Kuang-Yow Lian

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 Integral fuzzy control of DC-DC converters

In this paper, we propose a T-S fuzzy controller which combines the merits of: i) the capability for dealing with nonlinear systems; ii) the powerful LMI approach to obtain control gains; iii) the high performance of integral controllers; iv) the workable rigorous proof for exponential convergence of error signals; and v) the flexibility on tuning decay rate. The output regulation problems of a basic buck converter and a zero-voltage-transition (ZVT) buck converter are used as application examples to illustrate the control performance of the proposed methodology. First, we consider a general nonlinear system which can represent the large-signal models of the converters. After introducing an added integral state of output regulation error and taking coordinate translation on an equilibrium point, the resulting augmented system is represented into a Takagi-Sugeno (T-S) fuzzy model. Then, the concept of parallel distributed compensation is applied to design the control law whereby the control gains are obtained by solving linear matrix inequalities (LMIs). An interesting result is that the obtained control law is formed only by the linear state feedback signals weighted by grade functions. In addition, the robustness analysis is carried out when uncertainty and disturbance are taken into consideration. The performance of numerical simulations and practical experiments results is satisfactory.

Output Tracking Control for Fuzzy Systems Via Output Feedback Design

Fuzzy observer-based control design is proposed to deal with the output tracking problem for nonlinear systems. For the purpose of tracking design, the new concept of virtual desired variables and, in turn the so-called generalized kinematics are introduced to simplify the design procedure. In light of this concept, the design procedure is split into two steps: i) Determine the virtual desired variables from the generalized kinematics; and ii) Determine the control gains just like solving linear matrix inequalities for stabilization problem. For immeasurable state variables, output feedback design is proposed. Here, we focus on a common feature held by many physical systems where their membership functions of fuzzy sets satisfy a Lipschitz-like property. Based on this setting, control gains and observer gains can be designed separately. Moreover, zero tracking error and estimation error are concluded. Three different types of systems, including nonlinear mass-spring systems, dc-dc converters, and induction motors are considered to demonstrate the design procedure. Their satisfactory simulation results verify the proposed approach

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.

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.

CHAOTIC CONTROL USING FUZZY MODEL-BASED METHODS

In this paper, we propose a fuzzy tracking control for chaotic systems with immeasurable states. First we represent the chaotic and reference systems into T–S fuzzy models. Some properties concerning the premise variable selection and controller placement for chaotic systems are discussed. When considering immeasurable states, an observer is designed along with the controller to track a reference model which is a fixed point, a stable nonlinear system, or a chaotic system. For different premise variables between the plant and reference models, a robust approach is used to deal with the problem. The conditions for dealing with the stability of the overall error system are formulated into LMIs. Since the simultaneous solution to both the controller and observer gains with disturbances are not trivial, a two-step method is utilized. The methodology proposed above is applied to both continuous-time and discrete-time chaotic systems. Two well-known examples, the Chuas circuit for continuous-time and Henon map for discrete-time, are used in numerical simulations and DSP-based experiments. The results verify the validity of theoretical derivations.

Sliding-mode motion/force control of constrained robots

A sliding-mode controller is proposed for the simultaneous position and force control of constrained robot manipulators with parametric uncertainties. Based on this controller, the trajectories of the closed-loop system can reach a stable sliding surface in finite time. Under this condition, the asymptotic convergence of the motion error and force error can be successfully ensured with improved results compared to previous studies.

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.

Steady motions of gyrostat satellites and their stability

The steady motions of a rigid body rotating about its maximum principal axis of inertia, while the radius vector lies in the direction of its minimum principal axis of inertia, is known to be stable in the sense of Lyapunov. Due in part to their stowed configuration in launch vehicles, however, satellites typically have an initial rotation about their minimum principal axis of inertia. Such rotation may be unstable in the presence of some dissipations. This paper investigates the effect of momentum wheels on the stability of steady motions. It is proved that the momentum wheels increase the effective moment of inertia of the gyrostat-satellite system about some desired axis. Stability of the steady rotation about the desired axis can be established only for the case when the moment of inertia of the axis aligned with the radius vector is smaller than that of the axis of linear momentum. A new set of stability criteria is obtained which includes the effects of the coupling between the orbital and attitude dynamics and may be useful in the design of attitude control systems for large spacecraft in low Earth orbit. >

Stability Conditions for LMI-Based Fuzzy Control From Viewpoint of Membership Functions

In this paper, we investigate the stability conditions for linear matrix inequality (LMI)-based fuzzy control design. Especially, we focus on the dependence of the stability upon membership functions. In general, the membership functions in the rule bases of Takagi-Sugeno (T-S) fuzzy model and controllers are the same and restricted between 0 and 1. In contrast to this setting, we obtain some new results when different membership functions are considered and their values lying outside the interval of [0,1] are allowed. Applying Lyapunov equation and a convex hull of fuzzy subsystems, we first establish a relationship between the stable interval characteristic polynomial and a set of feasible LMIs. Then Kharitonovs theorem gives an insight for the solvability of stabilization problems using LMI-based design and, this leads that the membership functions have an influence on stability. On the other hand, the LMI condition leads to the well-known results for LMI-based fuzzy control design. We further indicate that the different LMI conditions arise due to the same or different membership functions and find their own applications on adaptive fuzzy control. Finally, if the unit interval constraint is removed, an LMI condition for global stability is obtained