Fuzzy Dynamical Systems Research Articles

Observer‐based PID control for fuzzy dynamic systems with memory triggering protocol

AbstractThis paper addresses the issue of observer‐based proportional–integral–derivative control for Takagi–Sugeno fuzzy dynamic systems using a memory triggering protocol. To tackle the challenges of managing nonlinear systems, the Takagi–Sugeno fuzzy approach is employed to approximate these systems with a series of local linear models. A novel memory event‐triggering mechanism is introduced, utilizing a computer's storage unit to store historical data and adjust the triggering threshold based on this data, thereby reducing unnecessary network resource usage. Given that the system state can be affected by external disturbances and become unpredictable, an observer‐based proportional–integral–derivative controller is designed to manage these uncertainties. Finally, a car‐damper‐spring model is presented to validate the proposed methodology.

Incremental attribute reduction for dynamic fuzzy decision information systems based on fuzzy knowledge granularity

Rough set-based attribute reduction is a powerful technique for data preprocessing in data mining. Knowledge granularity, as a reliable measure for assessing uncertainty in decision information systems (DIS), finds applicability in attribute reduction within such systems. Nevertheless, the limitation arises from the fact that static attribute reduction methods fail to effectively utilize the information contained in acquired data and promptly update knowledge due to the continuous evolution of data. In addition, existing incremental methods based on knowledge granularity are designed exclusively for symbolic data and lack the capability to handle real-valued data. Inspired by this, our study focuses on the attribute reduction approach for fuzzy decision information systems (FDIS) that encompass object variations by utilizing fuzzy knowledge granularity. Firstly, fuzzy knowledge granulation is defined to quantify uncertainty within FDIS, and utilized to determine the importance of attributes for attribute reduction. Additionally, the incremental mechanisms and attribute reduction algorithms are investigated for adding an object and an object set to FDIS, respectively. Moreover, an explication of how the incremental mechanism for increasing an object set can be viewed as a generalization of the mechanism used for a single object is provided. Finally, comparative experiments on various datasets are conducted to validate the effectiveness and efficiency of the proposed incremental algorithms. The results demonstrate that our algorithms achieve superior classification accuracy and while requiring minimal computing time when compared to the comparative algorithms.

Selection and Promotion of Rural Revitalization Path Mode Incorporating Fuzzy Dynamic Planning

Rural revitalization refers to efforts aimed at renewing and invigorating rural communities to enhance their economic, social, and environmental well-being. To promote the appropriate development in rural revitalization it is necessary to select and promote the appropriate scheme with effective planning, this paper presented effective rural revitalization strategies with the advanced methodology of Genetic Ant Swarm Fuzzy (GAsF), to assess and optimize interventions across various dimensions. The constructed GAsF model implementation of the genetic algorithm-based ant swarm optimization the key features related to the revitalization are estimated. The estimated features are categorized with the fuzzy dynamic planning model for the classification of the program in rural revitalization with the path model implementation in the fuzzy dynamic planning system. Through the computed features classification is performed for the estimation of the features in the programs. Results stated that strategies such as the "Ecotourism Development Strategy" and the "Community Empowerment Program" as particularly promising, demonstrating strong performance in economic, social, and environmental dimensions. Simulation analysis demonstrated that the propose GAsF model achieved the classification accuracy of 0.98 with significant green development values. Through the fuzzy dynamic modelling the GAsF optimize the best fitness value for the ecotourism development value of 0.93.

