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Lyapunov Stability Analysis and Lyapunov Stability Analysis and On-Line Monitoring On-Line Monitoring

Bojan Cukic, Edgar Fuller, Srikanth Gururajan, Martin Mladenovski, Sampath Yerramalla

NASA OSMA SAS

July 20-22, 2004

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Research Heaven,West Virginia

PROBLEM

• Adaptive Systems– Adaptability at the cost of uncertainty.– Extensive testing is not sufficient for (I)V&V– Incomplete learning vs. excessive training– Lack of prior known, existing, or practiced V&V 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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Research Heaven,West Virginia

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 (Murphy’s Rule)

index of monitor streams

– Interpret multiple-monitor data streams with Fuzzy Logic (Mamdani) data fusion technique

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IMPORTANCE/BENEFITS

• V&V 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 (IV&V) 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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• 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

Accomplishments – Online Monitoring Tool

Video Clip

C1_movie

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• 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

Accomplishments – Online Monitoring Tool

Video Clip

N1_movie

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Research Heaven,West VirginiaNEXT 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.