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

Research Heaven, West Virginia 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.

Research Heaven, West Virginia 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

Research Heaven, West Virginia 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.

Research Heaven, West Virginia 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.

Research Heaven, West Virginia 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.

Research Heaven, West Virginia Failed Flight Condition (1) Control surface failure (Locked Left Stabilator at imposed deflection, 3 Deg) Failure induced at cycle 600 of OLNN (corresponding to 100 th 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 C1_movie

Research Heaven, West Virginia 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 N1_movie

Research Heaven, West Virginia 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.