Nonlinear Fuzzy Systems Research Articles

H∞ Control of Fuzzy Impulsive Systems with Quantized Feedback

This paper is concerned with the problem of H∞ control of fuzzy nonlinear impulsive systems with quantized feedback. New results on the H∞ feedback control are established for one class of fuzzy nonlinear uncertain impulsive systems and one class of fuzzy nonlinear impulsive systems with nonlinear uncertainties by choosing appropriately quantized strategies and applying Lyapunov function approach, respectively.

Compactness of Family of Fuzzy Sets in L2 Space with Application to Optimal Control

The optimization of nonlinear feedback fuzzy system using the product-sum-gravity method is described in this paper. The fuzzy control discussed here is the nonlinear feedback control in which the feedback laws are determined by IF-THEN type fuzzy production rules through product-sum-gravity method. To prove existence of optimal control, we applied compactness of a set of membership functions in L2 space and continuity of the approximate reasoning, and prepared some propositions concerning product-sum-gravity method. By considering fuzzy optimal control problems as problems of finding the minimum (maximum) value of the integral cost (benefit) function on an appropriate set of membership functions, the existence of fuzzy optimal control is shown.

Robust fuzzy control of nonlinear fuzzy impulsive systems with time-varying delay

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is represented by the well-known T- S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. An example is given to demonstrate the effectiveness of the proposed method.

Periodicity of a class of nonlinear fuzzy systems with delays

The well known Takagi–Sugeno (T–S) model gives an effective method to combine some simple local systems with their linguistic description to represent complex nonlinear dynamic systems. By using the T–S method, a class of local nonlinear systems having nice dynamic properties can be employed to represent some global complex nonlinear systems. This paper proposes to study the periodicity of a class of global nonlinear fuzzy systems with delays by using T–S method. Conditions for guaranteeing periodicity are derived. Examples are employed to illustrate the theory.

Design of variable structure control for fuzzy nonlinear systems

In this paper, the variable structure control problem is presented for Takagi-Sugeno fuzzy systems with uncertainties and external disturbances. The sliding surfaces for the T-S fuzzy system are proposed by using a Lyapunov function and a fuzzy Lyapunov function, respectively. And we design the variable structure controllers such that the global T-S fuzzy system confined on the sliding surfaces is asymptotically stable. Two examples are given to illustrate the effectiveness of our proposed methods.

Control Design for Fuzzy Systems Based on Relaxed Nonquadratic Stability and $H_{\infty}$ Performance Conditions

In this paper, new approaches to Hinfin controller design for a class of discrete-time nonlinear fuzzy systems are proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, two relaxed conditions of nonquadratic stability with H infin norm bound are presented for this class of systems. The two relaxed conditions are shown to be useful in designing fuzzy control systems. By introducing some additional instrumental matrix variables, the two relaxed conditions are used to develop Hinfin controllers. In the control design, the first relaxed condition has fewer inequality constraints, but only admits a common additional matrix variable while the second one can admit multiple additional matrix variables. Finally, two examples are given to demonstrate the applicability of the proposed approach

Reliable memory feedback design for a class of nonlinear fuzzy systems with time-varying delay

: This paper is concerned with the robust reliable memory controller design for a class of fuzzy uncertain systems with time-varying delay. The system under consideration is more general than those in other existent works. The controller, which is dependent on the magnitudes and derivative of the delay, is proposed in terms of linear matrix inequality (LMI). The closed-loop system is asymptotically stable for all admissible uncertainties as well as actuator faults. A numerical example is presented for illustration.

Solution of non-linear fuzzy systems by decomposition of incremental fuzzy numbers

This paper presents a proposal for decomposing large uncertainties associated with fuzzy numbers, which can be useful for solving non-linear fuzzy problems with crisp coefficients. The proposed procedure is based on a property of incremental fuzzy numbers and improves the quality of solution of the linearization process. The methodology is illustrated by some numeric studies.

Bifurcations of fuzzy nonlinear dynamical systems

We present some recent developments of the fuzzy generalized cell mapping method (FGCM) in this paper. The topological property of the FGCM and its finite convergence of membership distribution vector are discussed. Powerful algorithms of digraphs are adopted for the analysis of topological properties of the FGCM systems. Bifurcations of fuzzy nonlinear dynamical systems are studied by using the FGCM method. A backward algorithm is introduced to study the unstable equilibrium solutions and their bifurcation. We have found that near the deterministic bifurcation point, the fuzzy system undergoes a complex transition as the control parameter varies. In this transition region, the steady state membership distribution is dependent on the initial condition. If we use the measure and topology of the α-cut (α=1) of the steady state membership function of the persistent group representing the stable fuzzy equilibrium solution to characterize the fuzzy bifurcation, assuming the uniform initial condition within the persistent group, the bifurcation of the fuzzy dynamical system is then completed within an interval of the control parameter, rather than at a point as is the case of deterministic systems.

An iterative method for solving dual fuzzy nonlinear equations

According to fuzzy arithmetic, dual fuzzy nonlinear system cannot be replaced by a fuzzy nonlinear system. In this paper we apply Newton’s method for solving a dual fuzzy nonlinear system.

Small-world networks of fuzzy chaotic oscillators

Small-world topology has been used to build lattices of nonlinear fuzzy systems. Chaotic units, ruled by linguistic description and with specified Lyapunov exponent, have been realized and connected using linear diffusion coefficient. The dynamic features of the networks versus the number of systems connected have been investigated to underline phenomena like spatiotemporal chaos and complete regularization. The synchronization characteristics in case of sparse long-term connections and the performances comparison with regular and random network configurations are shown.

Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach

The output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied. Our approach is based on the Takagi-Sugeno (T-S) fuzzy modeling method and a variable structure control (VSC) technique. Therefore, the systems considered are not and need not be in the triangular and parametric strict-feedback form, which are prevalent among adaptive model following control for nonlinear systems, or in the normal form, which pervades almost all existing results in neuro-fuzzy model following control approach. We first study the problem of stabilization of T-S fuzzy systems by using a VSC technique. A method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed. Then, the method is extended to design controllers for output tracking of T-S fuzzy nonlinear systems in two cases, i.e. systems which possess the so-called strong passive subsystems and strong stable zero dynamics, respectively. Finally, illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers. Simulation results show that the goal of output tracking can be achieved by the proposed controllers.

선박조타의 TSK 퍼지 비선형제어시스템 설계

This paper suggests a method to design TSK(Takagi-Sugeno-Kang) fuzzy nonlinear control system for automatic steering system which contains the nonlinear component of ship`s maneuvering equation. A TSk fuzzy model can be identified using input-output data and represent a nonlinear system very well. A TSK fuzzy controller can be designed systematically from a TSK fuzzy model because the consequent part of TSK fuzzy rule is a linear input-output equation having a constant term. Therefore, this paper suggests the method identifying the TSK fuzzy model and designing the TSK fuzzy controller based on the TSK fuzzy model for ship steering.

Stability of fuzzy control systems with bounded uncertain delays

Global exponential stability of fuzzy control systems with delays is studied. These delays in the fuzzy control systems are assumed to be any uncertain bounded continuous functions. Stability of systems with uncertain delays is interesting since in practical applications it is not easy to know the delays exactly. Conditions for global exponential stability of free fuzzy systems with uncertain delays are derived. Criteria for design of nonlinear fuzzy controllers to feedback control the stability of global nonlinear fuzzy systems are given. Theorems are proved via the method of functional differential inequalities analysis.

Piecewise Lyapunov stability conditions of fuzzy systems

In this paper we address the stability of a class of non-linear fuzzy systems that can be decomposed into a set of local models characterized as Takagi-Sugeno models. This new approach includes a consideration of the input membership functions. Via this approach, a reduction in the number of candidate Lyapunov functions and associated linear matrix inequalities (LMIs) is produced. This approach significantly reduces the computational load associated with determining closed loop stability as the input dimension increases.

Sensor Fault-Tolerant Control of an Induction Motor Drive System

This paper describes the application of a new fault-tolerant control scheme for nonlinear systems. The approach presented takes into account the stability and design of non-linear fuzzy inference systems based on Takagi-Sugeno (T-S) fuzzy models. The necessary conditions for eigenvalue assignability to a region in the s-plane are derived along with necessary conditions to guarantee the stability of adaptive fuzzy models for both diagnostic T-S fuzzy observers and controllers. The problem is solved using Linear Matrix Inequalities (LMI). The feasibility of this system architecture is demonstrated using a 3-phase induction motor laboratory rig as an example of a fault-tolerant system for applying principles of fault detection and isolation (FDI) and control system reconfiguration. The scheme uses the D space® software and digital signal processing to implement the fault detection and control system reconfiguration on the test rig.

Multiple-Model Fault-Tolerant Control of an Induction Motor in the Presence of Uncertainty

This paper describes the application of a new fault-tolerant control scheme for nonlinear systems. The approach presented takes into account the stability and design of non-linear fuzzy inference systems based on Takagi-Sugeno (T-S) fuzzy models. The necessary conditions for eigenvalue assignability to a region in the s-plane are derived along with necessary conditions to guarantee the stability of adaptive fuzzy models for both diagnostic TS fuzzy observers and controllers. The problem is solved using Linear Matrix Inequalities (LMI). The feasibility of this system architecture is demonstrated using a 3-phase induction motor laboratory rig as an example of a fault-tolerant system for applying principles of fault detection and isolation (FDI) and control system reconfiguration. The scheme uses the D space software and digital signal processing to implement the fault detection and control system reconfiguration on the test rig.

Takagi-Sugeno Fuzzy Fault-Tolerant Control of an Induction Motor

This paper demonstrates the application of a new fault-tolerant control scheme for a rail vehicle traction system using digital signal processing hardware and a representative induction motor testrig. The approach presented takes into account the stability and design of non-linear fuzzy inference systems based on Takagi-Sugeno (T-S) fuzzy models. The paper derives the necessary conditions for the assignability of eigenvalues to a region in the s-plane and the necessary conditions to guarantee the stability of adaptive fuzzy models. The problem is solved via the Linear Matrix Inequalities (LMI) method.

Supervisory Takagi-Sugeno Fuzzy Fault-Tolerant Control of a Rail Traction System

This paper investigates the development of a supervisory control system with qualitative tasks at the upper level and simple quantitative models at the lower level to control complex non-linear systems. A new quantitative approach for the stability of non-linear fuzzy inference systems using Takagi-Sugeno (T-S) fuzzy models is presented. The necessary conditions for the assignability of eigenvalues to a region in the s-plane and the necessary conditions to guarantee the stability of fuzzy models for both T-S fuzzy observers and T-S fuzzy controllers together are derived. The problem is solved via the Linear Matrix Inequality (LMI) method. The paper demonstrates the feasibility of this system architecture through application to a fault-tolerant design for a railway traction system using DSP in a hardware test-rig.

Fault-Tolerant Traction System Control Using Fuzzy Inference Modelling

This papers presents a new approach for the stability and design of non-linear fuzzy inference systems. The approach is based on Takagi-Sugeno (T-S) fuzzy models. The paper derives the necessary conditions for the assignability of eigenvalues to a region in the s-plane and the necessary conditions to guarantee the stability of fuzzy models. The problem is solved via the Linear Matrix Inequality (LMI) method. The paper demonstrates the application in fault-tolerant control in a railway traction system using DSP in a hardware test-ring.