“Chaotification” of Real Systems by Dynamic State Feedback

Abstract

Chaos - which, to the best of the knowledge of the authors, is the most complex behavior of deterministic dynamic systems - is observed in many systems modeled by nonlinear ordinary or partial differential and difference equations. The vast amount of chaos literature is mainly devoted to the analysis and implementation of chaotic dynamics and to chaos control, i.e., the design of controllers changing the behavior of an originally chaotic system so that it possesses a stable equilibrium or limit cycle. Against the mainstream chaos studies in control, a new field, called “chaotification” (also called “chaos anti-control” or “chaotization”) has emerged, in order to exploit chaotic behavior instead of escaping from it. This is inspired by limited but successful engineering applications of chaotic dynamics in cryptology, secure communication, and mixing of liquids. This paper presents a brief review of chaotic dynamics and chaos control. It also presents a novel chaotification method, which can be applied to any input state of a system that can be linearized, including linear controllable systems as special cases. The chaotification introduced - which is realized by a dynamic state feedback increasing the order of the open-loop system to have the same chaotic dynamics as a reference chaotic system - is used to “chaotify” a real dc motor to have the celebrated Lorenz chaotic dynamics.