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AdaptMC

A Control-Theoretic Approach for Achieving Resilience in Mixed-Criticality Systems

Alessandro V. Papadopoulos, Enrico Bini, Sanjoy Baruah, Alan Burns

Embedded system

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Mixed-criticality system

Monitoring System Control System(s) Operator Mgmt System Mission Mgmt System Monitoring System Control System(s) Operator Mgmt System Mission Mgmt System Each task has its

• wn criticality level

(from A to D)

A B C D

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Vestal model

• Fixed number of distinct criticality levels are defined throughout the

system LO and HI criticality

• Each piece of code in the system is characterised by

The criticality level (LO/HI) Two WCET parameter estimates

• Prior to run-time the timing behaviour of all functionalities is validated

according to the WCET parameter estimates

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What does happen at run-time if the WCET estimates are “wrong”?

Goals of this paper

• Shift the perspective from verification to resiliency

What happens when a budget over-run occurs?

• Analyse a control-based approach for ensuring run-time resiliency

How to adapt the behaviour at run-time?

• Provide hard real-time guarantees even with budget over- or under-runs

Is it possible to provide such guarantees?

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Outline

• AdaptMC: Control-based approach for run-time adaptation
• Evaluation
• Conclusion

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Definitions

HI

t = 0

LO HI LO HI LO

… time Budget over-run

HI

t = 0

LO HI LO LO

SH(1) SL(1) SH(2) SL(2) … time

HI

Budget under-run Planned Run-time

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Definitions and assumptions

• Assumptions
• 1. Executions rarely exceed the WCET values
• 2. When they do, it is by a “small amount”
• 3. The “small amount” can be bounded

Supply S Disturbance ε Tentative budget Q

SH(k + 1) = QH(k) + εH(k) SL(k + 1) = QL(k) + εL(k)

−εH ≤ εH ≤ εH −εL ≤ εL ≤ 0

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AdaptMC: Control-based approach

Mixed-critical system

QH(k) QL(k)

AdaptMC

QH QL SH(k) SL(k)

Control objectives

• Meet the target desired budgets
• Preserve the bandwidth of the

HI and LO critical systems

Measure the actual supply

εH(k) εL(k)

Compare it with a target desired budget Compute a tentative budget

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Deeper in AdaptMC

• The controller adjusts the tentative budgets
• Based on the actual supply and the target budget
• with

QH(k + 1) = QH(k) + uH(k) QL(k + 1) = QL(k) + uL(k) uH(k) = KHH(QH − SH(k)) + KHL γ (QL − SL(k)) uL(k) = γKLH(QH − SH(k + 1)) +KLL(QL − SL(k))

γ = QL QH

Design parameters

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Required properties

• 1. Compensation property
• 2. Stability of the closed-loop system
• 3. Bounding the resource supply

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Compensation property

• A disturbance on the HI/LO-criticality server results in an opposite or null

effect on the value of the supply of the LO/HI-criticality server

t = 0

HI LO HI

… time t = 0

HI LO HI

… time Planned Run-time

OVER-RUN!

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Compensation property

• A disturbance on the HI/LO-criticality server results in an opposite or null

effect on the value of the supply of the LO/HI-criticality server

t = 0

HI LO HI LO

… time t = 0

HI LO HI LO

… time Planned Run-time

COMPENSATE

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Stability

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KHLKLH KLL KHH

Stability

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

KHH KLL K1 K2 K3 K4 K5

KHLKLH = 0 KHLKLH = 0.01 KHLKLH = 0.02 KHLKLH = 0.05 KHLKLH = 0.1 KHLKLH = 0.2 KHLKLH = 0.3 KHLKLH = 0.35

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Ki = {KHH, KHL, KLH, KLL} K1 = {0.4, 0.1, 0.1, 0.35} K2 = {0.15, 0.1, 0.1, 0.15} K3 = {0.25, 0.1, 0.1, 0.25} K4 = {0.5, 0.1, 0.1, 0.5} K5 = {0.75, 0.1, 0.1, 0.75}

