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Spatial variation of temperature
EEG BP
Tackling New Frontiers in Modeling and Analysis of Cyber Physical Systems
EKG SpO2 Base Station Motion Sensor
Ayan Banerjee and Sandeep K.S. Gupta IMPACT Lab, CIDSE Arizona State University x = cos(θ )
.
y = sin(θ )
.
θ = w
.
Cyber-Physical System Model
Computing System Computing Requirements
Reliability Accuracy Throughput Latency Safety
Physical System Continuous physical process Actuator Physical Requirements
1. 2. 3. 4. 5.
Control Algorithm
Control Algorithm
Sensor Unintended Side Effects
1. Safety 2. Energy efficiency Dynamic contexts 3. Low carbon Random footprint
Multi-dimensional Partial Differential Equations
Processes
Cyber-Physical Interactions (CPI) SpatioTemporal Simplifying Assumptions
Linearity Time Invariance
Aggregate Effects
Low dimension Determinism
Dynamic Contexts
Independence of Computation & Physics Ignore emergent behavior
Challenges to CPS Modeling
Model based safety analysis and verification under context driven spatio-temporal aggregate cyber-physical interactions Hybrid models of CPI, theoretical and simulation based analysis, and automated synthesis of implementation from models
• Linearity assumptions are invalid
– Non-linear control systems
• Spatio-temporal considerations
– Solution of partial differential equations
• Dynamic contexts affect CPI
– Unified modeling of physical and cyber events
• Emergent behavior
– Theoretically unpredictable
Emergent Behavior
CPSes are complex systems - Emergent behavior: patterns arising out of a multiplicity of relatively simple interactions
Emergence cannot be predicted
Approximation of Emergence is necessary
-
Example: Multi drug interaction
Drug concentration for multi-channel infusion
50 45 40 35
Single Drug:
∂d (r, t) + ∇(u d (r, t)) = ∇(D(r)∇d (r, t)) + Γ(r )(d B (t) − d (r, t)) − λ d (r, t) ∂t
Infusion sites
Y - Axis
d – drug concentration at a distance r at time t, D and λ are constants Multi Drug Approximation:
30 25 20 15 10 5 0
∂d1 (r, t) + ∇(u d1 (r, t)) = ∇(D(r)∇d1 (r, t)) + Γ(r )(d B (t) − d (r, t)) − λ (d1 (r, t) + d 2 (r, t)) ∂t ∂d1 (r, t) + ∇(u d1 (r, t)) = ∇(D(r)∇d1 (r, t)) + Γ(r )(d B (t) − d (r, t)) − λ (d1 (r, t) + d 2 (r, t)) ∂t
Time = 10s 500s 100s
Simultaneous solution of free boundary problems
0
5
10
15
20
25
30
35
40
45
50
X - Axis
CPS Modeling Course
• Defining CPSes
– Study systems models of CPSes in different domains
• Control Systems
– Focus on non-linear time variant analysis (Lyapunov)
• Abstract Mathematics
– Theory of real numbers, vector spaces, convexity theory
• Differential Equations
– Exact and finite error solutions of non-linear partial differential equations
• Formal Methods
– Stochastic hybrid automata and reachability theory
• Theory of Emergence
Solutions and Tools
• Spatio-Temporal Hybrid Automata
– Hybrid model checking for CPS
• Applied to drug infusion systems
• BAND-Aide: Simulation analysis of CPI
– Applied on body sensor networks and data centers
• Evaluation of CPI under Dynamic contexts
– Applied on wearable infusion pumps
• Health-Dev: Safety assured automatic code generation for healthcare systems
Effective characterization of CPI in some mathematical form
Thank You
EEG BP
Tackling New Frontiers in Modeling and Analysis of Cyber Physical Systems
EKG SpO2 Base Station Motion Sensor
Ayan Banerjee and Sandeep K.S. Gupta IMPACT Lab, CIDSE Arizona State University x = cos(θ )
.
y = sin(θ )
.
θ = w
.
Cyber-Physical System Model
Computing System Computing Requirements
Reliability Accuracy Throughput Latency Safety
Physical System Continuous physical process Actuator Physical Requirements
1. 2. 3. 4. 5.
Control Algorithm
Control Algorithm
Sensor Unintended Side Effects
1. Safety 2. Energy efficiency Dynamic contexts 3. Low carbon Random footprint
Multi-dimensional Partial Differential Equations
Processes
Cyber-Physical Interactions (CPI) SpatioTemporal Simplifying Assumptions
Linearity Time Invariance
Aggregate Effects
Low dimension Determinism
Dynamic Contexts
Independence of Computation & Physics Ignore emergent behavior
Challenges to CPS Modeling
Model based safety analysis and verification under context driven spatio-temporal aggregate cyber-physical interactions Hybrid models of CPI, theoretical and simulation based analysis, and automated synthesis of implementation from models
• Linearity assumptions are invalid
– Non-linear control systems
• Spatio-temporal considerations
– Solution of partial differential equations
• Dynamic contexts affect CPI
– Unified modeling of physical and cyber events
• Emergent behavior
– Theoretically unpredictable
Emergent Behavior
CPSes are complex systems - Emergent behavior: patterns arising out of a multiplicity of relatively simple interactions
Emergence cannot be predicted
Approximation of Emergence is necessary
-
Example: Multi drug interaction
Drug concentration for multi-channel infusion
50 45 40 35
Single Drug:
∂d (r, t) + ∇(u d (r, t)) = ∇(D(r)∇d (r, t)) + Γ(r )(d B (t) − d (r, t)) − λ d (r, t) ∂t
Infusion sites
Y - Axis
d – drug concentration at a distance r at time t, D and λ are constants Multi Drug Approximation:
30 25 20 15 10 5 0
∂d1 (r, t) + ∇(u d1 (r, t)) = ∇(D(r)∇d1 (r, t)) + Γ(r )(d B (t) − d (r, t)) − λ (d1 (r, t) + d 2 (r, t)) ∂t ∂d1 (r, t) + ∇(u d1 (r, t)) = ∇(D(r)∇d1 (r, t)) + Γ(r )(d B (t) − d (r, t)) − λ (d1 (r, t) + d 2 (r, t)) ∂t
Time = 10s 500s 100s
Simultaneous solution of free boundary problems
0
5
10
15
20
25
30
35
40
45
50
X - Axis
CPS Modeling Course
• Defining CPSes
– Study systems models of CPSes in different domains
• Control Systems
– Focus on non-linear time variant analysis (Lyapunov)
• Abstract Mathematics
– Theory of real numbers, vector spaces, convexity theory
• Differential Equations
– Exact and finite error solutions of non-linear partial differential equations
• Formal Methods
– Stochastic hybrid automata and reachability theory
• Theory of Emergence
Solutions and Tools
• Spatio-Temporal Hybrid Automata
– Hybrid model checking for CPS
• Applied to drug infusion systems
• BAND-Aide: Simulation analysis of CPI
– Applied on body sensor networks and data centers
• Evaluation of CPI under Dynamic contexts
– Applied on wearable infusion pumps
• Health-Dev: Safety assured automatic code generation for healthcare systems
Effective characterization of CPI in some mathematical form
Thank You