Fuzzy Dynamical Systems Research Articles

Stable indirect adaptive switching control for fuzzy dynamical systems based on T–S multiple models

A new indirect adaptive switching fuzzy control method for fuzzy dynamical systems, based on Takagi–Sugeno (T–S) multiple models is proposed in this article. Motivated by the fact that indirect adaptive control techniques suffer from poor transient response, especially when the initialisation of the estimation model is highly inaccurate and the region of uncertainty for the plant parameters is very large, we present a fuzzy control method that utilises the advantages of multiple models strategy. The dynamical system is expressed using the T–S method in order to cope with the nonlinearities. T–S adaptive multiple models of the system to be controlled are constructed using different initial estimations for the parameters while one feedback linearisation controller corresponds to each model according to a specified reference model. The controller to be applied is determined at every time instant by the model which best approximates the plant using a switching rule with a suitable performance index. Lyapunov stability theory is used in order to obtain the adaptive law for the multiple models parameters, ensuring the asymptotic stability of the system while a modification in this law keeps the control input away from singularities. Also, by introducing the next best controller logic, we avoid possible infeasibilities in the control signal. Simulation results are presented, indicating the effectiveness and the advantages of the proposed method.

A novel dropout compensation scheme for control of networked T–S fuzzy dynamic systems

This paper considers the problem of H∞ state feedback control for networked nonlinear systems under unreliable communication links with packet dropouts. The nonlinear plant in this paper is described by a Takagi–Sugeno (T–S) fuzzy model. The packet dropouts in both sensor-to-controller (S/C) and controller-to-actuator (C/A) channels are considered, which are modeled by Bernoulli processes. A new compensation scheme for the estimation of missing packets is proposed, and a piecewise state feedback controller is designed so that the resulting closed-loop control system is stochastically stable with guaranteed H∞ performance. Then the results are extended to the case when both network-induced delays and packet dropouts exist in communication links. Finally, some numerical examples are given to illustrate the procedure of the proposed approaches and the optimal H∞ performance in comparison to the existing approaches.

Discrete and fuzzy dynamical genetic programming in the XCSF learning classifier system

A number of representation schemes have been presented for use within learning classifier systems, ranging from binary encodings to neural networks. This paper presents results from an investigation into using discrete and fuzzy dynamical system representations within the XCSF learning classifier system. In particular, asynchronous random Boolean networks are used to represent the traditional condition-action production system rules in the discrete case and asynchronous fuzzy logic networks in the continuous-valued case. It is shown possible to use self-adaptive, open-ended evolution to design an ensemble of such dynamical systems within XCSF to solve a number of well-known test problems.

State Observer Based Dynamic Fuzzy Logic System for a Class of SISO Nonlinear Systems

This paper presents an observer based dynamic fuzzy logic system (DFLS) scheme for a class of unknown single-input single-output (SISO) nonlinear dynamic systems with external disturbances. The proposed approach does not need the availability of the state variables. Within this scheme, the DFLS is employed to identify the unknown nonlinear dynamic system. The control law and parameter adaptation laws of the DFLS are derived based on Lyapunov synthesis approach. The control law is robustfied in H8 sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions, it guarantees the boundedness of all the signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. The proposed method is applied to an inverted pendulum system to verify the effectiveness of the proposed algorithms.

Adaptive fuzzy control of aircraft wing-rock motion

In the paper, two adaptive fuzzy control schemes including indirect and direct frameworks are developed for suppressing the wing-rock motion that is a highly nonlinear aerodynamic phenomenon in which limit cycle roll oscillations are experienced by aircraft at high angles of attack. In the two control topologies, a dynamic fuzzy system called Extended Sequential Adaptive Fuzzy Inference System (ESAFIS) is constructed to represent the dynamics of the wing-rock system. ESAFIS is an online learning fuzzy system in which the rules are added or deleted based on the input data. In the indirect control scheme, the ESAFIS is used to estimate the nonlinear dynamic function and then a stable indirect fuzzy controller is designed based on the estimator. In the direct control scheme, the ESAFIS controller is directly designed to imitate an ideal stable control law without determining the model of the dynamic function. Different from the original ESAFIS, the adaptive tuning algorithms for the consequent parameters are established in the sense of Lyapunov theorem to ensure the stability of the overall control system. A sliding mode controller is also designed to compensate for the modelling errors of ESAFIS by augmenting the indirect/direct fuzzy controller. Finally, comparisons with a neuron control scheme using the RBF network and a fuzzy control scheme with Takagi–Sugeno (TS) system are presented to depict the effectiveness of the proposed control strategies. Simulation results show that the proposed fuzzy controllers achieve better tracking performance with dynamically allocating the rules online.