An investigation on the recurrent function of the Pythagorean fuzzy cellular topological dynamical system

This study is about Pythagorean fuzzy cellular topological dynamical system which is generated using Pythagorean fuzzy cellular space. A dynamical system receives input for a certain function and performs an iterative procedure for that same function. A continuous function can be employed in a topological dynamical system and the same function is iterated again and again. As it is an iterative process, there is a perspective that the views of every individual may be ambiguous or imprecise. To overcome this uncertainty, Pythagorean fuzzy sets are employed in dynamical system. Fixing a boundary on the Pythagorean fuzzy dynamical system culminates in a Pythagorean fuzzy cellular topological dynamical system. It is shown that the Pythagorean fuzzy cellular space is compact, normal and homeomorphic and it is called the Pythagorean fuzzy cellular topological dynamical system. The Pythagorean fuzzy sets in the Pythagorean fuzzy cellular topological dynamical system are iterated under the action of Pythagorean fuzzy cellular continuous map. Then, the Pythagorean fuzzy orbit* set is obtained. Additionally, it is discussed that the stipulated dynamical system is topologically transitive and different aspects of topological transitivity are investigated.

Fuzzy fractional delay differential inclusions driven by hemivariational inequalities in Banach spaces

This paper investigates a novel class of nonlinear dynamical fuzzy systems referred to as fuzzy fractional delay differential hemivariational inequalities (FFDDHVIs) in Banach spaces. These systems integrate fractional fuzzy differential inclusions with delay and hemivariational inequalities. The existence theorem for the HVIs is established based on the KKM theorem. Moreover, specific propositions are proved, covering the superpositional measurability and the upper semicontinuity for the HVIs. Next, by using the fixed points theorem, we establish the existence and compactness of mild solution sets for the FFDDHVIs under certain mild conditions. Finally, As an illustrative application, we investigate a frictional quasistatic contact problem for viscoelastic materials, in which the friction and contact conditions are described by the Clarke generalized gradient of nonconvex and nonsmooth functionals.

An Integrated Instruction and a Dynamic Fuzzy Inference System for Evaluating the Acquirement of Skills through Learning Activities by Higher Middle Education Students in Mexico

Background: The evaluation of the development of a student’s abilities and skills through a learning activity is a topic strongly questioned by the education system in Mexico. Several instruments have been developed to achieve said evaluation. However, these involve both qualitative and subjective assessment, thereby avoiding the possibility of unambiguously verifying the development of a student’s aptitudes. Methods: We developed a new instrument composed of an integrated instruction and a dynamic fuzzy inference system. Integrated instruction is a table that contains a set of instructions and a set of indicators that make it possible to evaluate knowledge, procedure, and attitude without establishing qualitative or subjective criteria to rank them. The dynamic fuzzy inference system assesses indicators under a criterion to demonstrate the development of a student’s abilities and skills. Results: The method was applied to three different learning activities, where the assessment was precise and transparent for the student, contributing to an extraordinary identification of the acquainted knowledge, procedure, and attitude that the student displayed to develop the activity. Conclusions: Our instrument evaluates the development of abilities and skills without ambiguity or subjectivity, making efficient feedback possible and allowing it to be perfected without difficulties for future adaptations.

Lyapunov stability of fuzzy dynamical systems based on fuzzy-number-valued function granular differentiability

Lyapunov stability theory provides a powerful technique for stability analysis of dynamical systems, particularly for the stability of nonlinear dynamical system. This paper deals with the stability of fuzzy dynamical systems using a novel notion called granular fuzzy Lyapunov function. In order to analyze the stability, some new notions are introduced such as fuzzy equilibrium point, the ball of fuzzy state space, granular fuzzy 2-norm and etc. Based on the concept of fuzzy-number-valued function granular differentiability, two theorems are proved for calculation. Moreover, using granular fuzzy Lyapunov function, the granular fuzzy local stability theorem is proposed, and two definitions of exponential stability and like-Lyapunov stability are generalized. Finally, several examples are given to illustrate the proposed theorems.

