2 research outputs found
Observer-based chaos synchronization for secure communications
Chaos, with reference to chaos theory, refers to an apparent lack of order in a system
that, nevertheless, obeys particular laws or rules. The chaotic signals generated by
chaotic systems have some properties such as randomness, complexity and sensitive
dependence on initial conditions, which make them particularly suitable for secure
communications. Since the 1990s, the problem of secure communication, based on
chaos synchronization, has been thoroughly investigated and many methods, for instance,
robust and adaptive control approaches, have been proposed to realize the
chaos synchronization. However, from systems theory perspective, it may seem obvious
that many robust and adaptive control methods could be considered for possible
attacks against secure communication.
In this thesis, we introduce the concept of secure chaos synchronization from the control
theoretic view point. A new secure communication system, based on the chaos
synchronization, is proposed and its security is analyzed, both theoretically and numerically
Computational Intelligence and Complexity Measures for Chaotic Information Processing
This dissertation investigates the application of computational intelligence methods in the analysis of nonlinear chaotic systems in the framework of many known and newly designed complex systems. Parallel comparisons are made between these methods. This provides insight into the difficult challenges facing nonlinear systems characterization and aids in developing a generalized algorithm in computing algorithmic complexity measures, Lyapunov exponents, information dimension and topological entropy. These metrics are implemented to characterize the dynamic patterns of discrete and continuous systems. These metrics make it possible to distinguish order from disorder in these systems. Steps required for computing Lyapunov exponents with a reorthonormalization method and a group theory approach are formalized. Procedures for implementing computational algorithms are designed and numerical results for each system are presented. The advance-time sampling technique is designed to overcome the scarcity of phase space samples and the buffer overflow problem in algorithmic complexity measure estimation in slow dynamics feedback-controlled systems. It is proved analytically and tested numerically that for a quasiperiodic system like a Fibonacci map, complexity grows logarithmically with the evolutionary length of the data block. It is concluded that a normalized algorithmic complexity measure can be used as a system classifier. This quantity turns out to be one for random sequences and a non-zero value less than one for chaotic sequences. For periodic and quasi-periodic responses, as data strings grow their normalized complexity approaches zero, while a faster deceasing rate is observed for periodic responses. Algorithmic complexity analysis is performed on a class of certain rate convolutional encoders. The degree of diffusion in random-like patterns is measured. Simulation evidence indicates that algorithmic complexity associated with a particular class of 1/n-rate code increases with the increase of the encoder constraint length. This occurs in parallel with the increase of error correcting capacity of the decoder. Comparing groups of rate-1/n convolutional encoders, it is observed that as the encoder rate decreases from 1/2 to 1/7, the encoded data sequence manifests smaller algorithmic complexity with a larger free distance value