A Novel Legal Expert Based on Dynamic Fuzzy System in Manipulating Property Division upon Divorce

Legal expert system is an important research topic both in law research and computer science. This paper proposes a novel model for property division, which adopts latest marital law of PRC and dynamic fuzzy theory. Firstly, all up-to-dated clauses involved with property distribution in divorce were quantified to obtain related set elements. Then the dynamic fuzzy theory was applied to construct a membership function to calculate the weight of set elements. Ultimately， the appropriate degrees are calculated by optimum model. By testing, property division legal expert dynamic fuzzy system could consider questions scientifically, comprehensively and effectively.

基于动态模糊系统模型的压电陶瓷驱动器控制

As the nonlinear hysteresis characteristic of a Piezoelectric Ceramic Actuator(PZT) has a big impact on periodic ultra-precise tracking accuracy,this paper investigates a methodology which combines the Dynamic Fuzzy System(DFS) feed-forward based on Takagi-Sugeno(T-S) fuzzy rule with the PI control.The identification methods of DFS antecedent and consequent structures are introduced.Then,DFS feed-forward with PI control strategy of periodic trajectory tracking is proposed according to theories of direct inverse model control and iterative learning control.Finally,the tracking control experiment is performed on a 20Hz triangular trajectory and a sinusoidal desired trajectory.Experimental results indicate that the proposed control method can achieve 0.25% and 0.27% maximum tracking errors for triangular and sinusoidal trajectories,which are 52 and 64 times as accurate as that of PI control.Moreover,the maximum absolute tracking errors have been reduced to 5.1 nm and 5.5 nm,respectively.It concludes that the methodology can be easily implemented and has high periodic trajectory tracking accuracy.

ENTROPY AND MUTUAL INFORMATION OF EXPERIMENTS IN THE FUZZY CASE

In my previous papers ([18], [19]) the entropy of fuzzy partitions had been defined. The concept of the entropy of a fuzzy partition was used to define the entropy of a fuzzy dynamical system and to propose an ergodic theory for fuzzy dynamical systems ([19], [20]). In this paper, using my previous results related to the entropy of fuzzy partitions, a measure of average mutual information of fuzzy partitions is defined. Some properties concerning this measure are proved. It is shown that the entropy of fuzzy partitions can be considered as a special case of their mutual information. We obtain that subadditivity and additivity of entropy of fuzzy partitions are simple consequences of these properties. The suggested measures can be applied whenever it is need to know the amount of information that we obtain by realization of experiments, the results of which are fuzzy events.

Limit-cycle analysis of dynamic fuzzy control systems

The main purpose of this study is to predict limit cycles of a dynamic fuzzy control system by combining a stability equation, describing function and parameter plane. The stability of a linearized dynamic fuzzy control system is then analyzed using stability equations and the parameter plane method, with the assistance of a describing function method. This procedure identifies the amplitude and frequency of limit cycles that are clearly formed by the dynamic fuzzy controller in the parameter plane. Moreover, the suppression of the limit cycle by adjusting control parameters is proposed. Continuous and sampled-data systems are addressed, and the proposed approach can easily be extended to a fuzzy control system with multiple nonlinearities. Simulations are performed to demonstrate the effectiveness of the proposed scheme.

