Fuzzy State Feedback Controller Research Articles

Event-Triggered Extended Dissipative FTB for T-S Fuzzy Switched Systems With Mismatched Phenomena and Deception Attacks: A Multidomain Framework.

This article investigates the extended dissipative finite-time boundedness (ED-FTB) problem for fuzzy switched systems under deception attacks. To improve the network resource efficiency, a multidomain probabilistic event-triggered mechanism (MDPETM) is proposed. The mode mismatched phenomenon is modeled based on the switching delay information between the controller mode and the system mode. To extract the true signal generated by the MDPETM, a virtual delay concept is developed. The constraint that the controller and the system must have the same premise variables is removed. Based on the MDPETM, mismatched fuzzy state feedback controllers are first devised which may not share the same modes with the system. Then, by establishing fuzzy basis and controller mode-dependent Lyapunov functionals, sufficient criteria free of nonlinear terms existing in the literature are derived, which ensure the ED-FTB of the closed-loop system under admissible delays and deception attacks. Finally, an application-oriented one-link robotic arm system is utilized to validate the theoretical results.

Cooperative Adaptive Fuzzy Control for the Synchronization of Nonlinear Multi-Agent Systems under Input Saturation

This research explores the synchronization issue of leader–follower systems with multiple nonlinear agents, which operate under input saturation constraints. Each follower operates under a spectrum of unknown dynamic nonlinear systems with non-strict feedback. Additionally, due to the fact that the agents may be geographically dispersed or have different communication capabilities, only a subset of followers has direct communication with the leader. Compared to linear systems, nonlinear systems can provide a more detailed description of real-world physical models. However, input saturation is present in most real systems, due to various factors such as limited system energy and the physical constraints of the actuators. An auxiliary system of Nth order is introduced to counteract the impact of input saturation, which is then employed to create a collaborative controller. Due to the powerful capability of fuzzy logic systems in simulating complex nonlinear relationships, they are deployed to approximate the enigmatic nonlinear functions intrinsic to the systems. A distributed adaptive fuzzy state feedback controller is designed by approximating the derivative of the virtual controller by filters. The proposed controller ensures the synchronization of all follower outputs with the leader output in the communication graph. It is shown that all signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking errors converge to a small neighborhood around the origin. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.

Enhanced Resilient Fuzzy Stabilization of Discrete-Time Takagi-Sugeno Systems Based on Augmented Time-Variant Matrix Approach.

In this technical correspondence, the resilient fuzzy stabilization is enhanced in the direction of elevating the feasible stabilization region as large as possible while the same alert threshold is chosen as the recent one. To do this, the switching-type fuzzy state-feedback controller is designed with a set of switch modes so that more groups of gain matrices can be introduced to enhance the degree of freedom. What is far more important is that a novel augmented time-variant matrix approach is proposed in order to collect the proprietary features of normalized fuzzy weighting functions with regard to each switch mode. Then, all the obtained augmented time-variant matrices are split into a set of positive/negative matrices, which can be elaborately assigned into different monomials of our designing conditions under the framework of homogeneous polynomials. Therefore, less conservative results of resilient fuzzy stabilization are obtained even if some higher alert thresholds are chosen for probably ensuring the establishment of the involved precondition. Finally, the superiority of our approach is validated by giving some detailed comparisons on the benchmark example.

A new Takagi-Sugeno fuzzy system approach for fuzzy state feedback controller design and its application to malware propagation on heterogeneous complex network

Abstract— Nowadays, digital transformation has brought many great changes and is becoming an essential part of real life, however, it also goes along with a considerable likelihood of being targeted in cyberattack. Indeed, the more businesses embrace digital transformation or use online services, the more opportunities hackers have to expand their cyberattacks. Hence, there is an essential need on analyzing and predicting of cyberattack on network systems. For this aim, we propose to study a controlled fractional network-based SCIRS (Susceptible - Carrier - Infectious - Recovered - Susceptible) malware propagation model and its stabilization problem based on fractional interconnected Takagi-Sugeno fuzzy system. A fuzzy state feedback controller is proposed to asymptotically stabilize the unstable malware-free equilibrium of the proposed malware propagation model and then, we establish sufficient conditions in terms of linear matrix inequalities. The effectiveness of proposed approach is illustrated by a case study of SCIRS malware propagation model on heterogeneous complex network.

