The phase-following technique combines the use of return maps with signal averaging to accomplish the phase lock. The averaging makes the technique particularly robust to noise or other contamination in the drive signal.

Finally, the drive signal can be filtered or transformed, both of which can be undone at the response receiver to keep the transmitter and receiver acting chaotically but in synchronization with each other. This ability to mangle a chaotic signal and recover it has potential uses in private communications. A patent has been disclosed for filtering and unfiltering synchronous, chaotic signals. Several other approaches to control and exploit chaos have been found, and two other patents are pending.

Wavelets and Image Processing

Approaches to image processing using traditional Fourier methods characteristically have difficulty with edges because the Fourier basis fractions are spatially extended. Recently, an approach involving basis functions of finite extent, called wavelets, has been applied successfully to image processing. Although wavelets are finite, they need not all be of the same length. It has been proven that wavelets form a mathematically complete orthogonal basis set with which to represent a two-dimensional image with arbitrary accuracy. Further, a hierarchical set of wavelets, similar to geometric fractals, can be employed to cover an area. Wavelets can form a representation of fractals. Wavelets lend themselves to very rapid image processing using parallel computers. Images containing edges can be represented using wavelets, with acceptable loss of detail, with data compressed 100:1. As mentioned above, the efficiency of image fitting is a complex nonlinear problem. Commercial ventures are using the wavelet approach encoded on a chip as a contender in the high-definition television (HDTV) compression competition.


Image sensors are the first step in a system for visual pattern recognition. To reduce the communication load and improve speed, it is desirable to perform image processing in the sensor itself, before the image is read out to the rest of the system. The development of smart sensors that use distributed processing for this purpose has been actively pursued at a number of laboratories. The principles of operation make use of developments in electronic neural networks, cellular automata, and related fields.

The highly parallel architectures associated with neural network approaches are well suited to rapid signal processing for pattern recognition. For example, the Caltech group has produced a silicon retina that uses on-chip processing to do spatial and temporal derivatives for moving edge detection. In more recent work, an associated company has produced a commercial chip to optically read account numbers from checks. The vision chip project at the Massachusetts Institute of Technology has developed novel charge-coupled techniques for charge-coupled device (CCD) camera chips to do on-chip smoothing and recognition of orientation.

Robotics and Adaptive Control


Robots will be increasingly important for a wide range of applications in the military. The optimal control of robotic arms and actuators is an interesting problem in nonlinear dynamics. Robot arms typically consist of a number of rotary joints connected together, each with its own sensors and actuators; the choice of the most efficient individual motions of these joints to accomplish a single collective motion can be a surprisingly complex problem in nonlinear optimization. Training robots to accomplish specific tasks via a series of procedures or examples is also an important and active area. For example, researchers at MIT and the University of Michigan have developed systems to train robots to maintain their balance while hopping or running and to bounce balls on a paddle, and researchers at the University of Utah have developed sophisticated techniques to program body motions of robots in human form for use in Disneyworld.

Nonlinear dynamics is important for problems in control of machines and target acquisition. Recent progress has been demonstrated in the stabilization of chaotically

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