Green Scheduling for Energy-Efficient Building Controls"
Prof. Rahul Mangharam
Director, Real-Time & Embedded Systems Lab
Dept. Electrical & Systems Engineering
Dept. Computer & Information Science
University of Pennsylvania
rahulm@seas.upenn.edu
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Green Scheduling for Energy-Efficient Building Controls"
With Truong X. Nghiem, Madhur Behl and Willy Bernal
Published in: Green Computing’11, CDC’11, ACC’12,
CDC’12, BuildSys’12, RTSS’12, ACC’13,2 ICCPS’14
Example
The Peak Power Minimization Problem
supply = demand
111 million viewers watch the SuperBowl
During a commercial, millions of refrigerators and microwaves trigger
simultaneously, causing massive spikes in the energy demand
Human behavior and environmental conditions are responsible for high
temporal correlation of energy demand.
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Madhur Behl (Univ of Penn)
Green Scheduling
February 24, 2012
10 /
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5 days electric bill è $1.5 Million
5
Penn’s Electricity Demand in 2011
2011 Hourly Power Consumption for UPenn depicted with 95 percentile "Shoulder Days"
120
12 days highest demand
cost
$1.9 million
(6.76% total bill)
Power Consumption (in MW)
100
80
60
40
20
0
01
Total bill: $28.3 million
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03
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Green Scheduling
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12
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Peak Electricity Demand is Expensive!
2011 Hourly Real Time Mkt prices based on Locational Marginal Pricing (LMP) for PECO by PJM
Peak
$817/MWh
800
700
600
27 x
$/MW-h
500
400
300
200
Normally
$30/MWh
100
0
01
02
03
04
05
06
Green Scheduling
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11
7
12
Time of Day
Green Scheduling
Peak Hours
8
12am
11pm
10pm
9pm
8pm
7pm
6pm
5pm
4pm
3pm
2pm
1pm
11am
12pm
10am
9am
8am
7am
6am
5am
4am
3am
2am
1am
12am
Electricity demand (MW)
Peak Electricity Demand is Expensive!
Time of Day
Green Scheduling
Peak Hours
9
12am
11pm
10pm
9pm
8pm
7pm
6pm
5pm
4pm
3pm
2pm
1pm
11am
12pm
10am
9am
8am
7am
6am
5am
4am
3am
2am
1am
12am
Electricity demand (MW)
Peak Demand Reduction
Economic
incentive to
reduce peak
demand
Time of Day
Green Scheduling
Peak Hours
10
12am
11pm
10pm
9pm
8pm
7pm
6pm
5pm
4pm
3pm
2pm
1pm
11am
12pm
10am
9am
8am
7am
6am
5am
4am
3am
2am
1am
12am
Electricity demand (MW)
How to Reduce Peak Demand?
Electricity demand (MW)
Peak Demand Reduction Approaches
•  Operate on coarse
grainedloads
Scheduling
Turn off devices
time scales
(demand/load
Dim
lights
•  Do not guarantee a quality
of
shifting)
Adjust thermostat
performance
Time of Day
Peak Hours
Green Scheduling
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12am
11pm
10pm
9pm
8pm
7pm
6pm
5pm
4pm
3pm
2pm
1pm
11am
12pm
10am
9am
8am
7am
6am
5am
4am
3am
2am
1am
12am
...
