Nonlinear Fuzzy Systems Research Articles

Predictive Controller for Large-Scale Fuzzy Polynomial Systems

This paper presents an innovative method to tackle the predictive-control challenges associated with large-scale fuzzy polynomial systems comprising interconnected polynomial fuzzy systems. This study models large-scale nonlinear fuzzy systems in a polynomial framework, which can reduce the number of fuzzy rules. We derive the conditions for controller synthesis in the main theorem using the Lyapunov theory and sum-of-squares technique. Simulation results confirm the validity and efficiency of this approach.

A switched system approach to exponential stabilization of interval type-2 fuzzy nonlinear systems with packet dropouts

This paper investigates the exponential stabilization problem for interval type-2 (IT2) fuzzy system with parameter uncertainties and packet dropouts. The sample-and-hold characteristic is simulated by employing an input delay methodology, and we present a model for the packet dropout phenomenon using switched approach. Some novel two-side delay-dependent looped-functionals are proposed by considering state information in the intervals from tr to t and t to tr+1 which relaxes the monotonic constraint of the Lyapunov–Krasovskii functional (LKF) and enhances the utilization of the actual sampling pattern. Additionally, some free-weighting matrices, slack matrices, the bound information in membership functions (MFs) and the signs of the first-order time derivative of fuzzy MFs are used to obtain a novel relaxed sufficient conditions for exponential stabilization of interval type-2 fuzzy systems (IT2 FS). Based on the LKF theory, new relaxed sufficient conditions with linear matrix inequalities (LMIs) constraints are derived. According to the criterion, sampled-data controller is devised to ensure that the closed-loop system is exponential stabilization. Finally, an illustrative example is presented to demonstrate the practicality and effectiveness of the method proposed. Comparative analysis highlights the simplicity and practicality of the suggested algorithm.

Robust Control Based on Adaptative Fuzzy Control of Double-Star Permanent Synchronous Motor Supplied by PWM Inverters for Electric Propulsion of Ships

This study presents the development of an adaptive fuzzy control strategy for double-star PMSM-PWM inverters used in ship electrical propulsion. The approach addresses the current and speed tracking challenges of double-star permanent magnet synchronous motors (DSPMSMs) in the presence of parametric uncertainties. Initially, a modeling technique employing a matrix transformation method is introduced, generating decoupled and independent star windings to eliminate inductive couplings, while maintaining model consistency and torque control. The precise DSPMSM model serves as the foundation for an unknown nonlinear backstepping controller, approximated directly using an adaptive fuzzy controller. Through the Lyapunov direct method, system stability is demonstrated. All signals in the closed-loop system are ensured to be uniformly ultimately bounded (UUB). The proposed control system aims for low tracking errors, while also mitigating the impact of parametric uncertainties. The effectiveness of the adaptive fuzzy nonlinear control system is validated through tests conducted in hardware-in-the-loop (HIL) simulations, utilizing the OPAL-RT platform, OP4510.

Fuzzy control of singular fractional order multi-agent systems with actuator saturation

In this paper, a T-S fuzzy model is established to describe nonlinear fuzzy singular fractional order multi-agent systems (SFOMASs) exhibiting actuator saturation when the order is between 0 and 2. We focus on the case where the system state is difficult to measure or cannot be directly measured, so it needs to be estimated based on other measurable signals. To this end, a fuzzy observer is designed, which can process fuzzy or imprecise input and output signals through fuzzy processing. Then the observer-based leader-following consensus problem of fuzzy SFOMASs with actuator saturation is addressed. To address input saturation, we use some mathematical tools to represent the saturated linear feedback on the convex hull, which is then transformed into seeking the optimal solution of linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed approach is verified through the adoption of a numerical example.

Retracted: Robust Adaptive Control for a Class of T-S Fuzzy Nonlinear Systems with Discontinuous Multiple Uncertainties and Abruptly Changing Actuator Faults

Retracted: Robust Adaptive Control for a Class of T-S Fuzzy Nonlinear Systems with Discontinuous Multiple Uncertainties and Abruptly Changing Actuator Faults

Guaranteed Set-Membership Estimation for Local Nonlinear Uncertain Fuzzy Systems Subject to Partially Decouplable Unknown Inputs

Local nonlinear fuzzy systems are useful for control solutions due to their ability to handle unmeasurable/inexact premise variables and reduce computational complexity. However, their estimation problems still require further development. This paper addresses this issue by investigating set-membership estimation for a class of discrete-time local nonlinear uncertain Takagi–Sugeno fuzzy systems with guaranteed performance. We propose a new observer architecture that solves partially decouplable unknown inputs and converts nonlinear error dynamics into a linear parameter-varying type. Using the systematic <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _\infty$</tex-math></inline-formula> -technique, the design conditions in the form of linear matrix inequalities ensure stability and output performance of the state estimation. We also derive a straightforward and effective zonotopic analysis method, considering the fuzzy and local nonlinear context, for less conservative results without using any specific interval set computation. Furthermore, a fast fault detection logic is proposed as an application of the set-membership estimation. Finally, we demonstrate the feasibility and advantages of our approach through three compelling examples, showcasing its efficacy in different scenarios.

