A Control Algorithm for Chaotic Physical Systems
Abstract
Control algorithms that exploit chaos's unique properties can vastly improve the performance of many practical and useful systems. The program "Perfect Moment" is built around such an algorithm. Given a differential equation and two points in the system's state space, it automatically maps the space, chooses a set of trajectory segments from the maps, uses them to construct a composite path between the points, and causes the system to follow that path by monitoring the state and switching parameter values at the segment junctions. The creation of and search through the maps are computationally intensive processes. However, the sensitivity of a chaotic system's state-space topology to the parameters of its equations and the sensitivity of the paths of its trajectories to the initial conditions make this approach rewarding in spite of its computational demands. This program and its results are illustrated with several examples, among them the driven single pendulum and its electronic analog, the phase-locked loop. In this particular case, strange attractor bridges, which traverse boundaries of basins of attraction and thus alter the reachability of different state space points, can be used to broaden the capture range of the circuit.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1991
- Accession Number
- ADA260098
Entities
People
- Elizabeth Bradley
Organizations
- Massachusetts Institute of Technology