Motivation
Un-coordinated Control Systems
HVAC (Heating,Ventilation and Air Conditioning) systems, chiller
systems and lighting systems operate independently of each other
frequently result in temporally correlated energy demand surges (peaks)
Madhur Behl (Univ of Penn)
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Green Scheduling
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November 29, 2011
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GREEN SCHEDULING
APPROACH
Green Scheduling
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Demand
Green Scheduling (GS) Approach
Load
•  Dynamics
•  Constraints
Disturbances
Load
•  Dynamics
•  Constraints
Disturbances
Green Scheduling
Load
•  Dynamics
•  Constraints
Disturbances
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Green Scheduling (GS) Approach
Demand
Peak constraint
Load
•  Dynamics
•  Constraints
Disturbances
Load
•  Dynamics
•  Constraints
Disturbances
Green Scheduling
Set a peak
constraint
Load
•  Dynamics
•  Constraints
Disturbances
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Green Scheduling (GS) Approach
Coordinate dynamical loads
1.  Under peak envelope
2.  Satisfy safety constraints
Load
•  Dynamics
•  Constraints
Disturbances
Demand
Peak constraint
Load
•  Dynamics
•  Constraints
Disturbances
Green Scheduling
Load
•  Dynamics
•  Constraints
Disturbances
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From Control to Scheduling
•  Control loops are
abstracted as tasks
•  Extract temporal
parameters across
multiple control loops
•  Compute a global
schedule, reduce peak
power by de-correlating
systems
Green Scheduling
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GS: Analysis & Synthesis
Demand
Peak constraint
Schedulability analysis
Is a peak constraint
feasible? (how to choose a
peak constraint?)
Coordinate dynamical loads
1.  Under peak envelope
2.  Satisfy safety constraints
How to schedule the loads
safely under a feasible
peak constraint?
Schedule/Control Synthesis
Green Scheduling
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GS Control/Scheduling Structure
weather
occupancy
...
Schedulability analysis
Feasible Peak
Minimization
Peak constraint
Scheduling Controller
Zone i
xi
on/o↵
Scheduling synthesis
Green Scheduling
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for the systems.
Scheduling controller: operates the systems to satisfy the peak
GS Control/Scheduling
Structure
constraint
(set by peak minimization) while
maintaining climate
conditions.
weather
occupancy
...
Feasible Peak
Minimization
Peak constraint
Scheduling Controller
on/off
Demand
Zone i
xi
re-compute peak constraint
t
Green Scheduling
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From Control to Scheduling
In Energy Control Systems
Execution time is dependent on
Plant Dynamics: dimensions of the room, ingress and egress airflow
Environmental Conditions: outside weather, human occupancy, air
quality
Initial State
Tasks have elastic execution times where a task may have to
perform more work, the longer its response time.
Aim: keep the state of a system within a deadband
Both are resource contrained problems
Here the resource is electricity/energy as opposed to a processor
PSU (power supply unit) scheduling instead of CPU scheduling.
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Madhur Behl (Univ of Penn)
Green Scheduling
February 24, 2012
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First Order Task Model
x
b1
a1
h
l
b0
a0
ON OFF ON OFF ON
t
Simplified heat balance equation to model each zone
dxi
Ci
= Ki (Ta
dt
x i ) + Qi
(1)
Zone temperature is governed by the following affine di↵erential equation:
✓
◆
dxi
Ki
Ki
Qi
=
xi +
Ta +
= a i xi + b i
(2)
dt
Ci
Ci
Ci
Madhur Behl (Univ of Penn)
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Green Scheduling
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Geometric Interpretation
Intuitive and simple framework for scheduling a system of linear tasks.
Two linear tasks T1 and T2 , normalized
so that their bounds are both [0, 1]
Define a 2-dimensional state vector
x = [x1 , x2 ]T 2 R2
There are three scheduling modes:
Mode 0: T1 and T2 are OFF (vector v0 )
Mode 1: T1 is ON and T2 is OFF (v1 )
Mode 2: T1 is OFF and T2 is ON (v2 )
Scheduling Policy
Keeps x(t) within bounds (invariant set) using mode vectors v0 , v1 and v2
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Green Scheduling
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Scheduling Policy as Hybrid Automaton
States
Edges
correspondto
!
scheduling modes
!
switching between modes
correspondto
gij is the guard associated for each edge, for the transition from mode
i to mode j.
