Abstract
Much of engineering is concerned with the topic of optimization, and at the heart of much of our optimization is dynamical systems. Dynamical systems can be thought of as either non-linear continuous-time differential equations or difference equations. Chaos occurs in dynamical systems, and frequently in engineering we seek to avoid chaos. At times chaos becomes the central fascination.
This paper first introduces a situation in signal processing for neural systems in which chaos is the perhaps unexpected phenomena and the object of study. The focus then shifts to the topic of optimization of systems via dynamical systems, where traditionally chaos is avoided as much as possible. The essential dynamical system should converge in a very smooth manner to an optimal solution to some problem of interest. Our technical approach is summarized to optimization via dynamical systems is illustrated by an application in the area of robotics.
The key questions motivating this research are: Does the human brain exploit chaos for generating intelligence? Can our computing machines and control systems enhance their intelligence by a clever introduction of chaos?
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References
M. Buss, H. Hashimoto and J.B. Moore, “Dextrous Hand Grasping Force Optimization”, IEEE Transactions on Robotics and Automation, to appear, see also Proceedings of the IEEE Conference on Robotics and Automation, pp 1034–1039, Nagoya, Japan, May 1995.
M. Buss, L. Faybusovich, and J.B. Moore, “Dikin-Type Semidefinite Programming Algorithms for Dextrous Grasping Force Optimization”, International Journal of Robust and Nonlinear Control, submitted.
S.H. Chung, V. Krishnamurthy and J.B. Moore, “Adaptive Processing Techniques based on Hidden Markov Models for Characterizing Very Small Channel Currents Buried in Noise and Deterministic Interferences”, Philosophical Transactions of Royal Society, Vol. 334, 1991, pp. 357–384.
S.H. Chung, J.B. Moore, and L. Xia, P. Gage, L.S. Premkumar, “Characterization of Single Channel Currents using Digital Signal Processing Techniques based on Hidden Markov Models”, Phil. Trans, of Royal Society, London B, Vol. 329, September 1990, pp. 265–285, see also Proc. of Australian Physiological Society, Newcastle, September 1989.
I.B. Collings, V. Krishnamurthy and J.B. Moore, “On-line Identification of Hidden Markov Models via Recursive Prediction Error Techniques”, IEEE Transactions on Signal Processing, vol 42, no 12, pp 3535–3539, see also Proc. of IFAC World Congress, Sydney, July 1993, vol V, 423–426.
R.E. Elliott, L. Aggoun and J.B. Moore, Hidden Markov Models: Estimation and Control, Springer-Verlag, 1995, (361 pages).
U. Helmke and J.B. Moore, Optimization and Dynamical Systems, Springer-Verlag, 1993, (390 pages).
V. Krishnamurthy, J.B. Moore and S.H. Chung, “Hidden Markov Model Signal Processing in Presence of Unknown Deterministic Interferences”, IEEE Trans, on Automatic Control, Vol 38, Jan 1993, pp. 146–152, see also Conf. on Dec. and Control, Brighton UK, December 1991, pp. 662–667.
V. Krishnamurthy, J.B. Moore and S.H. Chung, “On Hidden Fractal Model Signal Processing”, Vol. 24, Issue No. 2, August 1991, pp. 177–191, see also Proc. of Int. Symp. on Information Theory and its Applications, Hawaii, December 1990, pp. 243–246.
V. Krishnamurthy, J.B. Moore and S.H. Chung, “Signal Processing of semi-Markov Models with Exponentially Decaying States”, Conference on Dec. and Control, Brighton UK, December 1991, Vol 3, pp. 2744–2749.
M. Mason and J. Salisbury, Robot Hands and the Mechanics of Manipulation, Cambridge, Massachusetts: MIT Press, 1995.
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© 1997 Birkhäuser Boston
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Moore, J.B. (1997). Dynamical Systems, Optimization, and Chaos. In: Judd, K., Mees, A., Teo, K.L., Vincent, T.L. (eds) Control and Chaos. Mathematical Modelling, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2446-4_13
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DOI: https://doi.org/10.1007/978-1-4612-2446-4_13
Publisher Name: Birkhäuser Boston
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