Non-Lipschitzian control algorithms for extended mechanical systems.
We derive the properties of a general control algorithm [Braiman et al., Phys. Rev. Lett. 90, 094301 (2003)] for quantities describing global features of nonlinear extended mechanical systems. The control algorithm is based on the concepts of non-Lipschitzian dynamics and global targeting. We show that (i) certain average quantities of the controlled system can be driven-exactly or approximately-towards desired targets which become linearly stable attractors for the system's dynamics; (ii) the basins of attraction of these targets are reached in very short times; and (iii) while within reasonably broad ranges the time-scales of the control and of the intrinsic dynamics may be quite different, this disparity does not affect significantly the overall efficiency of the proposed scheme, up to natural fluctuations.
Protopopescu
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Center for Engineering Science Advanced Research, Computing and Computational Sciences Directorate, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA.
Barhen
J
J