Scheduling policy ⇡ for the task set is simply a set of guards {gij }
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Madhur Behl (Univ of Penn)
Green Scheduling
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November 29, 2011
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Lazy Scheduling Policy: Hybrid Automaton
Lazy Policy : All tasks stay in their current modes as long as they are safe
g01 and g21 are both (x1  l1 );
g02 and g12 are both (x2  l2 );
g10 is (x1
g20 is (x2
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Madhur Behl (Univ of Penn)
Green Scheduling
h1 ^ x2 > l2 );
h2 ^ x1 > l1 ).
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Simulation: Two-Task System
Feasibility constraint: Keep temperature centered around mean 70 F
Heating system operates with a power of 12000 BTU/h or 3.517 kW
Cooling occurs through heat loss and does not consume any extra
power
Each time step of the algorithm is of 15 minute duration
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Task1
Task2
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Temperature (in ° F)
73
72
71
70
69
68
67
66
65
0
10
20
30
40
Time
50
60
70
80
Figure: Peaks occur when
28 tasks run independently 28
Madhur Behl (Univ of Penn)
Green Scheduling
November 29, 2011
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Simulation: Peak Reduction
Peak Reduction of 50%
2
2
1.8
1.6
1.6
Power Consumed in kW
Power Consumed in kW
1.8
1.4
1.2
1
0.8
0.6
0.4
1.2
1
0.8
0.6
0.4
0.2
0
0
1.4
0.2
10
20
30
40
Time
50
60
70
80
0
0
Figure: Power Consumption:
Independent Tasks
20
30
40
Time
50
60
70
80
Figure: Power Consumption: Lazy
Scheduling
Peak Power = 1.758 kW
Total Energy = 50.11 kWh
Madhur Behl (Univ of Penn)
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Peak Power = 0.879 kW
Total Energy = 45.72 kWh
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Green Scheduling
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Simulation: Lazy Scheduling
1
0.8
x2
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
x1
Figure: State-Space Trajectory
Tasks remain within thresholds
Modes only change in a lazy manner (near thresholds)
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Green Scheduling
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November 29, 2011
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Feedback
Event-triggered
•  Hierarchical,
ACC’13
distributed control
•  Pricing signal &
financial cost
Simple
Feedback
Feed-
forward
Control Strategy
Green Scheduling – So far…
•  More realistic
RTSS’12
IGCC’11
CDC’11
ACC’12
applications
CDC’12
with & without
load interaction
with & without
disturbances
Model complexity
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APPLICATION:
ENERGY-EFFICIENT OPERATION OF
MULTIPLE CHILLER PLANTS
Green Scheduling
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Peak Power Minimization
Peak Demand Reduction
Madhur Behl (mbehl@seas.upenn.edu)
Green Scheduling
Green Scheduling
RTSS 2012
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5 / 73
Chiller Plant Operation at Penn
Chilled water distribution system
at the University of Pennsylvania
Chiller Plant A
•  Over 4M gallons of chilled water (42 F) pumped into the campus.
•  Plant A consumes 26 MW at full capacity
•  Plant A and Plant B account for > 30% of total peak power
consumption (108 MW)
Green Scheduling
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COP vs. PLR
•  Approximate COP by quadratic function of PLR
COP = a0 + a1 PLR + a2 PLR2
Example:
If cooling load = 1000 RT1,
chiller capacity = 1250 RT,
then PLR = 1000/1250 = 0.8,
and COP obtained from
COP-PLR curve.
Refrigeration Ton is the amount of heat that must be removed to melt 1 Ton
of ice in 24h. 1 RT = 3517W
1
Green Scheduling
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Thermal Energy Storage (TES)
Thermal Energy Storage is used for demand shifting
and off loading chillers.
•  Long term: > 10 hours
•  Short term: < 2 hours
TES at Cornell University
Short-term Thermal Energy Storage can improve the
COP of the chiller plant.
Green Scheduling
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How TES Improves the COP?
Green Scheduling
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No Thermal Energy Storage
Inefficient
Green Scheduling
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TES Discharging
Efficient!
Green Scheduling
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TES Charging
Efficient!