Bounding the resource supply

t = 0 … time Z(1) Z(2) Z(3) S(1) S(2) S(3) Active intervals Idle intervals

I0 I1 I2 sbf(t) t σ

S(1)

σ

Z(1)

σ

S(2)

σ

Z(2)

σ

S(3)

σ

Z(3)

σS(n) = inf

n0 n0+n−1

∑

k=n0

S(k) σZ(n) = sup

n0 n0+n−1

∑

k=n0

Z(k)

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Bounding the resource supply

σS(n) = inf

n0 n0+n−1

∑

k=n0

S(k) σZ(n) = sup

n0 n0+n−1

∑

k=n0

Z(k) HI-Criticality σS(n) = nQH − εH풩HH(n) − εL 2 (ℐHL(n) + 풩HL) σZ(n) = nQL + εH풩LH(n) + εL 2 (ℐLL(n) + 풩LL) LO-Criticality σS(n) = nQL − εH풩LH(n) − εL 2 (ℐLL(n) + 풩LL) σZ(n) = nQH + εH풩HH(n) + εL 2 (풥HL(n) + 풩HL) 풩ij(n) =

∞

∑

k=0

|gij(k) − gij(k − n)| ℐiL(n) = sup

k {riL(k) − riL(k − n)}

풥iL(n) = sup

k {riL(k − n) − riL(k)}

with

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Proof and details in the paper

Evaluation — sbf

50 100 150 200 50 100 t sbfH(t)

hi-criticality

K1 K2 K3 K4 K5 50 100 150 200 50 100 t sbfL(t)

lo-criticality

K1 K2 K3 K4 K5

K1 maximises both the sbf

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Evaluation — Transient behaviour

−1 −0.5 0.5 1 ε εH εL 10 11 12 SH K1 K2 K3 K4 K5 10 20 30 40 50 60 70 80 90 100 7 8 9 10 k SL K1 K2 K3 K4 K5

K1 minimises the effect of the transient behaviour

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Baseline for comparison — PPA

• Period-Preserving Approach (PPA)

Simple approach When HI-criticality over-run, the LO-criticality server compensate by preserving the period

• where P is the target period that needs to be maintained

SH(k + 1) = QH + εH(k) SL(k + 1) = max(P − SH(k + 1),0) + εL(k)

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Comparative results

2 ε

AdaptMC

εH εL

PPA

εH εL 6 8 10 12 14 S SH SL SH SL 20 40 60 80 100 0.4 0.6 0.8 k SL/SH 20 40 60 80 100 k

Comparative results

2 ε

AdaptMC

εH εL

PPA

εH εL 6 8 10 12 14 S SH SL SH SL 20 40 60 80 100 0.4 0.6 0.8 k SL/SH 20 40 60 80 100 k

Impulsive disturbance

Comparative results

2 ε

AdaptMC

εH εL

PPA

εH εL 6 8 10 12 14 S SH SL SH SL 20 40 60 80 100 0.4 0.6 0.8 k SL/SH 20 40 60 80 100 k

Impulsive disturbance Constant disturbance

Comparative results

2 ε

AdaptMC

εH εL

PPA

εH εL 6 8 10 12 14 S SH SL SH SL 20 40 60 80 100 0.4 0.6 0.8 k SL/SH 20 40 60 80 100 k

Impulsive disturbance Constant disturbance Increasing disturbance

Conclusion and future work

• Control-theoretic approach for run-time adaptation in mixed-critical

systems Compensation property Stability conditions Supply bound functions

• Future work

Optimal gain calculation More criticality levels

!22

Questions, comments, remarks?

KHH KLL K1 K2 K3 K4 K5

Mixed- critical system

QH(k) QL(k)

AdaptMC

QH QL SH(k) SL(k) εH(k) εL(k)

I0 I1 I2 sbf(t) t σ

σ

σ

σ

σ

σ

Alessandro Papadopoulos alessandro.papadopoulos@mdh.se Code available: https://github.com/apapadopoulos/AdaptMC Artifact: http://drops.dagstuhl.de/opus/volltexte/2018/8969/