$H_{\infty }$ Asynchronous Admissibilization for Nonlinear Singular Delayed Hybrid Hydraulic Turbine Governing Systems With Impulsive Perturbations

This article researches <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> asynchronous admissibilization for nonlinear singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations. By exploiting Takagi-Sugeno (T-S) fuzzy technique, the fuzzy singular delayed hybrid hydraulic turbine governing system with impulsive perturbations is built, which can not only accurately and concisely describe the dynamic behaviors of the pipeline, but also resist damages for the hydraulic turbine system caused by sudden reasons. Then, the asynchronous fuzzy state feedback controller (FSFC) is designed by using parallel distributed compensation (PDC) technique, and the asynchronous mechanism (AM) between the modes of FSFC and the modes of controlled plant is depicted by a hidden Markovian model. By constructing an improved timer-dependent (T-D) Lyapunov-Krasovskii (L-K) functional, the new criteria about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> admissibilization for fuzzy singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations can be acquired. The gains of asynchronous FSFC are expressed by solving linear matrix inequalities (LMIs). Impulsive operators are successfully generalized and extended from <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}$</tex-math></inline-formula> to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}^{n\times n}$</tex-math></inline-formula> , which makes the approach presented in this article more universal. Finally, the simulation results prove the correctness and availability of the method provided in this article.

Actuator fault and Bernoulli random delay-based H∞ reliable fuzzy control of singular hybrid vehicle suspension systems with impulsive perturbations

The problem of actuator fault and Bernoulli random delay-based H∞ reliable fuzzy state feedback control of singular hybrid vehicle suspension systems (SHVSSs) with impulsive perturbations is studied in this paper. By taking the acceleration of each part of the suspension as the component of the system state, the vehicle suspension system is successfully extended to a singular vehicle suspension system. The regularity and non-impulsiveness of the time-varying delays SHVSSs with impulsive perturbations are proved via singular value decomposition (SVD) method. By means of constructing a novel Lyapunov-Krasovskii (L-K) functional embodied with Markovian jump modes and impulse times information, neoteric conditions are smoothly concluded under linear matrix inequalities (LMIs) framework, which guarantee that the closed-loop SHVSS acquires H∞ stochastic admissibilization. By exploiting Takagi-Sugeno (T-S) fuzzy technique and parallel-distributed compensation (PDC) method, a reliable Bernoulli random delay-based fuzzy mode-dependent feedback (FMDF) controller is proposed to handle the change of sprung mass and actuator fault of the controlled time-varying delays SHVSSs. Simulation results verify the validity of the method and riding comfort level of the vehicle.

Finite‐time dissipative control of fuzzy distributed parameter CPSs with quantization under cyber attacks

AbstractThe finite‐time dissipative control for a class of nonlinear distributed parameter Cyber‐Physical Systems (CPSs) is studied in this article. By replacing the nonlinear term with the Takagi‐Sugeno (T‐S) fuzzy model, the nonlinear distributed parameter CPSs are represented by a fuzzy parabolic partial differential equation (PDE). To reduce the transmission burden of communication channels, the state information is considered to be dynamically quantized before transmission. Then, a fuzzy state feedback controller under cyber attacks is designed. Sufficient design criteria for the fuzzy controller and the adjusting parameters of dynamic quantizer are developed to obtain the finite‐time dissipative performance of the fuzzy closed‐loop system by the free‐matrix inequality approach. Finally, a simulation study in a cascaded of two cylindrical lithium batteries is explored to validate the efficiency of the control strategy.

Designing a Switched Takagi-Sugeno Fuzzy controller for CDC semi-active suspensions with current input constraint

To prevent the degradation of control performance resulting from the use of the clipped approach, this paper presents a novel control strategy for CDC (continuous damping control) semi-active suspensions using the Takagi-Sugeno (T-S) fuzzy method based on a piecewise affine (PWA) vertical dynamics model. First, to account for the significant tension-compression asymmetry and dissipative constraint of CDC damper force, a piecewise damping-force model is developed with current serving as input. Due to the nonlinear terms, T-S fuzzy system is then utilized to describe the suspension system via the sector nonlinearity approach. Finally, a fuzzy state feedback controller considering the asymmetry saturation of the control current is designed for the obtained switched T–S fuzzy model with optimized H∞ performance for suspension system by using the parallel distributed compensation (PDC) scheme. Simulation and experimental results under sinusoidal, random and transient excitations show significant improvements of the proposed approach on ride comfort and road handling while guaranteeing the performance under the input current constraint.

Exponential Synchronization of Second-Order Fuzzy Memristor-Based Neural Networks With Mixed Time Delays via Fuzzy Adaptive Control

This article addresses the exponential synchronization problem for a class of fuzzy inertial memsirtor-based neural networks with mixed time-varying delays (FMINNs). Firstly, the inertial items are described as second-order systems and transformed into first-order systems by utilizing a appropriate variable substitution. Then the fuzzy state-feedback control strategy and fuzzy adaptive control strategy are designed to ensure the exponential synchronization under the framework of Filippov solutions. The exponential synchronization algebraic conditions are obtained by choosing a proper Lyapunov-Krasovskii functional (LKF). Finally, two numerical simulations are provided to validate the effectiveness and benefit of the proposed results.

