May 27, 2014 - Outline. NL example. EB-PID. Formulation. Cases. Simulations .... Computer science community wants control already operative ..... big e(ta). ︸ ︷︷ ︸ small. Strong overshoot when the control is updated (similar to saturated ...
Event based control: LCCC workshop on Cloud Control
A way to reduce reconfigurations in autonomic
N. Marchand
computing ?
Introduction Motivation Outline NL example
N. Marchand gipsa, Control Systems Department, Grenoble, FRANCE
EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
1 / 26
Outline LCCC workshop on Cloud Control
1
Introduction Motivation Outline of the talk
2
A highly nonlinear example
3
Event-based PID controller Formulation Illustrative cases Simulations MapReduce control
4
Event-based control
5
Conclusion
N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
2 / 26
Motivation to put control theory in computer science LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Dealing with the dynamics: time is crucial Mathematical tools to "control" a system By "control", we mean being able to define a control objective define control actions accordingly guarantee performances of the controlled system despite errors despite perturbations ü Facing everything that is unknown ü Guarantee stability
Many other area of control theory are relevant to computer science Fault tolerant control, fault detection, supervision, etc.
Nowadays control theory is everywhere... automotive, robotics, energy (grids, production, etc.), microelectronics (DVFS), etc.
...except maybe in computer science N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
3 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Languages difficulties Words Autonomic or Autonomous Time response Parameter Cloud
Computer science Controlled
Control theory Uncontrolled
Queuing + processing time variables you can change Set of interconnected computers
time needed to reach x% of the final value constants
Control
Parametrization
...
...
Look at Lund’s sky dx = f (x , u) dt
...
Interest of both communities No physics behind algorithms, applications, services, etc. "Let’s do things in cloud " (Sara Bouchenak from LIG-lab)
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Languages difficulties Words Autonomic or Autonomous Time response Parameter Cloud
Computer science Controlled
Control theory Uncontrolled
Queuing + processing time variables you can change Set of interconnected computers
time needed to reach x% of the final value constants
Control
Parametrization
...
...
Look at Lund’s sky dx = f (x , u) dt
...
Interest of both communities No physics behind algorithms, applications, services, etc. "Let’s do thingsControl in forcloud " (Sara Bouchenak from LIG-lab) computer science Control for control theoretician
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control
Languages difficulties Interest of both communities Computer science community wants control already operative Control community don’t care about computer sciences Except in Lund ! IFAC technical commitee on computer for control but none on control for computers (one on on mining..., see IFAC website)
No physics behind algorithms, applications, services, etc. "Let’s do things in cloud " (Sara Bouchenak from LIG-lab)
EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control
Languages difficulties Interest of both communities Computer science community wants control already operative Control community don’t care about computer sciences Except in Lund ! IFAC technical commitee on computer for control but none on control for computers (one on on mining..., see IFAC website)
No physics behind algorithms, applications, services, etc. "Let’s do things in cloud " (Sara Bouchenak from LIG-lab)
EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Languages difficulties Interest of both communities No physics behind algorithms, applications, services, etc. Building models is critical and unusual How do i put the system in the control theory normal form dx x = f (x , u) ? dt Frequency, poles, etc. are sometimes clear Control, outputs, sensors, etc. can disappear with a system update Evolution of a system can be discontinuous (robustness issue) No "tiredness", only crashes
RR
Model must capture main behavior BUT if too precise too complex if too complex inefficient for control (unrobust) Model for control is not classical modeling
Requires much more interaction than usual sciences
"Let’s do things in cloud " (Sara Bouchenak from LIG-lab)
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example
Languages difficulties Interest of both communities No physics behind algorithms, applications, services, etc. "Let’s do things in cloud computing" (Sara Bouchenak from LIG-lab)
EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Challenging difficulties Let’s start with the hardest things LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline
Languages difficulties Interest of both communities No physics behind algorithms, applications, services, etc. "Let’s do things in cloud control" (Sara Bouchenak from LIG-lab)
NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
4 / 26
Menu Starter: An short example of how bad computer system can be for control theory:
LCCC workshop on Cloud Control
Admission control for PostgreSQL database server
N. Marchand
Main dish: Introduction
Cloud control needs to
Motivation Outline
react to spikes (high frequency) reconfigure as less as possible (low frequency) L Antinomic !
NL example EB-PID Formulation Cases Simulations MapReduce control
Focus on Event-Based control More on event based PID Short presentation of extensions Assure SLA compliance in Hadoop Mapreduce
EB-Control Conclusion
Dessert: What need to be more efficient Hope it will be not too indigestible !
