Lyapunov Stability Analysis and On-Line Monitoring

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Lyapunov Stability Analysis and On-Line
Monitoring

• Bojan Cukic, Edgar Fuller, Srikanth Gururajan,
  Martin Mladenovski, Sampath Yerramalla
• NASA OSMA SAS
• July 20-22, 2004

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PROBLEM

• Adaptive Systems
• Adaptability at the cost of uncertainty.
• Extensive testing is not sufficient for (I)VV
• Incomplete learning vs. excessive training
• Lack of prior known, existing, or practiced VV
  techniques suitable for online adaptive systems
• Understanding of self-stabilization analysis
  techniques suitable for adaptive system
  verification.
• Investigate effective means to determine the
  stability and convergence properties of the
  learner in real-time.

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APPROACH

• Online Monitoring
• Derive understanding of the self-stabilization
  analysis techniques suitable for neural network
  verification.
• Develop an analysis model and show its
  applicability for run-time monitoring.
• Investigate the applicability of the developed
  analysis method with respect to the currently
  developed verification /certification techniques.
• Confidence Evaluation
• Validate output from monitors using
  Dempster-Schafer (Murphys Rule) index of monitor
  streams
• Interpret multiple-monitor data streams with
  Fuzzy Logic (Mamdani) data fusion technique

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IMPORTANCE/BENEFITS

• VV techniques suitable for non-deterministic
  systems are an open research subject.
• Through the analysis of the NASA systems, we
  learn more about the better design techniques for
  adaptability.
• Development of techniques and tools for
• Behavioral analysis of adaptive systems prior to
  the deployment.
• Run-time safety monitoring and pilot warning
  systems regarding the imminent threats or
  abnormal adaptive system behavior.
• Real-time compatibility
• Aim at tools which can be deployed off-line
  (IVV) and embedded in on-board computers.

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Relevance to NASA

• Artificial Neural Networks (ANN) play an
  increasingly important role in flight control and
  navigation, two focus areas for NASA.
• Autonomy and adaptability are important features
  in application domains that arise routinely at
  NASA.
• Autonomy is becoming an irreplaceable feature for
  future NASA missions.
• Interest expressed by Dryden/Ames to include our
  techniques into the future Intelligent Flight
  Control projects.
• Theory applicable to the future agent based
  applications planned by NASA.

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Accomplishments

• Studied the self-stabilizing properties of neural
  networks used in IFCS project.
• Defined multiple types of learning errors in DCS
  neural networks.
• Developed and applied stabilization analysis
  techniques to real-time flight simulator data.
• Developed stability monitors that assess the
  time-dependent risk functions for adaptive
  systems.
• Developed data fusion techniques to evaluate
  time-dependent confidence measures for on-line
  learning.

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Accomplishments Online Monitoring Tool

• Failed Flight Condition (1)
• Control surface failure (Locked Left Stabilator
  at imposed deflection, 3 Deg)
• Failure induced at cycle 600 of OLNN
  (corresponding to 100th frame of the monitors and
  confidence indicators)
• During the failure
• Software monitors show a spike
• Confidence indicators show a predominantly dip
• Indication an abnormal response in OLNN behavior
  

C1_movie
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Accomplishments Online Monitoring Tool

• No Failure (Nominal) Flight Condition
• No induced failures
• Software monitors show a no predominant spikes
• Confidence indicators show a smooth increase in
  confidence of OLNN learning.
• Indication no abnormal response in OLNN behavior
  

N1_movie
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NEXT STEPS

• Systematic analysis of robustness through
  extensive simulation
• Further experimentation with closed-loop flight
  simulation data.
• Probabilistic analysis of neural network
  performance in real-time setting.
• Predicting convergence rates in advance.
• Studying the theoretical basis of learning for
  the types of adaptive systems considered in
  future NASA missions.