Chian-Song Chiu

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.

Semi-decentralized adaptive fuzzy control for cooperative multirobot systems with H/sup /spl infin// motion/internal force tracking performance

We present a semi-decentralized adaptive fuzzy control scheme for cooperative multirobot systems to achieve H(infinity) performance in motion and internal force tracking. First, we reformulate the overall system dynamics into a fully actuated system with constraints. To cope with both parametric and nonparametric uncertainties, the controller for each robot consists of two parts: 1) model-based adaptive controller; and 2) adaptive fuzzy logic controller (FLC). The model-based adaptive controller handles the nominal dynamics which results in both zero motion and internal force errors for a pure parametric uncertain system. The FLC part handles the unstructured dynamics and external disturbances. An H(infinity) tracking problem defined by a novel performance criterion is given and solved in the sequel. Hence, a robust controller satisfying the disturbance attenuation is derived being simple and singularity-free. Asymptotic convergence is obtained when the fuzzy approximation error is bounded with finite energy. Maintaining the same results, the proposed controller is further simplified for easier implementation. Finally, the numerical simulation results for two cooperative planar robots transporting an object illustrate the expected performance.

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.

Fuzzy gain scheduling for parallel parking a car-like robot

This brief proposes a fuzzy gain scheduling strategy with an application on parallel parking car-like robots. First, the fuzzy gain scheduling strategy is introduced as a combination of a local path tracking controller and fuzzy rule based techniques. In light of human driver experience in parallel parking, the control goal is achieved by repeatedly scheduling parameters and tracking local paths. Meanwhile, a time-varying fuzzy sliding mode controller (TFSC) is developed as the local tracking controller to guarantee robust performance and fast tracking response for a segment of preplanned reference path. Different to traditional gain scheduling, the overall controller combining the TFSC and a fuzzy gain scheduler has advantages in regards of 1) a small data base; 2) an enlarged workspace of interest; and 3) allowing zero velocity crossing. Then, the scenario of parallel parking car-like robots is implemented in presence of nonholonomic and input saturation constraints. Finally, numerical simulation and practical experiment are carried out to show the expected performances.

Induction motor control with friction compensation: an approach of virtual-desired-variable synthesis

In this paper, the speed control problem of induction motors suffering from substantial friction force is considered. Here, a semi-current-fed model for induction motors and LuGres dynamic model for friction force are used. To reflect practical situations, rotor resistance, torque load, and friction parameters are assumed to be unknown. In the design methodology, a double-observer structure is applied to estimate the immeasurable friction states. On the other hand, in light of the principles of vector control and field orientation, a set of virtual desired variables (VDVs) are introduced to synthesize the control law. Therefore, using only measurable signals of rotor speed, stator voltage and current, an asymptotic adaptive tracking controller is designed. Numerical simulations and experiments are carried out to verify the theoretical results and show satisfactory performance.

Adaptive control of holonomic constrained systems: a feedforward fuzzy approximation-based approach

This paper proposes a novel adaptive fuzzy control scheme for the motion/force tracking control of holonomic constrained systems with poorly understood models and disturbances. Some disadvantages of traditional adaptive fuzzy controllers are removed here. In comparison to typical state-feedback fuzzy approximation, the uncertainties are compensated based on a feedforward fuzzy approximation (FFA), which takes desired commands as the premise variables of fuzzy rules. In detail, a unified control model is introduced for representing well-known holonomic systems with an environmental constraint or a set of closed kinematic chains. Then, the FFA-based fuzzy system, adaptation mechanism, and auxiliary-compensating control are derived to ensure robust motion and force tracking in a global manner. Furthermore, a feasible solution for the derived linear matrix inequality guarantees the attenuation of both disturbances and fuzzy parameter errors in an L/sub 2/-gain sense. Finally, two applications are carried out on: 1) a two-link constrained robot and 2) two planar robots transporting a common object. Numerical simulation results show the expected performance.

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.