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
5 / 26
A nonlinear system example Reject
LCCC workshop on Cloud Control
Control
Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control
Admission Monitor
N. Marchand
Service
Admission control Proxy Clients
EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
6 / 26
A nonlinear system example Reject
LCCC workshop on Cloud Control
Control
Introduction Motivation Outline NL example
EB-Control Conclusion
Service
Admission control Proxy
EB-PID Formulation Cases Simulations MapReduce control
Admission Monitor
N. Marchand
Clients
Model gives when saturated:
dN dt dα dt dTo dt
(1 −hα) · Ti − To i 1 α − N (1 − To ) = −∆ MPL Ti = =
h
N 1 T − −∆ o aN 2 +bN +c
i
N: number of concurrent request on the server α: abandon rate
To : Throughput of served requests Ti : Throughput of incoming requests MPL: Multi Processing Level, it is the control variable a, b, c and ∆: parameters
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
6 / 26
A nonlinear system example Model gives when saturated:
LCCC workshop on Cloud Control
N. Marchand Introduction
Motivation Outline
dN dt dα dt dTo dt
(1 −hα) · Ti − To i 1 α − N (1 − To ) = −∆ MPL Ti = =
h i N 1 T − −∆ o aN 2 +bN +c
NL example EB-PID Formulation Cases Simulations MapReduce control
3 Quite a pretty model
EB-Control Conclusion
N. Marchand (gipsa)
few variables/parameters easily identifiable fits well
LCCC workshop on Cloud Control
22/03/2012
7 / 26
A nonlinear system example Model gives when saturated:
LCCC workshop on Cloud Control
N. Marchand Introduction
Motivation Outline
dN dt dα dt dTo dt
(1 −hα) · Ti − To i 1 α − N (1 − To ) = −∆ MPL Ti = =
h i N 1 T − −∆ o aN 2 +bN +c
NL example EB-PID Formulation Cases Simulations MapReduce control
3 Quite a pretty model
EB-Control
few variables/parameters easily identifiable fits well
40
30
Ne
Conclusion
50
20
10
0
−10
0
1
2
3
4
5
6
time (h)
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
7 / 26
A nonlinear system example Model gives when saturated:
LCCC workshop on Cloud Control
N. Marchand Introduction
Motivation Outline
dN dt dα dt dTo dt
(1 −hα) · Ti − To i 1 α − N (1 − To ) = −∆ MPL Ti = =
h i N 1 T − −∆ o aN 2 +bN +c
NL example EB-PID
3 Quite a pretty model
EB-Control Conclusion
few variables/parameters easily identifiable fits well
0.4 0.35 0.3
rejection rate (%)
Formulation Cases Simulations MapReduce control
0.25 0.2 0.15 0.1 0.05 0
0
1
2
3
4
5
time (h)
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
7 / 26
A nonlinear system example Model gives when saturated:
LCCC workshop on Cloud Control
N. Marchand Introduction
Motivation Outline
dN dt dα dt dTo dt
(1 −hα) · Ti − To i 1 α − N (1 − To ) = −∆ MPL Ti = =
h i N 1 T − −∆ o aN 2 +bN +c
NL example EB-PID
3 Quite a pretty model
EB-Control Conclusion
few variables/parameters easily identifiable fits well
5
4
Throughput (req/s)
Formulation Cases Simulations MapReduce control
3
2
1
0
−1
0
1
2
3
4
5
6
time (h)
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
7 / 26
A nonlinear system example Model gives when saturated:
LCCC workshop on Cloud Control
N. Marchand Introduction
Motivation Outline
dN dt dα dt dTo dt
(1 −hα) · Ti − To i 1 α − N (1 − To ) = −∆ MPL Ti = =
h i N 1 T − −∆ o aN 2 +bN +c
NL example EB-PID Formulation Cases Simulations MapReduce control
3 Quite a pretty model
EB-Control Conclusion
N. Marchand (gipsa)
7 Not an easy model
few variables/parameters easily identifiable fits well
LCCC workshop on Cloud Control
Model is highly nonlinear Not in the standard form for control theory Control is the level saturation of an exogenous input
22/03/2012
7 / 26
A nonlinear system example LCCC workshop on Cloud Control N. Marchand
Controlled thanks nonlinear control theory (Lyapunov) Stability is guaranteed for any value of the parameters No danger of miss-identification
Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
8 / 26
A nonlinear system example Controlled thanks nonlinear control theory (Lyapunov) Stability is guaranteed for any value of the parameters
LCCC workshop on Cloud Control
No danger of miss-identification
N. Marchand 100
Introduction
Formulation Cases Simulations MapReduce control
2
70
Workload mix
EB-PID
80
60 50 40
20 10 0
0
10
20
30
40
50
0
5
10
Time (min)
Conclusion
Latency (s)
10
25
30
35
40
40
Latency with ConSer Latency with ad−hoc control 1 Latency with ad−hoc control 2 Lmax
Abandon rate with ConSer Abandon rate with ad−hoc control 1 Abandon rate with ad−hoc control 2 αmax
35 30
8
6
4
25 20 15 10
2
0 0
20
Rejection rate control
14
12
15
Time (min)
Latency control
EB-Control
N. Marchand (gipsa)
1
30
Abandon rate (%)
NL example
90
Workload amount (#clients)
Motivation Outline
5
10
20
30
Time (min)
40
50
0
0
LCCC workshop on Cloud Control
10
20
30
40
50
Time (min)
22/03/2012
8 / 26
Menu LCCC workshop on Cloud Control N. Marchand
Main dish: Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
Cloud control needs to react to spikes (high frequency) reconfigure as less as possible (low frequency) L Antinomic !