Robust Control for Fuzzy Dynamical Systems: Uniform Ultimate Boundedness and Optimality

We propose a new approach for the control design of fuzzy dynamical systems. The system may contain uncertainty, which includes unknown parameter and input disturbance. The uncertainty lies within a prescribed fuzzy set. The control structure is deterministic, and, hence, not if-then rule-based. The desired controlled system performance includes uniform boundedness and uniform ultimate boundedness. In addition, we propose a quadratic cost index, which reflects the fuzzy system performance. We then formulate a control parameter design problem as a constrained optimization problem. It is proven that the global solution to this problem always exists and is unique. The closed-form solution and the closed-form minimum cost are derived.

<i>H</i><sub>∞</sub> Filtering for Nonlinear Systems with Time Delays via Takagi-Sugeno Fuzzy Model

State estimation is an important topic in controller design. H∞filtering problem is discussed for fuzzy dynamical systems with time delays by using Takagi-Sugeno (T-S) model. Fuzzy H∞filter is obtained such that the filtering error system is stable and guarantees a prescribed estimation error level. Delay-dependent Lyapunov functional approach is employed to lower the conservativeness of the filter design. Therefore, the results of fuzzy H∞filter are delay-dependent. An example is given to illustrate the proposed results.

Stability of motion of nonlinear systems with fuzzy characteristics of parameters

We study the stability of stationary solutions of fuzzy dynamical systems by the generalized direct Lyapunov method.

Extended dynamic fuzzy logic system for a class of MIMO nonlinear systems and its application to robotic manipulators

SUMMARYThis paper presents an indirect adaptive fuzzy control scheme for a class of unknown multi-input multi-output (MIMO) nonlinear systems with external disturbances. Within this scheme, the dynamic fuzzy logic system (DFLS) is employed to identify the unknown nonlinear MIMO systems. The control law and parameter adaptation laws of DFLS are derived based on the Lyapunov synthesis approach. The control law is robustified in H∞ sense to attenuate external disturbance, model uncertainties, and fuzzy approximation errors. It is shown that under appropriate assumptions it guarantees the boundness of all signals in the closed-loop system and the asymptotic convergence to zero of tracking errors. An extensive simulation on the tracking control of a two-link rigid robotic manipulator verifies the effectiveness of the proposed algorithms.

Classification of EMG signals using combined features and soft computing techniques

The motor unit action potentials (MUPs) in an electromyographic (EMG) signal provide a significant source of information for the assessment of neuromuscular disorders. Since recently there were different types of developments in computer-aided EMG equipment, different methodologies in the time domain and frequency domain has been followed for quantitative analysis of EMG signals. In this study, the usefulness of the different feature extraction methods for describing MUP morphology is investigated. Besides, soft computing techniques were presented for the classification of intramuscular EMG signals. The proposed method automatically classifies the EMG signals into normal, neurogenic or myopathic. Also, multilayer perceptron neural networks (MLPNN), dynamic fuzzy neural network (DFNN) and adaptive neuro-fuzzy inference system (ANFIS) based classifiers were compared in relation to their accuracy in the classification of EMG signals. Concerning the impacts of features on the EMG signal classification, different results were obtained through analysis of the soft computing techniques. The comparative analysis suggests that the ANFIS modelling is superior to the DFNN and MLPNN in at least three points: slightly higher recognition rate; insensitivity to overtraining; and consistent outputs demonstrating higher reliability.

A Non-Fragile H∞ Output Feedback Controller for Uncertain Fuzzy Dynamical Systems with Multiple Time-Scales

This paper determines the designing of a non-fragile H∞ output feedback controller for a class of nonlinear uncertain dynamical systems with multiple timescales described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a non-fragile H∞ output feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this paper.

Nondeterministic fuzzy automata

To handle fuzzy uncertainty in system modeling, nondeterministic finite automata have been generalized into fuzzy automata. After a reexamination of the notions of fuzzy automata in the literature, we ascertain that the fundamental property—nondeterminism—in nondeterministic finite automata has not been well embodied in the generalization. In order to reflect nondeterminism in fuzzy automata, we introduce nondeterministic fuzzy automata with or without ϵ-moves and fuzzy languages recognized by them. Like nondeterministic finite automata, nondeterministic fuzzy automata provide a mathematical representation of nondeterministic dynamic fuzzy systems. Moreover, we show that (deterministic) fuzzy automata, nondeterministic fuzzy automata, and nondeterministic fuzzy automata with ϵ-moves are all equivalent in the sense that they recognize the same class of fuzzy languages, which is an extension of the well-known equivalence among finite automata, nondeterministic finite automata, and nondeterministic finite automata with ϵ-moves.