A dynamic fuzzy rule-based inference system using fuzzy inference with semantic reasoning

The challenge of making flexible, standard, and early medical diagnoses is significant. However, some limitations are not fully overcome. First, the diagnosis rules established by medical experts or learned from a trained dataset prove static and too general. It leads to decisions that lack adaptive flexibility when finding new circumstances. Secondly, medical terminological interoperability is highly critical. It increases realism and medical progress and avoids isolated systems and the difficulty of data exchange, analysis, and interpretation. Third, criteria for diagnosis are often heterogeneous and changeable. It includes symptoms, patient history, demographic, treatment, genetics, biochemistry, and imaging. Symptoms represent a high-impact indicator for early detection. It is important that we deal with these symptoms differently, which have a great relationship with semantics, vary widely, and have linguistic information. This negatively affects early diagnosis decision-making. Depending on the circumstances, the diagnosis is made solo on imaging and some medical tests. In this case, although the accuracy of the diagnosis is very high, can these decisions be considered an early diagnosis or prove the condition is deteriorating? Our contribution in this paper is to present a real medical diagnostic system based on semantics, fuzzy, and dynamic decision rules. We attempt to integrate ontology semantics reasoning and fuzzy inference. It promotes fuzzy reasoning and handles knowledge representation problems. In complications and symptoms, ontological semantic reasoning improves the process of evaluating rules in terms of interpretability, dynamism, and intelligence. A real-world case study, ADNI, is presented involving the field of Alzheimer’s disease (AD). The proposed system has indicated the possibility of the system to diagnose AD with an accuracy of 97.2%, 95.4%, 94.8%, 93.1%, and 96.3% for AD, LMCI, EMCI, SMC, and CN respectively.

Game-Theoretic Optimization Toward Diffeomorphism-Based Robust Control of Fuzzy Dynamical Systems With State and Input Constraints

Game-Theoretic Optimization Toward Diffeomorphism-Based Robust Control of Fuzzy Dynamical Systems With State and Input Constraints

A dynamic fuzzy group recommender system based on intuitionistic fuzzy choquet integral aggregation

A dynamic fuzzy group recommender system based on intuitionistic fuzzy choquet integral aggregation

On the boundedness of solutions of some fuzzy dynamical control systems

<abstract> <p>The asymptotic behavior of solutions of fuzzy control systems is a component of the study of fuzzy control theory. The study of stability for T-S (Takagi-Sugeno) fuzzy systems, which process qualitative data through linguistic expressions, is the subject of this paper. Asymptotic stability is conservative in many real-world applications due to measurement noise and other disruptions. The ultimate limit, which indicates that the mistakes stay in a specific area close to the origin after a long enough amount of time, is a crucial characteristic that is frequently defined for such systems. We are interested with the problem of the state feedback controller for T-S fuzzy models with uncertainties where the global exponential ultimate boundedness of solutions is studied for certain fuzzy control systems. We use common quadratic Lyapunov function and parallel distributed compensation controller techniques to study the asymptotic behavior of the solutions of fuzzy control system in presence of perturbations. An example demonstrating the validity of the main result is discussed.</p> </abstract>

Stability analysis of fuzzy differential equation for prey–predator system underZ-number fuzzy and granular differentiability concept

The stability analysis is one of the basic problems in the field of system, prey–predator, production inventory control, signal processing etc. The goal of stability analysis for prey–predator and production inventory control model is to determine the region of the different variables and parameters at which the system is stable or unstable. This paper explores an uncertain prey–predator model where both prey and predator populations are fuzzy variables. Also we have considered all the prey–predator parameters of the system are imprecise. This fuzzy prey–predator model is converted to an equivalent crisp model using granular differentiability approach. The condition of local stability is obtained mathematically by analysis the eigenvalues of characteristic equation. And also we introduced a production inventory model as a case study of fuzzy dynamical system to illustrate the efficiency of the result and practical aspects.