Focus on Event-Based control More on event based PID Short presentation of extensions Assure SLA compliance in Hadoop Mapreduce
Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
9 / 26
Event-based sampling vs. periodic sampling LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example
Periodic sampling Sampling periodically on time Analogical to Riemann’s integral Well known theory (Shannon, etc.)
xi xi +1 xi −1 xi +2 xi +3 ti
ti +1
ti +2
ti +3
EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Event-based sampling Sampling on level’s At first glance close to Lebesgues integral Different extension : Outside event (event-triggered) State/output dependent sampling (self-triggered)
xi xi −1
xi +1 xi +2
ti
ti +1
ti +2
Should reduce transmission/computation Few theory N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
10 / 26
PID controller Classical work LCCC workshop on Cloud Control
ysp
e
PID
u
y PLANT
N. Marchand Introduction Motivation Outline NL example EB-PID
Classical PID In the frequency domain:
Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
µ
U(s) = K E (s) +
1 E (s) + Td sE (s) Ti s
¶
Discrete time version (hnom : sampling period, N tunes the filter): up (tk )
=
Ke(tk )
ui (tk +1 )
=
ud (tk )
=
u
=
ui (tk ) + Ki hnom e(tk ) ¢ Td KTd N ¡ u (t )+ e(tk ) − e(tk −1 ) Td + Nhnom d k −1 Td + Nhnom up + ui + ud
LCCC workshop on Cloud Control
22/03/2012
11 / 26
PID controller LCCC workshop on Cloud Control
Sampling ysp
N. Marchand
e
PID
u
y PLANT
Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Idea: do ¯¯ not update the ¯¯ control if y is close to ysp , typically if ¯¯e(ta ) − e(t ¯¯ a−1 ) ≤ qnom
No need to respect Shannon Bad behavior of the integral part
sampling instants
qnom
qnom linked to precision and noise
signal
h(ta ) ta−1
N. Marchand (gipsa)
LCCC workshop on Cloud Control
h(ta+1 ) time
ta ta+1
22/03/2012
12 / 26
What can happen (1/3) ? Simple integrator
LCCC workshop on Cloud Control
=u
Level-crossing sampling ⇒ update the control when e(x) = 0 Trajectory : xi +1 = xi + (ti +1 − ti ) · u Sampling instants ti
N. Marchand Introduction Motivation Outline
Sampling set: Te ,k ,x0 := {ti } ⊃ {0}
NL example EB-PID
dx dt
1
Formulation Cases Simulations MapReduce control
k(x) = −x, e(x) = 0 when |x | = exp(−κ), κ ∈ Z Te ,k ,x0 := j · (1 − exp(−1)), j ∈ N closed-loop system is globally asymptotically stable the solution is defined on [0, ∞[ the sampling set depends upon x0 ©
EB-Control Conclusion 2
ª
1
k(x) = −x 2 , e(x) = 0 when |x | = κ1 , κ ∈ Z x0 = 1 ⇒ ti +1 − ti = p 1 i (i +1) closed-loop system is globally asymptotically stable Zeno phenomenon: the solution is defined only on [0, 1.86[
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
13 / 26
What can happen (1/3) ? Simple integrator
LCCC workshop on Cloud Control
=u
Level-crossing sampling ⇒ update the control when e(x) = 0 Trajectory : xi +1 = xi + (ti +1 − ti ) · u Sampling instants ti
N. Marchand Introduction Motivation Outline
Sampling set: Te ,k ,x0 := {ti } ⊃ {0}
NL example EB-PID
dx dt
1
Formulation Cases Simulations MapReduce control
k(x) = −x, e(x) = 0 when |x | = exp(−κ), κ ∈ Z Te ,k ,x0 := j · (1 − exp(−1)), j ∈ N closed-loop system is globally asymptotically stable the solution is defined on [0, ∞[ the sampling set depends upon x0 ©
EB-Control Conclusion 2
ª
1
k(x) = −x 2 , e(x) = 0 when |x | = κ1 , κ ∈ Z x0 = 1 ⇒ ti +1 − ti = p 1 i (i +1) closed-loop system is globally asymptotically stable Zeno phenomenon: the solution is defined only on [0, 1.86[
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
13 / 26
What can happen (1/3) ? Simple integrator
LCCC workshop on Cloud Control
=u
Level-crossing sampling ⇒ update the control when e(x) = 0 Trajectory : xi +1 = xi + (ti +1 − ti ) · u Sampling instants ti
