Lyapunov Stability Analysis and On-Line Monitoring

1. Lyapunov Stability Analysis and On-Line Monitoring Bojan Cukic, Edgar Fuller, Srikanth Gururajan, Martin Mladenovski, Sampath Yerramalla NASA OSMA SAS July 20-22, 2004

2. 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.

3. 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

4. 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.

5. 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.

6. 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.

7. 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

8. 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

9. 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.