Cooperative game-oriented optimal robust control for an uncertain wheeled mobile robot with position constraints

The trajectory tracking control performance of the wheeled mobile robot (WMR) is subject to position constraints, system uncertainties, and external disturbances. This paper explores the mechanism of the position constraints (equality and inequality) and considers the system uncertainties to be time-varying but bounded with fuzzy prescribed bounds. To solve the position constraints and uncertainties problems, a cooperative game-oriented optimal robust control method is proposed to provide high-precision, fast-response performance and robustness for WMR. First, a creative diffeomorphism transformation is proposed to convert the bounded state variables (subject to inequality constraints) into unbounded state variables. Accordingly, a restructured WMR system with the new state variables is established, which is free from inequality constraints. The uncertainties’ bound is described as a fuzzy number by employing fuzzy set theory, which builds the fuzzy dynamic system of the WMR. Second, the control goal for this study is to drive the WMR to follow the position constraints despite uncertainties. An optimal robust control is developed to guarantee that the tracking errors of the WMR converge to a predefined neighborhood of origin. Using Lyapunov stability analysis, a fuzzy performance index is constructed, including steady-state performance, time performance, and control effort. The fuzzy performance index is employed as the cost function based on the cooperative game theory. The optimal control design is formulated to seek the Pareto-optimal solution of control parameters. Finally, the stability analysis and comparative experiments demonstrate that the proposed control algorithm can ensure the WMR’s superior trajectory tracking convergence performance and strong robustness against uncertainties/disturbances.

Some Shadowing Properties in Fuzzy Dynamical System

In this paper we introduce the notions (L- , two – sided limit shadowing, negative ) for fuzzy dynamical systems and prove that properties (fuzzy , fuzzy L- , fuzzy two – sided limit shadowing) are invariant under fuzzy

Design, analysis, and application of fixed-time convergence fuzzy ZNN model realized by dynamic fuzzy logic system for time-varying Sylvester equation

Due to the strengths of zeroing neural network (ZNN) in dealing with time-varying problems and the advantages of fuzzy logic system (FLS) in uncertain computing, a fixed-time convergence fuzzy ZNN (FTCFZNN) model realized by the FLS with dynamic membership functions is proposed for solving time-varying Sylvester equation (TVSE). The introduction of the dynamic membership functions in the FLS is one of the most meaningful attributes of this paper, and such a FLS is called the dynamic FLS (DFLS). The design parameter of the FTCFZNN model is the fuzzy parameter generated by the DFLS. Meanwhile, the fuzzy parameter is also employed in the proposed adaptive activation function, which makes the FTCFZNN model possess fixed-time convergence with less upper bound and has a better adaptable ability. Moreover, a series of theoretical analyses reflect the superior fixed-time convergence and adaptive robustness of the FTCFZNN model. Numerical simulations demonstrate the predominant performance of the FTCFZNN model and its effectiveness in solving the TVSE compared with serval existing ZNN models. Finally, the FTCFZNN model is applied to realize the consensus of multi-agent systems, which shows the application value of the FTCFZNN model.

Tracking Control of a Class of Fuzzy Dynamical Systems under the Concept of Granular Differentiability

In this work, the tracking control of a class of uncertain linear dynamical systems is investigated. The uncertainty is considered to be represented as fuzzy numbers, and hence, these uncertain dynamical systems are referred to as fuzzy linear dynamical systems, which are presented in the form of fuzzy differential equations (FDEs). The solution of an FDE is found using an approach called relative-distance-measure fuzzy interval arithmetic and under the granular differentiability concept. The control objective is to provide a control law such that the output of the system tracks a desired reference input in the presence of uncertainties. To this end, a theorem is proposed, which suggests that the control law should take the form of a feedback of fuzzy states with fuzzy gains and a fuzzy pre-compensator. However, since the fuzzy states of the system may not always be measurable, a fuzzy observer is designed for the estimation of such fuzzy states. It is also clearly shown that the generalized Hukuhara differentiability concept is unable for solving the problem examined in this study. Finally, the efficiency of the approach is examined for a plane landing control problem.

