Tung-Sheng Chiang

Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems

This paper presents synthesis approaches for synchronization and secure communications of chaotic systems by using fuzzy model-based design methods. Many well-known continuous and discrete chaotic systems can be exactly represented by T-S fuzzy models with only one premise variable. According to the applications on synchronization and signal modulation, the general fuzzy models may have either i) common bias terms; or ii) the same premise variable and driving signal. Then we propose two types of driving signals, namely, fuzzy driving signal and crisp driving signal, to deal with the asymptotical synchronization and secure communication problems for cases i) and ii), respectively. Based on these driving signals, the solutions are found by solving LMI problems. It is worthy to note that many well-known chaotic systems, such as Duffing system, Chuas circuit. Rasslers system, Lorenz system, Henon map, and Lozi map can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either the fuzzy driving signal or the crisp driving signal. Finally, several numerical simulations are shown to verify the results.

LMI-based fuzzy chaotic synchronization and communications

Addresses synthesis approaches for signal synchronization and secure communications of chaotic systems by using fuzzy system design methods based on linear matrix inequalities (LMIs). By introducing a fuzzy modeling methodology, many well-known continuous and discrete chaotic systems can be exactly represented by Takagi-Sugeno (T-S) fuzzy models with only one premise variable. Following the general form of fuzzy chaotic models, the structure of the response system is first proposed. Then, according to the applications of synchronization to the fuzzy models that have common bias terms or the same premise variable of drive and response systems, the driving signals are developed with four different types: fuzzy, character, crisp, and predictive driving signals. Synthesizing from the observer and controller points of view, all types of drive-response systems achieve asymptotic synchronization. For chaotic communications, the asymptotical recovering of messages is ensured by the same framework. It is found that many well-known chaotic systems can achieve their applications on asymptotical synchronization and recovering messages in secure communication by using either one type of driving signals or all. Several numerical simulations are shown with expected satisfactory performance.

Adaptive synchronization design for chaotic systems via a scalar driving signal

Using a scalar driving signal, synchronization for a class of chaotic systems has been developed. For chaotic systems characterized by nonlinearity, which depend only on the available output, a unified approach is developed by carefully extending the conventional adaptive observer design. For exactly known chaotic systems, an exponential convergence of synchronization is achieved in the large. When mismatched parameters are presented, this method performs the asymptotic synchronization of output state in the large. The convergence of the estimated parameter error is related to an implicit condition of persistent excitation (PE) on internal signals. From the broad spectrum characteristics of the chaotic driving signal, we reformulate the implicit PE condition as an condition on injection inputs. If this condition is satisfied, the estimated parameters converge to true values and exponential synchronization of all internal states is guaranteed. Two typical examples, including Duffing-Holmes system and Chuas circuit, are considered as illustrations to demonstrate the effectiveness of the adaptive synchronizer. Furthermore, the robustness of adaptive synchronization in the presence of measurement noise is considered where the update law is modified. Finally, numerical simulations and DSP-based experiments show the validity of theoretical derivations.

Secure communications of chaotic systems with robust performance via fuzzy observer-based design

This paper presents a systematic design methodology for fuzzy observer-based secure communications of chaotic systems with guaranteed robust performance. The Takagi-Sugeno fuzzy models are given to exactly represent chaotic systems. Then, the general fuzzy model of many well-known chaotic systems is constructed with only one premise variable in fuzzy rules and the same premise variable in the system output. Based on this general model, the fuzzy observer of chaotic system is given and leads the stability condition of a linear-matrix inequality problem. When taking the fuzzy observer-based design to applications on secure communications, the robust performance is presented by simultaneously considering the effects of parameter mismatch and external disturbances. Then, the error of the recovered message is stated in an H/sup /spl infin// criterion. In addition, if the communication system is free of external disturbances, the asymptotic recovering of the message is obtained in the same framework. The main results also hold for applications on chaotic synchronization. Numerical simulations illustrate that this proposed scheme yields robust performance.