Green Scheduling
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Multiple chiller plants with TES
Uncoordinated operation among multiple chiller plants
can cause large spikes in total electricity consumption.
Our goal is to coordinate multiple chiller plants to
reduce their aggregate peak power consumption.
Green Scheduling
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GS for Chiller Plants
•  Consider m > 1 chiller plants.
•  Each plant has a short term TES system.
•  Compute modes for each hour h, h = 0,1,...,H, based on
load forecasting.
•  Charging mode: water level increases with rate ai,h > 0;
•  Discharging mode: water level decreases with rate bi,h < 0.
Behl, M.; Nghiem, T. X.; Mangharam, R., Green Scheduling for Energy-Efficient Operation
of Multiple Chiller Plants, RTSS 2012.
Green Scheduling
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Single chiller plant with TES
•  Say PLR = 0.34 i.e., in region B
•  Plant can operate in optimal regions 1 and 2 if a TES
is available.
Green Scheduling
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GS for Chiller Plants
Schedule the operating modes ui(t), t ≥ 0, of all plants
such that:
Green Scheduling
Reduce peak demand
•  Safety Constraint:
li ≤ xi(t) ≤ hi ∀t, i
•  Peak Constraint:
n
X
i=1
ui (t)  k(t)
8t
x1 , a1 , b1
xm , am , bm
u1
um
Optimize COP
Optimize COP
···
Chiller Plant 1
Green Scheduling
Chiller Plant m
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Simulation Setup
Three chiller plants, each containing 3 chillers.
•  Lower safety threshold: 3m
•  Upper safety threshold: 13.5m
•  Time step = 15 mins
Chiller plant configuration in the simulation
Plant 1
3 chillers rated at 1250 RT, 1200 hp
Plant 2
3 chillers rated at 1250 RT, 1200 hp
Plant 3
3 chillers rated at 1000 RT, 900 hp
Tchws
5.5°C (42°F)
Tcwr
20°C (68°F)
∆T
10°C
Green Scheduling
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Average Hourly Load Profile
Green Scheduling
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Simulation Scenarios
1.  Case 1: No Thermal Energy Storage present
2.  Case 2: Thermal Energy Storage with uncoordinated
operation
3.  Case 3: Thermal Energy Storage with (discrete-time)
Green Scheduling
Green Scheduling
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Simulation Result: Power Demand
Green Scheduling
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Simulation Result: Power Demand
Green Scheduling
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Cumulative Power Consumption (MWh)
Cumulative Energy Consumption
80
No TES
TES without GS
TES with GS
60
40
20
0
6a
7a
8a
9a 10a 11a 12p 1p
2p
3p
4p
5p
6p
7p
Hour of day (6am – 8pm)
Green Scheduling
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8p
Electricity Pricing Policy
PECO’s demand pricing rate structure:
Block
kWh’s in Block
Charges (cents per kWh)
First Block
80 × peak
24.94
Second Block
80 × peak
12.67
Third Block
Remaining
8.64
Green Scheduling
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Simulation Result Summary
Green Scheduling leads to the lowest electricity bill.
Peak
(MW)
Energy Consumption
(MWh) single day
Expected
Monthly Bill ($)
%
savings
No TES
6.40
80.9
292,801
-
On-Off
with TES
7.38
66.1
274,266
6.33
GS with
TES
6.48
61.4
243,461
16.85
Green Scheduling
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SCHEDULING SYNTHESIS:
DISCRETE-TIME FEEDBACK SCHEDULING
Green Scheduling
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Discrete-time Green Scheduling
•  Consider discrete-time dynamics
x(t + 1) = Ax(t) + B0 + Bu(t) + W d(t), 8t 2 N
for a finite time horizon [0, T].