Nonlinear fuzzy forecasting system for wind speed interval forecasting based on self-adaption feature selecting and Bi-LSTM

Nonlinear fuzzy forecasting system for wind speed interval forecasting based on self-adaption feature selecting and Bi-LSTM

Observer-Based Finite-Time Event-Triggered Control for Stochastic T-S Fuzzy Nonlinear Systems with Time-Varying Delay

Observer-Based Finite-Time Event-Triggered Control for Stochastic T-S Fuzzy Nonlinear Systems with Time-Varying Delay

Practical stability of fractional-order nonlinear fuzzy systems

In this paper, we present a practical Mittag–Leffler stability for a new class of fractional-order nonlinear Takagi–Sugeno fuzzy uncertain systems. Based on fractional-order Lyapunov stability theory and the parallel distributed compensation (PDC) controller techniques, we show the convergence of the solutions of the closed-loop considered system toward a neighborhood of the origin. Furthermore, a numerical example is given to show the applicability of the main result.

Dynamic Analysis of Fuzzy Systems

In this work, a new methodology for the dynamic analysis of non-linear systems is developed by applying the Mamdani fuzzy model. With this model, parameters such as settling time, peak time and overshoot will be obtained. The dynamic analysis of non-linear fuzzy systems with triangular membership functions is performed, and linguistic variables describing overly complex or ill-defined phenomena are used to fit the model. Scaling factors will simplify the modification of the variables, making them easier to find the system model. The specifications of second-order characteristics in the time domain, such as overshoot and peak time, will be represented graphically. As a case study, the proposed methods are implemented to analyse the dynamics of a tank and a simple pendulum for first-order and second-order systems, respectively, where it is observed that the proposed methodology offers highly positive results.

Computational Mathematics: Solving Dual Fully Fuzzy Nonlinear Matrix Equations Numerically using Broyden’s Method

Fuzzy numbers have many applications in various mathematical models in both linear and nonlinear forms. In the form of a nonlinear system, fuzzy nonlinear equations can be constructed in the form of matrix equations. Unfortunately, the matrix equations used to solve the problem of dual fully fuzzy nonlinear systems are still relatively few found in the publication of research results. This article attempts to solve a dual fully fuzzy nonlinear equation system involving triangular fuzzy numbers using Broyden’s method. This article provides the pseudocode algorithm and the implementation of the algorithm into the MATLAB program for the iteration process to be carried out quickly and easily. The performance of the given algorithm is the fastest in finding system solutions and provides a minimum error value.

Application of Nonlinear Differential Equation in Electric Automation Control System

Abstract This article uses fifth-order nonlinear differential equations to describe the dynamic process of electrical automation control systems. This method first derives the equivalent system of the nonlinear fuzzy global system and then uses the orthogonal polynomial series expansion technique and its integral operation matrix. The local manifold at the dominant unstable equilibrium point of a single-machine infinite-bus system after a failure described by a two-dimensional quadratic nonlinear differential equation is calculated, and the stability boundary of the power system is obtained. The research results show that the output frequency fluctuation of the electrical automation control system is small after the algorithm is adopted, and the intelligent control system can accurately diagnose and warn the electrical faults. The system can meet the requirements of online voltage coordinated control.

Decision making on the mappings' ideal solution of a fuzzy non-linear matrix system of Kannan-type

Since proving many fixed point theorems in a given space requires either growing the space itself or growing the self-mapping that works on it, both of these options are good. The operators' ideal generated by a weighted binomial matrix in the Nakano sequence space of extended s-fuzzy functions is constructed. Some structures for it based on geometry and topology are presented. It has been proven that the Kannan contraction operator has a unique fixed point in this class. Lastly, sufficient conditions such that a fuzzy non-linear matrix system of Kannan-type has a unique solution in this ideal class are investigated and a numerical example to explain our results are given.

Exponential stability and stabilization of positive T‐S fuzzy delayed systems

AbstractThe analysis of positive nonlinear delayed systems is of great importance for many real‐world applications. Such systems' stability and stabilization assessment is still an open topic, and there is limited literature on this field. Moreover, further convergence conditions should be considered for many experimental processes, such as exponential stability analysis, which is highly important. Considering the above, we deal in this study with the problem of exponential stability and stabilization of nonlinear fuzzy positive systems with delay. We establish exponential stability criteria using Lyapunov–Krasovskii functional (LKF) and a delay bi‐decomposition approach for bounded and time‐varying delayed systems. The obtained results are then extended to the exponential stabilization case. The control law is designed using Parallel distributed compensation (PDC). The proposed approach, formulated in terms of linear matrix inequalities (LMIs), allows reducing the conservativeness of the delay‐dependent conditions. A comparative study is presented to illustrate the superiority of our method. Moreover, simulation results for the two tanks process show the advantages of the proposed control design.

