# Presentation: 290392

## Lyapunov Stability Analysis and On-Line Monitoring 

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

## 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. **

## 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

## 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.

## 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.**

## 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.**

## Accomplishments – Online Monitoring Tool

**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

## Accomplishments – Online Monitoring Tool

**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

## 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.**