Abstract
Control algorithms that exploit chaotic behavior can vastly improve the performance of many practical and useful systems. Phase-locked loops, for example, are normally designed using linearization. The approximations thus introduced lead to lock and capture range limits. Design techniques that are equipped to exploit the real nonlinear nature of the device loosen these limitations. The program Perfect Moment is built around a collection of such techniques. Given a differential equation and two points in the system's state space, it automatically selects and maps the region of interest, 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 via appropriate parameter changes at the segment junctions. Rules embodying theorems and definitions from nonlinear dynamics are used to limit complexity by focusing the mapping and search on the areas of interest. Even so, these processes are computationally intensive. Ho...
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