N. Marchand Introduction Motivation Outline
Sampling set: Te ,k ,x0 := {ti } ⊃ {0}
NL example EB-PID
dx dt
1
Formulation Cases Simulations MapReduce control
k(x) = −x, e(x) = 0 when |x | = exp(−κ), κ ∈ Z Te ,k ,x0 := j · (1 − exp(−1)), j ∈ N closed-loop system is globally asymptotically stable the solution is defined on [0, ∞[ the sampling set depends upon x0 ©
EB-Control Conclusion 2
ª
1
k(x) = −x 2 , e(x) = 0 when |x | = κ1 , κ ∈ Z x0 = 1 ⇒ ti +1 − ti = p 1 i (i +1) closed-loop system is globally asymptotically stable Zeno phenomenon: the solution is defined only on [0, 1.86[
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
13 / 26
What can happen (2/3) ? 3 LCCC workshop on Cloud Control
x0 = 1 ⇒ ti +1 − ti = i +11 closed-loop system is globally asymptotically stable limti +1 − ti = 0 when limti = ∞ Infinitely fast sampling at infinity
N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
k(x) = −x, e(x) = 0 when |x | = κ1 , κ ∈ Z
4
k(x) = −x 3 , e(x) = 0 when |x | = exp(−κ), κ ∈ Z x0 = 1 ⇒ ti +1 − ti = exp(2i) · [1 − exp(−1)] closed-loop system is globally asymptotically stable limti +1 − ti = ∞ when limti = ∞ Shannon’s condition is inconsistent the solution is defined on [0, ∞[ Infinitely slow sampling at infinity
LCCC workshop on Cloud Control
22/03/2012
14 / 26
What can happen (2/3) ? 3 LCCC workshop on Cloud Control
x0 = 1 ⇒ ti +1 − ti = i +11 closed-loop system is globally asymptotically stable limti +1 − ti = 0 when limti = ∞ Infinitely fast sampling at infinity
N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
k(x) = −x, e(x) = 0 when |x | = κ1 , κ ∈ Z
4
k(x) = −x 3 , e(x) = 0 when |x | = exp(−κ), κ ∈ Z x0 = 1 ⇒ ti +1 − ti = exp(2i) · [1 − exp(−1)] closed-loop system is globally asymptotically stable limti +1 − ti = ∞ when limti = ∞ Shannon’s condition is inconsistent the solution is defined on [0, ∞[ Infinitely slow sampling at infinity
LCCC workshop on Cloud Control
22/03/2012
14 / 26
What can happen (3/3) ? Unstable system:
LCCC workshop on Cloud Control
Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
= (x + u)3
xi +u −u 1−2(ti +1 −ti )·(xi +u )2
Solution is: xi +1 = p
N. Marchand Introduction
dx dt
5
k(x) = −2x, e(x) = 0 when |x | = exp(−κ), κ ∈ Z and initial condition x0 = 1 ti +1 − ti =
· ¸ exp(2i ) 1 · 1− 2 2 (2−exp(−1))
closed-loop system is globally asymptotically stable limti +1 − ti = ∞ when limti = ∞ Shannon’s condition is inconsistent the solution is defined on [0, ∞[
Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
15 / 26
What can happen (3/3) ? Unstable system:
LCCC workshop on Cloud Control
Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
= (x + u)3
xi +u −u 1−2(ti +1 −ti )·(xi +u )2
Solution is: xi +1 = p
N. Marchand Introduction
dx dt
5
k(x) = −2x, e(x) = 0 when |x | = exp(−κ), κ ∈ Z and initial condition x0 = 1 ti +1 − ti =
· ¸ exp(2i ) 1 · 1− 2 2 (2−exp(−1))
closed-loop system is globally asymptotically stable limti +1 − ti = ∞ when limti = ∞ Shannon’s condition is inconsistent the solution is defined on [0, ∞[
Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
15 / 26
PID controller LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline
We focus on the integral part What happens one waits too long before updating the control ? The integral part grows because h(ta ) grows: ui (ta ) = ui (ta−1 ) + Ki h(ta )e(ta ) | {z }| {z } big small
NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
Strong overshoot when the control is updated (similar to saturated PID without antiwindup)
Solution: replace the product h · e by a bounded function he: ui (ta ) = ui (ta−1 ) + Ki he(ta ) | {z } limited
Saturation, Exponential forgetting factor, Hybrid, etc.