H∞.. admissibilization for time-varying delayed nonlinear singular impulsive jump systems based on memory state-feedback control

This paper addresses the problem of H∞ admissibilization for time-varying delayed nonlinear singular impulsive jump systems based on memory fuzzy state-feedback control. New criteria to guarantee the H∞ admissibility for the fuzzy time-varying delayed singular impulsive jump systems are obtained by establishing the improved timer-dependent Lyapunov–Krasovskii functional. The singular value decomposition technique is utilized to eliminate internal impulses, and the memory fuzzy state-feedback controller is successfully designed by using parallel distribution compensation technique to inhibit the effects of external unstable impulses and time-varying delays. The gains of the desired memory fuzzy state-feedback controller are obtained through solving linear matrix inequalities. Finally, the rightness and validity of the obtained results are demonstrated by two simulation examples containing the bio-economic system.

Admissible Control for Non-Linear Singular Systems Subject to Time-Varying Delay and Actuator Saturation: An Interval Type-2 Fuzzy Approach

Applied in many fields, nonlinear systems involving delay and algebraic equations are referred to as singular systems. These systems remain challenging due to saturation constraints that affect actuators and cause harm to their operation. Furthermore, the complexity of the problem will increase when uncertainty also simultaneously affects the system under consideration. To address this issue, this paper investigated a feasible control strategy for nonlinear singular systems with time-varying delay that are subject to uncertainty and actuator saturation. The IT-2 fuzzy model was adopted to describe the dynamic of the non-linear delayed systems using lower and upper membership functions to deal with the uncertainty. Moreover, the polyhedron model was applied to characterize the saturation function. The goal of the control approach was to design a relevant IT2 fuzzy state feedback controller with mismatched membership functions so that the closed-loop system is admissible. On the basis of an appropriate Lyapunov–Krasovskii functional, sufficient delay-dependent conditions were established and an optimization problem was formulated in terms of linear matrix inequality constraints to optimize the attraction domain. Simulation examples are provided to verify the effectiveness of the proposed method.

New fuzzy control design for photovoltaic system using LMI technique

The T-S Fuzzy model-based technique (T-S: Takagi-Sugeno) is used in this research to offer a new fuzzy state feedback control for solar systems with output charge. We discuss a DC-DC boost converter to manage the output power of a solar panel array under shifting meteorological circumstances. To reach optimal power point, a T-S reference model is employed to create a fuzzy state feedback control that must be tracked. Solving a series of linear matrix inequalities (LMIs) yields controller gains. Furthermore, the proposed solution reduces the oscillation disadvantage near the highest power point while simultaneously shortening the tracking time. Finally, simulation of the solar system employing the proposed state feedback control shows that the proposed approach is effective even in the face of climate change.

Robust stability and fuzzy controller synthesis for a class of hybrid re-entrant manufacturing systems

This paper addresses the problem of stability analysis and state feedback fuzzy control design for multi-line re-entrant manufacturing systems (RMSs) with impulse-type state jumps. Under the impulse effect, the RMS is modeled as a hyperbolic impulsive partial differential equation (IPDE) that possesses hybrid characteristics. Then, a matrix inequality condition depending on the discrete dynamic information is presented to deal with the jump behavior of the IPDE at impulse instants. Moreover, a robust fuzzy controller based on the parallel distributed compensation scheme is derived to render the RMS to a desired producing mode with steady feeding and output rates. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the proposed robust fuzzy controller.

Robust Stability Analysis and Feedback Control for Uncertain Systems With Time-Delay and External Disturbance

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods.

Design of equivalent‐input‐disturbance estimator based modified repetitive control with adaptive periodic event‐triggered for time‐varying delay nonlinear systems

AbstractThis article addresses the problems of the disturbance rejection and the periodic signal tracking for a class of time‐varying delay nonlinear systems subjected to unknown exogenous disturbances. To approximate the nonlinearity of the system, a Takagi‐Sugeno (T‐S) fuzzy model has been used. The proposed modified repetitive controller (MRC) scheme based on the equivalent‐input‐disturbance (EID) estimator improves the performance of periodic and aperiodic unknown disturbances rejection effectively and achieves good tracking performance for periodic references. Furthermore, an adaptive periodic event triggered mechanism based fuzzy state observer (APETM‐FSO) has been utilized to reduce data transmission, energy consumption, and computational burden, save the resources of communication. With the help of a designed adaptive event triggering condition, the APETM can detect the event occurrence, which is described by exceeding the error signal to a predetermined threshold. Only when the event occurs, the current data are transmitted otherwise, data can be kept unchanged using a zero‐order hold. Hence, The MRC, EID, and APETM‐FSO based on a time‐varying delay T‐S fuzzy model construct the overall system. Then, to achieve the asymptotic stability of the overall system subjected to unknown disturbances, sufficient conditions based on the Lyapunov–Krasovskii functional stability theory and linear matrix inequalities (LMIs) are derived. In addition, the FSO and fuzzy state feedback controller gains are designed using the matrix decomposition and LMI approaches. Simulation results with comparative study are presented to demonstrate the effectiveness and feasibility of the proposed scheme.