LMI-based fuzzy chaotic synchronization and communication

This paper presents linear matrix inequalities (LMI) based fuzzy chaotic synchronization and communication. We propose a modulated Takagi-Sugeno (T-S) fuzzy model. The modulated T-S fuzzy model is constructed by choosing the common factor or the only one variable of nonlinear terms in chaotic systems as the premise variable of fuzzy rules and output signal. Following this model, some restricting conditions required in Tanaka et al. (1998) can be relaxed. This simplified design framework can be applied to many well-known chaotic systems. Also, for chaotic communications, this modulated T-S fuzzy model illustrates asymptotical recovering of the message.

DISCRETE-TIME CHAOTIC SYSTEMS: APPLICATIONS IN SECURE COMMUNICATIONS

The general design for dead-beat and asymptotic synchronizers for a large class of discrete-time chaotic systems is proposed. According to whether the form of the transmitter output (drive signal) is linear, nonlinear or the sum of two, different system structures for synchronization discussions are held. Secure communications is then applied taking into consideration to which state in the transmitter masks the message. Examples of different secure communication schemes are discussed, with a comparison given of the various schemes based on the performance of the receivers ability to recover the message. To accomodate the uncertainty existing in the transmitter parameters, an extended Kalman filter (EKF) algorithm is utilized to estimate both the parameters and states when the message is already embedded. To overcome the problem of high error rates of recovered messages while simultaneously estimating parameters, two alternative methods, namely linear output scheme and indirect scheme, are presented to improve the performance. Numerical simulations for secure communications illustrate a binary signal as the message is recovered and recognizable at the receivers end.

FUZZY MODEL-BASED APPROACH TO CHAOTIC ENCRYPTION USING SYNCHRONIZATION

This paper proposes a fuzzy model-based chaotic encryption approach using synchronization. The cryptosystem uses T–S fuzzy models to exactly represent discrete-time chaotic systems into separate linear systems. Then the synchronization problem is solved using linear matrix inequalities. The advantages of this approach are: the general and systematic T–S fuzzy model design methodology suitable for well-known Lure type discrete-time chaotic systems; flexibility in selection of chaotic signals for cryptosystem secure key generator; and multiuser capabilities. Especially taking a chaotic superincreasing sequence as an encryption key enhances the chaotic communication structure to a higher-level of security compared to traditional masking methods. In addition, numerical simulations and DSP-based experiments are carried out to verify the validity of theoretical results.

Learning convergence analysis for Takagi-Sugeno Fuzzy Neural Networks

In this paper, we provide a mathematical formulation of the Takagi-Sugeno Fuzzy Neural Network (TS-FNN) to study convergence properties. Note that we describe both information retrieval and learning rules by algebraic equations in matrix form. We then investigate the convergence characteristics and learning behaviors for the TS-FNN by use of these algebraic equations and the eigenvalues of derived matrices. Numerical examples are carried out to further verify the analysis.

Fuzzy model-based discrete-time Chiang type chaotic cryptosystem

We propose a class of chaotic system a so-called Chiang type chaotic system. First the chaotic system is represented by T-S fuzzy models. Then based on this type of chaotic system, a new cryptosystem is developed. The advantage of this cryptosystem is a significant increase in the plaintext to chaotic signal ratio which is beneficial in coping with channel noise. In addition, this cryptosystem allows increase of the power of plaintext and maintains high security.

SYNCHRONIZATION AND SECURE COMMUNICATION FOR CHAOTIC SYSTEMS: THE MODULATED FUZZY SYSTEM DESIGN

This paper presents a modulated T–S fuzzy model that can be applied to both continuous/discrete chaotic synchronization, chaotic model following and secure communication. The modulated T–S fuzzy model is constructed by choosing the common factor or the only variable of nonlinear terms in chaotic systems as the premise variable of fuzzy rules and output signal. Following this model, fuzzy chaotic synchronization is achieved by utilizing linear matrix inequalities design and some restricting conditions can be relaxed. This simplified design framework can be applied to many well-known chaotic systems. Also, for chaotic communications, this modulated T–S fuzzy model illustrates asymptotical recovering of the message. Moreover, the usage of combinational states as the coupling signal for Lure type systems is taken into consideration. In this case, the receiver design for synchronization and secure communication is also proposed. The simulation results are shown with expected satisfactory performance.