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
16 / 26
PID controller Simulation result LCCC workshop on Cloud Control
First order system:
N. Marchand
H(s) =
Introduction Motivation Outline
G
PID controller: Kp = 1.83, Ti = 0.457 and sampling rate 0.05s
NL example EB-PID
EB-Control
Periodic sampling 400 samples
First order system −− Time−triggered PI control Setpoint and measured signal 2 Position [m]
Formulation Cases Simulations MapReduce control
where G = 1 and τ = 1
1+τ·s
1
Conclusion
setpoint time−based control
h(t) [s]
0
N. Marchand (gipsa)
0
2
4
6
0
2
4
6
8
10 12 time [s] Sampling intervals (time-based control)
14
16
18
20
14
16
18
20
0.05 0
8
10 time [s]
LCCC workshop on Cloud Control
12
22/03/2012
17 / 26
PID controller Simulation result LCCC workshop on Cloud Control
First order system:
N. Marchand
H(s) =
Introduction Motivation Outline
EB-PID
Evend based PID with saturated h · e
128 samples
First order system −− Control without safety limit (saturation of the integral gain)
Setpoint and measured signal 2 Position [m]
EB-Control
where G = 1 and τ = 1
1+τ·s
PID controller: Kp = 1.83, Ti = 0.457 and sampling rate 0.05s
NL example
Formulation Cases Simulations MapReduce control
G
1 setpoint time−based control saturation
Conclusion 0 2
4
6
8
0
2
4
6
8
10 12 time [s] Sampling instants (saturation)
14
16
18
20
14
16
18
20
Instants
0
N. Marchand (gipsa)
10 time [s]
LCCC workshop on Cloud Control
12
22/03/2012
17 / 26
PID controller Simulation result LCCC workshop on Cloud Control
First order system:
N. Marchand
H(s) =
Introduction Motivation Outline
EB-PID
Evend based PID with exponential forgetting 124 samples
First order system −− Control without safety limit (exponential forgetting factor of the sampling interval) Setpoint and measured signal 2 Position [m]
EB-Control
where G = 1 and τ = 1
1+τ·s
PID controller: Kp = 1.83, Ti = 0.457 and sampling rate 0.05s
NL example
Formulation Cases Simulations MapReduce control
G
1 setpoint time−based control exponential
Conclusion 0 2
4
6
8
0
2
4
6
8
10 12 time [s] Sampling instants (exponential)
14
16
18
20
14
16
18
20
Instants
0
N. Marchand (gipsa)
10 time [s]
LCCC workshop on Cloud Control
12
22/03/2012
17 / 26
PID controller Simulation result LCCC workshop on Cloud Control
First order system:
N. Marchand
H(s) =
Introduction Motivation Outline
EB-PID
Evend based PID with hybrid h · e 108 samples
First order system −− Control without safety limit (hybrid algorithm) Setpoint and measured signal 2 Position [m]
EB-Control
where G = 1 and τ = 1
1+τ·s
PID controller: Kp = 1.83, Ti = 0.457 and sampling rate 0.05s
NL example
Formulation Cases Simulations MapReduce control
G
1 setpoint time−based control hybrid
Conclusion 0 2
4
6
8
10 time [s] Sampling instants (hybrid)
12
14
16
18
20
0
2
4
6
8
10 time [s]
12
14
16
18
20
Instants
0
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
17 / 26
nts. e¯ and d¯ are related and have . Indeed, ...
L RESULTS
using the event-based approach can be seen in Figure 3.
