Use of Chaos in a Lyapunov Dynamic Game

  • J. Skowronski (Mechanical Engineering, University of Southern California) ;
  • W. J. Grantham (Mechanical and Materials Engineering, Washington State University) ;
  • Lee, B. (Department of Mechanical and Automotive Engineering, Keimyung University)
  • Published : 2003.11.01

Abstract

Feedback strategies of a qualitative competitive game between two players can be designed such as to influence parameters of a mechanical system to induce chaotic behavior. The purpose is to reduce the options and effects of the opponent's strategy. We show it on a case with dynamics specified by a nonautonomous Duffing equation with the players represented by damping and external forcing, respectively. It seems however that the conclusions can be made valid generally.

Keywords

References

  1. Arderna, M. D., Skowronski, J. M., 1989, 'Coordination Controllers for Multi-arm Manipulators-A Case Study', Adv. Control & Dyn. Systems, Acad. Press
  2. Awrejcewicz, J., 1988, 'Chaotic Motion in a Nonlinear Oscillator with Friction,' KSME International Journal, Vol. 2, No. 2
  3. Filippov, A. F., 1977, 'Existence of Solutions of Generalized Differential Equations,' Math Notes, Vol. 10, pp. 1267-1272
  4. Lee, B. S., 1995, 'Chaos Maximizing Optimal Control,' KSME International Journal, Vol. 9, No. 4
  5. Skowronski, J. M., 1986, Control dynamics of robotic manipulators, Academic Press
  6. Skowronski, J. M. and Stonier, R. J., 1987, 'The Barrier in the Pursuit-Evasion Game with Two Targets,' Int. J. Computers & Math. Appl., Vol. 13, pp. 37-45 https://doi.org/10.1016/0898-1221(87)90092-7
  7. Skowronski, J. M. and Vincent, T. L., 1988, 'Playability with and Without Capture,' J. Opt. Th. Appl., Vol. 36 https://doi.org/10.1007/BF00934341
  8. Skowronski, J. M., 1989, Control of nonlinear mechanical systems, Plenum, NY
  9. Thompson, J. M. T. and Stewart, H. B., 1986, Nonlinear dynamics and chaos, Wiley
  10. Ueda, V., 1980, 'Explosion of Strange Attractors Exhibited by Duffing Equation,' in R. H. Helleman (ed), Nonlinear Dynamics, N. Y. Ac. Sci., pp. 422-434