝑘 (𝛾))𝑢(𝑘) 𝐵 𝛾 = 𝐵1(𝛾), … , 𝐵𝑁(𝛾)

Robustness to packet losses via routing redundancy

Method 𝜸∗ 𝒎𝒂𝒙(|𝒆𝒊𝒈(𝑺)|) Comp.

Time (s)

min𝜸 max |𝑒𝑖𝑔 𝑆 | (0.0957,0.3627,0.1797,0.2322) 0.385 46

Gerschgorin (0.2127,0.2128,0.1968,0.1884) 0.502 19

Actuation error (0.0955,0.2849,0.3042,0.3154) 0.5848 1.2

Robustness to packet losses via routing redundancy

Collaboration with Telecom Italia Streaming

service YouTube

server Router 2

Router 3

Router 4 Router 1

Objective: End-to-end QoS, performance and QoE model-based analysis:

• Define different performance metrics for different services:

– packet losses & bursts, average/max delay, average/min/max data rate

• Model service specific traffic footprint:

– http, ftp, mailing, video streaming

• Model TCP congestion avoidance algorithms;

– TCP-SAK, Cubic, Reno

• Model router parameters:

– packet loss, delay, buffer status

• Take into account network topology

Appropriate modeling level of abstraction

– Packet-level models: [e.g. Omnet++]

• Extremely accurate

• Large computational requirements for large-scale simulations

• Difficult to relate network parameters and QoS

– Aggregate fluid-like models: [Floyd et Al. SIGCOMM2000, Misra et al. PERFORMANCE1999, Misra et al. SIGCOMM2000]

• Keep track of the average queue sizes, transmission rates, drop rates, etc

• Mostly capture steady-state behavior

• Detailed transient behavior during congestion control cannot be captured

Appropriate modeling level of abstraction

– Packet-level models: [e.g. Omnet++]

• Extremely accurate

• Large computational requirements for large-scale simulations

• Difficult to relate network parameters and QoS

– Aggregate fluid-like models: [Floyd et Al. SIGCOMM2000, Misra et al. PERFORMANCE1999, Misra et al. SIGCOMM2000]

• Keep track of the average queue sizes, transmission rates, drop rates, etc

• Mostly capture steady-state behavior

• Detailed transient behavior during congestion control cannot be captured

– Hybrid systems models: • Combine continuous time dynamics and discrete-time logic

• Complexity reduction through continuous approximation of discrete variables

• Abstraction level of traffic flow and packet losses accurate up to round-trip-time: model discrete events such as packet losses

M.D. Di Benedetto, A. Di Loreto, A. D'Innocenzo, T. Ionta. Modeling of traffic congestion and re-routing in a service provider network. IEEE ICC, 2014.