Some Chaotic Properties of Discrete Fuzzy Dynamical Systems

Letting (X, d) be a metric space, f : X → X a continuous map, and (ℱ(X), D) the space of nonempty fuzzy compact subsets of X with the Hausdorff metric, one may study the dynamical properties of the Zadeh′s extension . In this paper, we present, as a response to the question proposed by Román‐Flores and Chalco‐Cano 2008, some chaotic relations between f and . More specifically, we study the transitivity, weakly mixing, periodic density in system (X, f), and its connections with the same ones in its fuzzified system.

A New Approach to the Control Design of Fuzzy Dynamical Systems

A new approach to the control design for fuzzy dynamical systems is proposed. For a fuzzy dynamical system, the uncertainty lies within a fuzzy set. The desirable system performance is twofold: one deterministic and one fuzzy. While the deterministic performance assures the bottom line, the fuzzy performance enhances the cost consideration. Under this setting, a class of robust controls is proposed. The control is deterministic and is not if-then rules-based. An optimal design problem associated with the control is then formulated as a constrained optimization problem. We show that the problem can be solved and the solution exists and is unique. The closed-form solution and cost are explicitly shown. The resulting control is able to guarantee the prescribed deterministic performance and minimize the average fuzzy performance.

Design of robust‐optimal controllers with low trajectory sensitivity for uncertain Takagi–Sugeno fuzzy model systems using differential evolution algorithm

SUMMARYBy integrating the robust stabilizability condition, the orthogonal‐function approach (OFA) and the Taguchi‐sliding‐based differential evolution algorithm (TSBDEA), an integrative computational approach is presented in this paper to design the robust‐optimal fuzzy parallel‐distributed‐compensation (PDC) controller with low trajectory sensitivity such that (i) the Takagi–Sugeno (TS) fuzzy model system with parametric uncertainties can be robustly stabilized, and (ii) a quadratic finite‐horizon integral performance index for the nominal TS fuzzy model system can be minimized. In this paper, the robust stabilizability condition is proposed in terms of linear matrix inequalities (LMIs). Based on the OFA, an algebraic algorithm only involving the algebraic computation is derived for solving the nominal TS fuzzy feedback dynamic equations. By using the OFA and the LMI‐based robust stabilizability condition, the robust‐optimal fuzzy PDC control problem for the uncertain TS fuzzy dynamic systems is transformed into a static constrained‐optimization problem represented by the algebraic equations with constraint of LMI‐based robust stabilizability condition; thus, greatly simplifying the robust‐optimal PDC control design problem. Then, for the static constrained‐optimization problem, the TSBDEA has been employed to find the robust‐optimal PDC controllers with low trajectory sensitivity of the uncertain TS fuzzy model systems. A design example is given to demonstrate the applicability of the proposed new integrative approach. Copyright © 2011 John Wiley & Sons, Ltd.

RTM (Robot Technology Middleware) Based Dynamic Interrupt System for Communication Between Humans and Robots

A dynamic fuzzy interrupt system is proposed to optimize responsiveness of robots in humans-robots communication. The system guarantees a continuous and efficient human-robot interaction by assigning priority to the given instruction and it remains immune to distractions caused by conflicting instructions. The system is embedded in the robot technology components that are able to implement by different programming languages, under the different operating system. Experiments to simulate actions of mascot robot system such as the eye robot, mobile robot, and information retrieval engine involving 10,000 instructions show a 14% improvement in the system responsiveness and a delay time of less than 2 seconds. The implementation of home party scenario between four humans (a host and three guests) and five eye robots shows the affective communication, and confirms to facilitate casual communication between humans and robots with limited interruption.