Design of Broad Learning-Based Self-Healing Predictive Control for Sludge Bulking in Wastewater Treatment Process

Self-healing control plays a crucial role in taking remedial action to minimize the adverse impacts of sludge bulking in wastewater treatment process (WWTP). However, since sludge bulking is a strong nonlinear and complex process with multiple fault conditions, the conventional self-healing control is difficult to obtain reliable performance. Thus, the purpose of this paper is to design a broad learning-based self-healing predictive controller (BL-SHPC) for sludge bulking in WWTP. The main innovations of the proposed controller are threefold. First, a dynamic fuzzy broad learning system (DFBLS) with an adaptive expansion strategy (AES) is used to identify the fault conditions of sludge bulking. Then, the fault features of sludge bulking can be comprehensively extracted with desirable performance. Second, a prioritized multi-objective optimization algorithm (PMOOA)-based predictive control, which considers the objective correlation and preference of fault conditions, is presented to obtain the optimal solutions to achieve self-healing. Then, the proposed controller can feasibly and precisely readjust manipulated variables to eliminate the sludge bulking. Third, the stability of the developed controller is proved by the Lyapunov stability theorem. Then, the stability analysis can ensure the successful application of BL-SHPC. Finally, the proposed BL-SHPC is tested on the Benchmark Simulation Model No.2 (BSM2) to validate its merits. The simulation results indicate that the proposed controller can obtain superior self-healing ability for sludge bulking in WWTP.

Fuzzy dynamical system for robot learning motion skills from human demonstration

Learning from demonstration (LfD) is an intuitive strategy for transferring human motion skills to robots in an agile and adaptable manner. The major goal of LfD is to identify significant movement primitives (MPs) from human demonstrations and then recompose those intrinsic primitives to adapt to a variety of new situations. However, maintaining the simplicity of MPs representation while guaranteeing their adaptability is not an easy undertaking. To achieve these two goals, two approaches are possible: (1) learning models that can capture and utilize the inherent patterns and main characteristics of the human demonstrations, and (2) dynamical systems that can respond to perturbations online without requiring to re-plan the entire trajectory. In this paper, we present a novel and efficient model that combines these two benefits to formulate MPs using a fuzzy dynamical system (Fuzzy-DS), which enables robots to adaptively alter the learned motion skills to meet various additional constraints in the process of performing tasks. Due to the joint use of a fuzzy inference system and a dynamic system, Fuzzy-DS is well-suited to human inputs and intuitive fuzzy rules, resulting in a computationally efficient model. To verify the effectiveness of the proposed method, experiments have been designed where the robot learned a plant pruning task and a pick-and-place task, subsequently, it can replicate and generalize these tasks to novel situations.

New extension to fuzzy dynamic system and fuzzy fixed point results with an application

<abstract><p>In this paper we introduce the notion of fuzzy dynamic system in $ b $ -metric-like space. By applying this, discuss some new refinements of the $ F $-fuzzy Suzuki-type fixed point results for the fuzzy operators are presented. Also, establish the concept fuzzy dynamic system instead of the Piscard iterative sequence, which improves the existing results for such analysis as those presented here. Includes some tangible instances and an application are given to highlight the usability and validity of the theoretical results.</p></abstract>

Optimal design of robust control based on compound form: steady-state performance and control cost

In this paper, we propose an optimal robust control for dealing with the uncertain fuzzy dynamical systems. First, a dynamical system is established with uncertainty. The uncertainty is nonlinear, time varying, and is regarded as bounded. The bound exists within a specified fuzzy set. Then, a robust control is proposed to ensure the system performance. The proposed control is deterministic, which is not on the basis of the IF-THEN rule. Besides, to achieve better performance, a performance index, including both the steady-state performance measurement and the control cost measurement of the system, is proposed. Furthermore, a fuzzy dynamical model of the robot joint module system is established with parameters uncertainty and external disturbance. By using the proposed optimal robust control, the performance of the dynamical system is not only definitely ensured but also optimized.