Taming Chaotic Circuits

摘要

Control algorithms that exploit chaotic behavior and its precursors can vastlyimprove the performance of many practical and useful systems. Phase-locked loops, for example, are normally designed using linearization. This approximation hides the global dynamics that lead to lock and capture range limits. Design techniques that are equipped to exploit the real nonlinear and chaotic nature of the device can loosen these limitations. The program Perfect Moment is built around a collection of such techniques. Given a differential equation, a control parameter, and two state-space points, the program explores the system's behavior, automatically choosing interesting and useful parameter values and constructing state-space portraits at each one. It then chooses a set of trajectory segments from those portraits, uses them to construct a composite path between the objectives, and finally causes the system to follow that path by switching the parameter value at the segment junctions. Rules embodying theorems and definitions from nonlinear dynamics are used to limit computational complexity by identifying areas of interest and directing and focusing the mapping and search on these areas. Even so, these processes are computationally intensive. 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 state perturbations make this approach rewarding in spite of its computational demands.... Nonlinear dynamics, Controlling chaos, Design assistant, Phase-locked loop, Chaos.