MapReduce control
Event-based algorithm Simple PI controller
(M IHALY )
LCCC workshop on
Reference service time
Service time
#nodes
Timeyr(k)based y(k) onducted online, in Grid5000, upi(k) based (4 updates) + e(k)(8 updates) vs. Event Cloud Control ZPI ZMR nodes. Grid5000 is a French N. Marchand ure made up of a 5000 CPUs, MapReduce System PI controller mputing research. It provides a Introduction y(k) e scale distributed experiments, Motivation cluster used for the test has a Outline Fig. 3. Event-based PI feedback Control Architecture GHz, internal RAM memory NL an example and infiniband network. The EB-PID ementation framework Apache Formulation The results of implementing the Event Based PI controller ghCases level MRBS benchmarking on the same system as previously described are given in Simulations riments. A data intensive BI Figure 7. MapReduce rkload. The BI benchmark concontrol stem for a wholesale supplier. EB-Control tes a typical business oriented Fig. 5. Closed loop experiments - Time Based PI Control Fig. 7. Closed loop experime Conclusion unt of data (10GB here). To s Apache Hive is deployed on SQL like queries to a series of [7] Hadoop. H des in the cluster were on the http://hadoop.apache.org/doc work skews. [8] N. Marchand, S. Durand, a formula for event-based st in Matlab and all the measureTransactions on Automatic time. The service time1 and the [9] A. Sangroya, D. Serrano, an d from the cluster. The number ability of MapReduce Syste Distributed Systems (SRDS ed to ensure the service time 2012. nges in the number of clients. [10] A. Seuret, C. Prieur, and are implemented in Linux Bash systems by means of event Fig. 4. Closed loop experiments - Event Based PI Control
Time based fee
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MapReduce control Simple PI controller with feedforward Time based PI feedback control.
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d control. 100% more clients are added
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[7] Hadoop. Hadoop 1.1.2 release notes. http://hadoop.apache.org/docs/r1.1.2/releasenotes.html. [8] N. Marchand, S. Durand, and J. F. Guerrero-Castellanos. A general formula for event-based stabilization of nonlinear systems. IEEE Transactions on Automatic Control, 58(5):1332–1337, 2013. [9] A. Sangroya, D. Serrano, and S. Bouchenak. Benchmarking Dependability of MapReduce Systems. In IEEE 31st Symposium on Reliable Distributed Systems (SRDS), pages 21 – 30, Irvine, CA, 8-11 Oct. Time (min) 2012. [10] A. Seuret, C. Prieur, and N. Marchand. Stability of nonlinear by means of event-triggered algorithms.Control Journal Fig.systems 6. Closed loopworkshop experiments Eventsampling Based Feedforward LCCC on- Cloud Control 0 0
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NL example
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Introduction
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N. Marchand
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Time based (18 updates) vs. Event based (6 updates)
ed PI feedback control.
Motivation Outline
Time based fee
250
LCCC workshop on Cloud Control
[7] Hadoop. H http://hadoop.apache.org/doc [8] N. Marchand, S. Durand, a formula for event-based st Transactions on Automatic [9] A. Sangroya, D. Serrano, an ability of MapReduce Syste Distributed Systems (SRDS 2012. [10] A. Seuret, C. Prieur, and systems by means of event of Mathematical Control an [11] T. White. Hadoop: the defin 22/03/2012
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More food for people in control theory LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
Event-based control is really recent Now exist : Almost basic linear control where carried in an event-based framework (PID, LQR, etc.) Sontag’s general formula has been extended A lot of strategies based on Lyapunov theory exist Many practical implementations even on noisy and unstable systems Early results are appearing for time-delayed systems
Remain to clarify Real number of control updates All what it brings (in good and bad) is not clear Frequency analysis is less convenient
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Conclusion LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
People always adopt control theory ... Ecological constraints: car industry (in the 90’s) Nuclear plant: from the beginning (and one must be sure it works) Cost constraints: Petrol industries (in late 50’s) Energy constraints: Embedded systems (in the 00’s) Crash risks: Smart Grids (nowadays)
In all cases it was (is) a question of money Is it a question of money in cloud computing ? Before adopting control theory, intuitive control was the strategy Theory is the only way (control theory, game theory, queuing theory, etc.) to face safely complexity to guarantee results (even in unknown/unpredictable environment) to have flexibility
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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Conclusion LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
People always adopt control theory ... under constraint Ecological constraints: car industry (in the 90’s) Nuclear plant: from the beginning (and one must be sure it works) Cost constraints: Petrol industries (in late 50’s) Energy constraints: Embedded systems (in the 00’s) Crash risks: Smart Grids (nowadays)
In all cases it was (is) a question of money Is it a question of money in cloud computing ? Before adopting control theory, intuitive control was the strategy Theory is the only way (control theory, game theory, queuing theory, etc.) to face safely complexity to guarantee results (even in unknown/unpredictable environment) to have flexibility
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
21 / 26
Conclusion LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
People always adopt control theory ... under constraint Ecological constraints: car industry (in the 90’s) Nuclear plant: from the beginning (and one must be sure it works) Cost constraints: Petrol industries (in late 50’s) Energy constraints: Embedded systems (in the 00’s) Crash risks: Smart Grids (nowadays)