•  Safety constraint: x(t) ∈ S ⊂ Rn ∀t
•  Initial state x(0) ∈ S
•  Xf ⊆ S: set of desired final states at time T: x(T) ∈ Xf
Discrete-time
•  Define theGreen
set of Scheduling
admissible discrete-time schedules
Define U(k(·), S, x0 , Xf ) as the set of all discrete-time schedules
u : {0, 1, . . . , T 1} ⌅ {0, 1}m such that:
1
2
3
m
i=1
ui ( ) ⇥ k( ) for all ; ⇤ Peak constraint
x( ) ⇧ S for all ; ⇤ Safety constraint
x(T ) ⇧ Xf . ⇤ Terminal state is reached
TES dynamics:
Green Scheduling
xi ( + 1) = fi (xi ( ), ui ( ), )
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Robust Backward Reachable Sets
Robust backward reachable set operator:
Given any X ⊆ S at time step t, define operator
1
Rt (X) = {x ⇥ S : ⌅u :
X
i
ui
k(t) ⇧ f (x, u, d) ⇥ X ⇤d ⇥ D}
which is the set of safe states that can reach X with
some admissible control u, regardless of the
constrained disturbance d.
Rt 1 (X)
maps to
via some admissible u
for all d in D
Green Scheduling
X
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Pre-compute Backward in Time
•  Using robust backward reachable set operator,
compute a sequence of sets {Xt : t = 0,1,...,T}
backward in time from XT = Xf : Xt = R−1t(Xt+1)
X0
X1
…
XT = Xf
•  Each Xt is the set of safe states from which and from
time step t, the system state can reach the final set Xf
safely under the time-varying peak constraint k(·).
Green Scheduling
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MLE+: Matlab Toolbox for Integrated Modeling and Controls for Energy-­‐Efficient Buildings 1
EnergyPlus Building
Model
2
System Identification
3
Control Design in
Matlab
Willy Bernal, Madhur Behl, Truong Nghiem and Rahul Mangharam 5 Control Deployment
4
Simulation Results
58
MLE+: Design and Deployment IntegraAon of Energy-­‐
Efficient Building Controls Willy Bernal, Madhur Behl, Truong Nghiem and Rahul Mangharam Test-­‐Bed Dashboard MLE+ BACnet 59
Integrated Modeling: HVAC System
CentralHVAC
Occupancy Setpoints
HVAC System
•
Temperature Setpoints according
to Schedule
•
Central HVAC Model
•
VAV Boxes
VAV Boxes
NREL: Campus-­‐Wide SimulaFon Courtesy of NREL Campus Simulation: Two Building Example
Return
Supply
Chiller Plant
Office B1
Office B2
Overview
ü  Air-cooled Electric
Chiller.
o  10kW
ü  2 Small Office
Buildings.
o  50 people
o  5 zone
o  400m2
ü  Shared Chilled Water
Loop.
MLE+ Cloud Analytics: Overview
MLE+ Coordinator
(Local)
EnergyPlus
Template File
Control Knobs/
Parameters
Master
Cloud Coordinator
Model
EC2
Define Variable
Range
Define Optimization
Method
Analyze Results
Mod
Mod
Mod
EC2
els
els
Extract
Model
els
Mod
Mod
Mod
EC2
els
els
Model
els
Parameter
Mod
Mod
Mod
els
Extract
els
Model
els
Simulate
Parameter
Extract
Parameter
Simulate
Simulate
Cyber-Physical Systems
•  Intersection of Computation, Controls & Communication
–  Safety-critical and Life-critical systems
•  Tightly coupled with (Messy) Physical Plants
–  Interesting Domains: Medical, Energy, Automotive…
•  New Interesting Problems involving:
–  Scheduling and Control
–  From Verified Models to Verified Code of Closed-loop
Systems
64
Research Focus
Networked Cyber-Physical Systems
Medical Device
Network CPS
Automotive CPS
Software & Systems Industrial Control Nets Automotive Plug-n-Play
Real-Time
Parallel Computing
Distributed Real-Time Systems
and
Real-Time Network Protocols
Modeling & Tools for Virtualization and Deployment
Domain-specific Platforms
Energy-efficient
Building Automation
Industrial Control
& Actuation Networks
Feedback-based Medical
Device Networks