A Study on Particle Filter based Synchronization of Uncertain Chaos Systems

DoctorChaos systems occur in many real-world engineering and scientific problems.Such systems exhibits aperiodic behavior that depends very sensitively on initial condition and parameter variation. As the result, long-term prediction of the chaos systems is impossible in general.One of the most successful applications of chaos system is the communication and signal processing. Chaotic signals generated by a chaos system are typically broadband, noise-like and difficult to predict, thus they can be used to mask information on signals and to modulate waveforms in spread spectrum systems and to encrypt data for enhancing security. However the chaos systems defy synchronization because chaos system yields un-predictable phenomena of their behavior, thus synchronization of chaos systems has been an interesting issue. Since Pecora and Carroll showed that chaos systems can be synchronized with drive-response framework, the chaos synchronization has been extensively studied. Although various successful synchronization methods were proposed, almost all of the research consider the time-invariant chaos system with the model known exactly. However, in practice, system uncertainties as well as disturbing noise are inevitable, which are caused by parameter variation, parameter uncertainties, unknown parameters, un-modeled dynamics, modeling error. Therefore, the synchronization scheme without considering these uncertainties often fails to synchronization or performance degradation occurs. Therefore, in this thesis, we consider the synchronization of chaos systems with uncertainties, Especially we consider chaos systems with stochastic parameter uncertainties.Because chaos systems have unstable dynamics in general and the stochastic parameter uncertainties affect systems as like multiplicative noise, analytic approach to synchronize two chaos system has inevitable limitation. Hence, in the paper, an approach using the particle filter(PF) that is one of the Bayesian state estimation method and based on Monte-Carlo simulation scheme. Compared to conventional filtering methods such as the extended Kalman filter, the PF has less restrictive characteristics on nonlinearity of the system and statistics of disturbing noises.In order to apply the PF for synchronizing two chaos system with stochastic parameter uncertainties, we propose two particle filtering methods with prediction-correction structure. First, for a special class of chaos system that has stochastic uncertainties in linear part of the system, we introduce a method to correct particles drawn from a simple proposal density function, which minimizes the upper-bound of maximum error variance. Next, we propose a new PF for general stochastic uncertain chaos systems, which uses the kernel density estimation scheme. Finally, as an application of PF based chaos synchronization, we propose an M-ary secure chaos communication scheme under Rayleigh fading channel using maximum a posteriori (MAP) estimation method