In all cases it was (is) a question of money Is it a question of money in cloud computing ? Before adopting control theory, intuitive control was the strategy Theory is the only way (control theory, game theory, queuing theory, etc.) to face safely complexity to guarantee results (even in unknown/unpredictable environment) to have flexibility
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
21 / 26
Conclusion LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
People always adopt control theory ... under constraint Ecological constraints: car industry (in the 90’s) Nuclear plant: from the beginning (and one must be sure it works) Cost constraints: Petrol industries (in late 50’s) Energy constraints: Embedded systems (in the 00’s) Crash risks: Smart Grids (nowadays)
In all cases it was (is) a question of money Is it a question of money in cloud computing ? Before adopting control theory, intuitive control was the strategy Theory is the only way (control theory, game theory, queuing theory, etc.) to face safely complexity to guarantee results (even in unknown/unpredictable environment) to have flexibility
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
21 / 26
Conclusion LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
People always adopt control theory ... under constraint Ecological constraints: car industry (in the 90’s) Nuclear plant: from the beginning (and one must be sure it works) Cost constraints: Petrol industries (in late 50’s) Energy constraints: Embedded systems (in the 00’s) Crash risks: Smart Grids (nowadays)
In all cases it was (is) a question of money Is it a question of money in cloud computing ? Before adopting control theory, intuitive control was the strategy Theory is the only way (control theory, game theory, queuing theory, etc.) to face safely complexity to guarantee results (even in unknown/unpredictable environment) to have flexibility
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
21 / 26
Conclusion LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
People always adopt control theory ... under constraint Ecological constraints: car industry (in the 90’s) Nuclear plant: from the beginning (and one must be sure it works) Cost constraints: Petrol industries (in late 50’s) Energy constraints: Embedded systems (in the 00’s) Crash risks: Smart Grids (nowadays)
In all cases it was (is) a question of money Is it a question of money in cloud computing ? Before adopting control theory, intuitive control was the strategy Theory is the only way (control theory, game theory, queuing theory, etc.) to face safely complexity to guarantee results (even in unknown/unpredictable environment) to have flexibility
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Better sort things by speed Patience (to explain and to get results)
From the control theory side: More interest Building a theory that handles computer science problems
From both side: Spend more time together Mix techniques from both side
Some inspiring fields Embedded systems deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...
Electrical grids centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc. N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Better sort things by speed Patience (to explain and to get results)
From the control theory side: More interest Building a theory that handles computer science problems
From both side: Spend more time together Mix techniques from both side
Some inspiring fields Embedded systems deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...
Electrical grids centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc. N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Better sort things by speed Patience (to explain and to get results)
From the control theory side: More interest Building a theory that handles computer science problems
From both side: Spend more time together Mix techniques from both side
Some inspiring fields Embedded systems deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...
Electrical grids centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc. N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Better sort things by speed Patience (to explain and to get results)
From the control theory side: More interest Building a theory that handles computer science problems
From both side: Spend more time together Mix techniques from both side
Conclusion
Some inspiring fields Embedded systems deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...
Electrical grids centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc. N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Patience (to explain and to get results)
From the control theory side: More interest Building a theory that better handles computer science problems Adaptive methods/model free Large scale interconnected systems
From both side: Spend more time together
Some inspiring fields Embedded systems (deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...) Electrical grids (centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc.) N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Patience (to explain and to get results)
From the control theory side: More interest Building a theory that better handles computer science problems Adaptive methods/model free Large scale interconnected systems
From both side: Spend more time together
Some inspiring fields Embedded systems (deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...) Electrical grids (centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc.) N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
23 / 26
What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Patience (to explain and to get results)
From the control theory side: More interest Building a theory that better handles computer science problems Adaptive methods/model free Large scale interconnected systems
From both side: Spend more time together
Some inspiring fields Embedded systems (deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...) Electrical grids (centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc.) N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
23 / 26
What need to be improved LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
