Abstract
The paper presents the role of self-stabilization analysis in the design, verification and validation of the dynamics of an Adaptive Flight Control System (AFCS). Since the traditional self-stabilization approaches lack the flexibility to deal with the continuous adaptation of the neural network within the AFCS, the paper emphasizes an alternate self-stability analysis approach, namely Lyapunov’s Second Method. A Lyapunov function for the neural network is constructed and used in presenting a formal mathematical proof that verifies the following claim: While learning from a fixed input manifold, the neural network is self-stabilizing in a Globally Asymptotically Stable manner. When dealing with variable data manifolds, we propose the need for a real-time stability monitor that can detect unstable state deviations. The test results based on the data collected from an F-15 flight simulator provide substantial heuristic evidence to support the idea of using a Lyapunov function to prove the self-stabilization properties of the neural network adaptation.
This work was supported in part by NASA through cooperative agreement NCC 2-979. The opinions, findings, conclusions and recommendations expressed herein are those of the authors and do not reflect the views of the sponsors.
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Yerramalla, S., Fuller, E., Mladenovski, M., Cukic, B. (2003). Lyapunov Analysis of Neural Network Stability in an Adaptive Flight Control System. In: Huang, ST., Herman, T. (eds) Self-Stabilizing Systems. SSS 2003. Lecture Notes in Computer Science, vol 2704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45032-7_6
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