A T-S fuzzy state observer-based model predictive reset control for a class of fuzzy nonlinear systems with event-triggered mechanism

In this study, the problem of observer-based control for a class of nonlinear systems using Takagi-Sugeno (T-S) fuzzy models is investigated. The observer-based model predictive event-triggered fuzzy reset controller is constructed by a T-S fuzzy state observer, an event-triggered fuzzy reset controller, and a model predictive mechanism. First, the proposed controller utilizes the T-S fuzzy model and is constructed based on state observations and discrete sampling output, which can greatly reduce the occupation of communication resources. Then, the model predictive strategy for reset law design is designed in this paper. With a reasonable reset of the controller state at certain instants, the performance of the reset control systems is improved. Finally, the validity of the proposed method is illustrated by simulation. The merits of the proposed controller in improving transient performance and reducing the communication occupation are demonstrated by comparing its results with the output feedback fuzzy controller and the first-order fuzzy reset controller.

Input-to-State Stability of the Nonlinear Fuzzy Systems via Small-Gain Theorem and Decentralized Sliding-Mode Control

This article presents the input-to-state stability (ISS) and decentralized sliding-mode control of polynomial fuzzy interconnected systems by using the small-gain theorem. The contribution of this article is threefold. First, based on the boundedness of the solution of fuzzy interconnected subsystems, the sufficient conditions for the boundedness fuzzy interconnected system are provided. Second, the ISS small-gain theorem is extended to the polynomial fuzzy interconnected system for the number of membership functions being the same and different, and the trajectory-based ISS small-gain theorem is proposed. Third, the sliding surface based on state feedback is designed, and the stability of sliding-mode motion is analyzed for the fuzzy interconnected system. Finally, the effectiveness and superiority of the proposed method are illustrated by using a numerical example, a spring-connected double inverted pendulum system, and comparison with the existing results.

Dwell-time-dependent memory based state feedback controller design for switched Takagi–Sugeno fuzzy nonlinear systems

This paper presents the memory-based Takagi–Sugeno (T-S) fuzzy state feedback controller (SFC) for switched nonlinear systems based on the admissible edge-dependent average dwell time (AEDADT) rule. Different from the existing studies, the fuzzy dependent exponential Lyapunov–Krasovskii functional (LKF) is introduced for switched nonlinear systems, which include the notion of the derivative of membership functions based on the switching idea. Besides that, when compared to the traditional SFC framework, a time-varying delay is involved with the AEDADT switching rule in control gain matrices that are considered for the first time to tackle the stabilization problem. Further, the AEDADT switching property is considered for proposed nonlinear systems, and it contributes to getting more information about previous modes. Based on the proposed membership function dependent exponential LKF, new sufficient conditions are carried out to stabilize the proposed nonlinear systems in terms of the linear matrix inequalities (LMIs) technique. To support the applicability and efficacy of the proposed controller scheme, the tunnel diode circuit system model is illustrated. Also, the feasibility of the obtained results is verified by the numerical example.

Impulsive consensus of nonlinear fuzzy multi-agent systems under DoS attack

In this paper, the impulsive consensus of fuzzy nonlinear multi-agent systems is investigated under denial-of-service (DoS) attack. By constructing discontinuous Lyapunov function, some sufficient conditions are derived to guarantee the consensus of the nonlinear T–S fuzzy multi-agent systems in the presence of DoS attack. Different from the existing results of impulsive consensus of multi-agent systems under DoS attack, the method proposed in this paper can flexibly deal with both the problems of communication interruption and topology switching. Finally, two numerical examples are given to verify the effectiveness of the main results.

State and Fault Estimation for T–S Fuzzy Nonlinear Systems Using an Ensemble UKF

State and Fault Estimation for T–S Fuzzy Nonlinear Systems Using an Ensemble UKF

TS Fuzzy Robust Sampled-Data Control for Nonlinear Systems with Bounded Disturbances

We investigate robust fault-tolerant control pertaining to Takagi–Sugeno (TS) fuzzy nonlinear systems with bounded disturbances, actuator failures, and time delays. A new fault model based on a sampled-data scheme that is able to satisfy certain criteria in relation to actuator fault matrix is introduced. Specifically, we formulate a reliable controller with state feedback, such that the resulting closed-loop-fuzzy system is robust, asymptotically stable, and able to satisfy a prescribed H∞ performance constraint. Linear matrix inequality (LMI) together with a proper construction of the Lyapunov–Krasovskii functional is leveraged to derive delay-dependent sufficient conditions with respect to the existence of robust H∞ controller. It is straightforward to obtain the solution by using the MATLAB LMI toolbox. We demonstrate the effectiveness of the control law and less conservativeness of the results through two numerical simulations.