Place: Chauvenet 201 at 12:00 pm
Time: Friday, April 4Speaker: Erik Bollt, USMA
Title: Communicating With a High Powered Digital Transmitter Using Only Small Power Variations, Through Control of Chaos
Abstract: Recent work has proven the possibility of utilizing symbolic representation of controlled chaotic orbits for communications with chaotic signal generators. The evolution of trajectories of a chaotic dynamical system is equivalent to symbolic dynamics in an appropriate symbol space. The recent advent and physical applications of controlling chaos using the OGY (Ott, Grebogi, and Yorke) technique and a variety of targeting algorithms has proven that chaos can be mastered, and inherent instabilities can be taken as an advantage, allowing small deliberate perturbations to cause large signal variations. Coupling control of chaos through small perturbations with learning the grammar of the corresponding symbol dynamics means that the control perturbations are actually a coding scheme on the original dynamics. The application is to build a high powered signal generator, which operates intentionally in the chaotic regime, so that a small scale piggy-back controller circuit, on the micro-chip scale, has the ability to accurately manipulate high powered message bearing signals.
In this talk, we focus on the oxymoron of "controlling chaos," which is resolved in the definition of chaos, and we include examples from the speaker's research such as a low-energy transfer orbit to the Moon. We restrict our scope with a simplified example, in the interest of clarity; controlling symbol dynamics and communications will be developed in terms of the one-dimensional logistic map. The relevance of this simplification to the more general, and relevant differential equations describing electronic circuits will be discussed. In terms of a map-based description of the dynamics, relevant technical issues include: learning the variation of map iterates due to variations in control parameters, learning the semi- conjugacy, or coding function, between the dynamics of the map on the attractor and the grammar of the corresponding symbol dynamics, and finding the minimal grammar, which is dependent on the appropriate choice of the partition in phase space.