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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References
A. Arora, M. Demirbas and S. Kulkarni. Graybox Stabilization. International Conference on Dependable Systems and Networks (DSN’2001), Goteborg, Sweden, July 2001. 79
A. Arora. Stabilization. Encyclopedia of Distributed Computing, edited by Partha Dasgupta and Joseph E. Urban, Kluwer Academic Publishers, 2000. 79
Ingo Ahrns, Jorg Bruske, Gerald Sommer. On-line Learning with Dynamic Cell Structures. Proceedings of the International Conference on Artificial Neural Networks, Vol. 2, pp. 141–146, 1995. 82
William L. Brogan. Modern Control Theory. II Edition, Prentice-Hall Inc., 1985. 80
Jorg Bruske, and Gerald Sommer. Dynamic Cell Structures, NIPS, Vol. 7, Pages 497–504, 1995. 82
Jorg Bruske, Gerald Sommer. Dynamic Cell Structure Learns Perfectly Topology Preserving Map. Neural Computations, Vol. 7, No. 4, pp. 845–865, 1995.
Marc W. Mc. Conley, Brent D. Appleby, Munther A. Dahleh, Eric Feron. Computational Complexity of Lyapunov Stability Analysis Problems for a Class of Nonlinear Systmes. Society of industrial and applied mathematics journal of control and optimization, Vol. 36, No. 6, pp. 2176–2193, November 1998. 80
Edsger W. Dijkstra. Self-stabilizing systems in spite of Distributed Control. Communications of the Assocoation for Computing Machinery, 17(11), 643–644, 1974. 79
Bernard Friedland. Advanced Control System. Prentice-Hall Inc., 1996. 80
Bernd Fritzke. A Growing Neural Gas Network Learns Topologies. Advances in Neural Information Processing Systems, Vol. 7, pp. 625–632, MIT press, 1995.
Tom M. Heskes, Bert Kappen. Online Learning Processes in Artificial Neural Networks. Mathematical Foundations of Neural Networks, pp. 199–233, Amsterdam, 1993.
Charles C. Jorgensen. Feedback Linearized Aircraft Control Using Dynamic Cell Structures. World Automation Congress, ISSCI 050.1-050.6, Alaska, 1991. 78
J. L.W. Kessels. An Exercise in Proving Self-satbilization with a variant function. Information Processing Letters (IPL), Vol. 29, No.1, pp. 39–42, September 1998. 79
Teuvo Kohonen. The Self-Organizing Map. Proceedings of the IEEE, Vol. 78, No. 9, pp. 1464–1480, September 1990.
Thomas Martinetz, Klaus Schulten. Topology Representing Networks. Neural Networks, Vol. 7, No. 3, pp. 507–522, 1994. 82, 83
Kumpati S. Narendra, Kannan Parthasarathy. Identification and Control of Dynamic Systems Using Neural Networks. IEEE Transactions on Neural Networks, Vol. 1, No. 1, pp. 4–27, March 1990. 77
Kumpati S. Narendra. Intelligent Control. American Control Conference, San Diego, CA, May 1990. 77, 78
Jurgen Rahmel. On The Role of Topology for Neural Network Interpretation, Proc. of European Conference on Artificial Intelligence, 1996. 83
Orna Raz. Validation of Online Artificial Neural Networks (ANNs)-An Informal Classification of Related Approaches. Technical Report for NASA Ames Research Center, Moffet Field, CA, 2000. 77
N. Rouche, P. Habets, M. Laloy. Stability Theory by Liapunov’s Direct Method. Springer-Verlag, New York Inc. publishers, 1997.
Marco Schneider. Self-Stabilization. Assocoation for Computing Machinery (ACM) sureveys, Vol. 25, No. 1, March 1993.
The Boeing Company. Intelligent Flight Control: Advanced Concept Program. Project report, 1999. 78
Oliver Theel. An Exercise in Proving Self-Stabilization through Lyapunov Functions. 21st International Conference on Distributed Computing Systems, ICDS’01, April 2001. 79
Sampath Yerramalla, Bojan Cukic, Edgar Fuller. Lyapunov Stability Analysis of Quantization Error for DCS Neural Networks. Accepted for publication at International Joint Conference on Neural Networks (IJCNN’03), Oregon, July 2003. 87
Wen Yu, Xiaoou Li. Some Stability Properties of Dynamic Neural Networks. IEEE Transactions on Circuits and Systems, Part-1, Vol. 48, No. 2, pp. 256–259, February 2001.
Xinghuo Yu, M. Onder Efe, Okyay Kaynak. A Backpropagation Learning Framework for Feedforward Neural Networks, IEEE Transactions on Neural Networks, No. 0-7803-6685-9/01, 2001. 84
V. I. Zubov. Methods of A.M. Lyapunov and Their Applications. U.S. Atomic Energy Commission, 1957. 80
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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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DOI: https://doi.org/10.1007/3-540-45032-7_6
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