Johann Schumann and Pramod Gupta

1
Bayesian Verification Validation tools for
adaptive systems

• Johann Schumann and Pramod Gupta
• NASA Ames Research Center
• schumann_at_email.arc.nasa.gov
• pgupta_at_email.arc.nasa.gov

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Motivation for NN VV

• Fixed gain controllers cannot deal with
  catastrophic changes or degradation in plant
• Adaptive systems (e.g., NN) can react to
  unexpected situations through learning
• Relevance and potential
• IFCS NN controlled aircraft (F-15, C-17)
• UAV control
• Space exploration
• Any safety-critical application of NN control

• Basis for Case Study I
• Neuro-adaptive control (IFCS Gen-II)
• Network learns to compensate for deviations
  between plant and model
• Previous work
• SW VV process for NN-based control
• Confidence tool for dynamic monitoring

The major obstacle to the deployment of adaptive
and autonomous systems is being able to verify
their correct operation In Flight
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VV Issues our Approach

• Verification how to specify an unforseen event?
• Validation not possible to test all
  configurations

While traditional VV methods will remain useful,
these methods alone are insufficient to verify
and certify adaptive control systems for use in
safety-critical applications

• Our approach combines mathematical analysis,
  intelligent validation, and dynamic monitoring
  and supports specific software VV process,
• targets multiple aspects and phases of VV of
  adaptive control systems, and
• uses a unique combination of research in
• Neural Networks
• Control Theory
• Numerical Methods
• Bayesian Statistics

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Our Bayesian Approach
How good is the network performing at the moment?

• Traditional NN as a Black Box
• Here Look at probability distribution of the NN
  output
• Variance (confidence measure) depends on
• How well is the network trained?
• How close are we to well-known areas

Large variance bad estimate no reliable
result, just a guess

• Small variance good estimate

Our approach, based on a Bayesian approach,
provides a measure of how well the neural
network is performing at the moment
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Milestone I Envelope Tool

• Basis Adaptive NN-based controller
• Lyapunov error bound defines regions of eventual
  stability
• Regions where confidence is small might cause
  instability
• Informally a safe envelope is a region where
  the confidence level is sufficiently high
• Bayesian approach combined with sensitivity
  analysis
• Challenge methods for efficient determination
  of safe envelope

• Can help answer questions like
• How large is the current safe envelope?
• How far is the operational point from the edge?

Current status mathematical background
formulated, prototypical Matlab/Simulink
implementation designed, first simulation
experiments
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Confidence Envelope
Confidence Surface
bad
Safety Envelope area of good confidence
1/confidence
good
airspeed
altitude
The Envelope tool uses a Bayesian Approach to
calculate the current safety envelope
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Conclusions next steps

• Current work as scheduled toward deliverable
  (9/2004)
• prototypical implementation in Matlab/Simulink
• report on mathematical background and tool
• Getting Case Study I ready IFCS Gen-II simulink
  model
• Next steps in research
• system identification (sysID) estimate
  confidence of parameters
• other model representations (e.g., parameter
  tables with polynomial interpretation)
• Preparation of Case Study II and III