From the computer science side: Classification of problems in big classes Standardisation of inputs/outputs/variables for each class Co-design / Control aware software Patience (to explain and to get results)
From the control theory side: More interest Building a theory that better handles computer science problems Adaptive methods/model free Large scale interconnected systems
From both side: Spend more time together
Some inspiring fields Embedded systems (deadline problems, energy optimization, re-allocation, heterogeneous MPSoC, ...) Electrical grids (centralized/decentralized, providers/consumers, cascading failure, heterogeneity, etc.) N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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Feedback loops become essential to handle variability LCCC workshop on Cloud Control
Three nested loops are used (to dynamically manage energy on chips)
N. Marchand
1 Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vdd
Computational Nodes
fclk
EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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Feedback loops become essential to handle variability LCCC workshop on Cloud Control
Three nested loops are used (to dynamically manage energy on chips)
N. Marchand
1 Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vlevel
flevel
Voltage Controller
Vdd
Frequency Controller
fclk
Computational Nodes
EB-Control Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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Feedback loops become essential to handle variability LCCC workshop on Cloud Control
Three nested loops are used (to dynamically manage energy on chips)
N. Marchand
1 Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vlevel
flevel
Voltage Controller
Vdd
Frequency Controller
fclk
Computational Nodes ω
EB-Control Conclusion
Energy/Performance Controller
ωsp − ω
ωsp
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
24 / 26
Feedback loops become essential to handle variability LCCC workshop on Cloud Control
Three nested loops are used (to dynamically manage energy on chips)
N. Marchand
1 Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vlevel
flevel
Voltage Controller
Vdd
Frequency Controller
fclk
Computational Nodes ω
EB-Control
Energy/Performance Controller
Conclusion
ωsp − ω
Cluster
ωsp
λ
λsp
N. Marchand (gipsa)
λsp − λ
QoS Controller
LCCC workshop on Cloud Control
22/03/2012
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Feedback loops become essential to handle variability LCCC workshop on Cloud Control
Three nested loops are used (to dynamically manage energy on chips)
N. Marchand
1 Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vlevel
flevel
Voltage Controller
Vdd
Frequency Controller
fclk
Computational Nodes ω
EB-Control
Energy/Performance Controller
Conclusion
ωsp − ω
Cluster
ωsp
λ
λsp
N. Marchand (gipsa)
λsp − λ
QoS Controller
LCCC workshop on Cloud Control
22/03/2012
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Feedback loops become essential to handle variability LCCC workshop on Cloud Control N. Marchand
Three nested loops are used (to dynamically manage energy on chips) Also the approach used in smart grids 1
Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vlevel
flevel
Voltage Controller
Vdd
Frequency Controller
fclk
Computational Nodes ω
EB-Control
Energy/Performance Controller
Conclusion
ωsp − ω
Cluster
ωsp
λ
λsp
N. Marchand (gipsa)
λsp − λ
QoS Controller
LCCC workshop on Cloud Control
22/03/2012
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Feedback loops become essential to handle variability LCCC workshop on Cloud Control N. Marchand
Three nested loops are used (to dynamically manage energy on chips) Also the approach used in smart grids 1
Introduction Motivation Outline
2 3
Control of the voltage and the frequency Control of the energy-performance tradeoff Control of the applicative Quality of Service (QoS)
NL example EB-PID Formulation Cases Simulations MapReduce control
Vlevel
flevel
Voltage Controller
Vdd
Frequency Controller
fclk
Computational Nodes ω
EB-Control
Energy/Performance Controller
Conclusion
ωsp − ω
Cluster
ωsp
λ
λsp
N. Marchand (gipsa)
λsp − λ
QoS Controller
LCCC workshop on Cloud Control
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Grenoble Workshop on Autonomic Computing and Control LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control Conclusion
N. Marchand (gipsa)
Date: 27 may 2014 Location: Grenoble Organisation: Eric Rutten, INRIA and Stéphane Mocanu, Gipsa-lab Confirmed speakers: Karl-Erik ARZEN (Lund, Sweden) Alberto LEVA (Milano, Italy) Ada DIACONESCU (Telecom Paris-Tech, France) Suzanne LESECQ (CEA LETI) Didier DONSEZ (LIG) Bogdan ROBU (GIPSA) Eric RUTTEN (INRIA)
LCCC workshop on Cloud Control
22/03/2012
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35th International Summer School of Automatic Control LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
Date: September, 8-12, 2014 Location: Grenoble Focus: Modern Tools for Nonlinear Contral Confirmed lecturers: Didier HENRION Andrew TEEL Laurent PRALY Mirko FIACCHINI Luca ZACCARIAN
Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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35th International Summer School of Automatic Control LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
Date: September, 8-12, 2014 Location: Grenoble Focus: Modern Tools for Nonlinear Contral Confirmed lecturers: Didier HENRION Andrew TEEL Laurent PRALY Mirko FIACCHINI Luca ZACCARIAN
Conclusion
N. Marchand (gipsa)
LCCC workshop on Cloud Control
22/03/2012
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35th International Summer School of Automatic Control LCCC workshop on Cloud Control N. Marchand Introduction Motivation Outline NL example EB-PID Formulation Cases Simulations MapReduce control EB-Control
Date: September, 8-12, 2014 Location: Grenoble Focus: Modern Tools for Nonlinear Contral Confirmed lecturers: Didier HENRION Andrew TEEL Laurent PRALY Mirko FIACCHINI Luca ZACCARIAN
Conclusion
N. Marchand (gipsa)
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22/03/2012
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