Cooperative Position-based Formation-pursuit of Moving Targets by Multi-UAVs with Collision Avoidance

The paper focuses on the issue of capturing a moving target for multiple unmanned aerial vehicles (UAVs). The problem involves a group of UAVs to create a formation-pursuit in the encirclement of a moving target. Dynamic task allocation algorithm is used in 3D dynamic environments to efficiently allocate the target to several existing UAVs. Target information is disseminated to neighbor UAVs by the temporary leader of UAVs. For the formation-pursuit using a position-based strategy, destination points to create formation are made at the sphere coordinates around a moving target. Then the destination points are tracked using a fuzzy state feedback controller. Optimized artificial potential field (APF) algorithm is used to avoid collisions with targets, other UAVs, and static obstacles. Each UAV can choose the optimal trajectory to avoid obstacles and reset the formation after passing them. The simulation results show that multi-UAVs successfully surrounded and formed formation-pursuit of a moving target without colliding with the closest Euclidean distance between UAVs of 1.32957 m. UAVs with a target is 1.94359 m, and UAVs with static obstacles within a range of 1.60632 m.Keywords—formation-pursuit, multi-UAVs, obstacle avoidance, task allocation, tracking control.

Stability and Stabilization of Takagi–Sugeno Fuzzy Second-Fractional-Order Linear Networks via Nonreduced-Order Approach

The extensively studied fractional-order dynamical networks only contain a uniform fractional derivative, which restricts the scope of fractional-order investigation. One type of Takagi–Sugeno fuzzy second-fractional-order linear networks is established in this article. First, by defining a novel Lyapunov functional, a sufficient criterion is offered to ensure global asymptotic stability of the addressed networks with time delay. Second, a fuzzy state-feedback control scheme is designed for the Takagi–Sugeno fuzzy second-fractional-order delayed linear networks to achieve global stabilization. Third, considering that only a few scholars have worked on adaptive control of fractional-order networks, an adaptive control method is also designed to realize the global stabilization of the Takagi–Sugeno fuzzy second-fractional-order linear networks, which does not contain the sign function and chattering problem can be averted. All results, given as algebraic criteria, are proved directly from the Takagi–Sugeno fuzzy second-fractional-order networks without utilizing the reduced-order approach. Three simulation examples are conducted to show the validity of the theoretical results at last.

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.

Multi-Instant Gain-Scheduling Stabilization of Discrete-Time Takagi–Sugeno Fuzzy Systems Based on a Time-Variant Balanced Matrix Approach

This article is devoted to the development of multi-instant gain-scheduling stabilization of discrete-time Takagi–Sugeno fuzzy systems by developing a time-variant balanced matrix approach. Many of the reported advances have provided more and more relaxed results via choosing higher order dependent gain matrices, which will be a trouble in the case of real-time implementation. Therefore, a multi-instant gain-scheduling fuzzy state-feedback controller with different working modes is given to stabilize the closed-loop systems by updating the enabled pair of lower order gain matrices in cycle. For each possible working mode, the real-time situation information of the normalized fuzzy weighting functions can be fully considered by using a set of time-variant balanced matrices in accordance to certain rules and, thus, much freedom is introduced for proposing less conservative results. More importantly, our relaxed result is obtained without requiring higher order dependent gain matrices than the existing ones, i.e., its conservatism is reduced in a more meaningful way and thus it is more conducive to real-time implementation. Finally, both the effectiveness and the superiority of the proposed results are discussed and validated in the numerical section.

Periodic event-triggered modified repetitive control with equivalent-input-disturbance estimator based on T-S fuzzy model for nonlinear systems

In this paper, the periodic signal tracking and the disturbance rejection problems are considered for a class of time-varying delay nonlinear systems with unknown exogenous disturbances under limited communication resources. The Takagi–Sugeno (T-S) fuzzy model is used to approximate the nonlinear system. The developed scheme achieves periodic reference tracking and improves the performance of periodic and aperiodic unknown disturbances rejection effectiveley. This can be operated by incorporating the equivalent-input-disturbance (EID) estimator with the modified repetitive controller (MRC) scheme. Moreover, a fuzzy periodic event-triggered feedback observer (FPETFO) is proposed for the purpose of reducing the computational burden, energy consumption and saving communication resources. The periodic event-triggered technique is designed to observe the occurrence of an event which is described by an error signal. When this error signal exceeds a prescribed threshold, the event occurs and the current data are transmitted; otherwise, there is a zero-order hold to keep data unchanged. The overall system consists of MRC, EID and FPETFO based on a T-S fuzzy model. Then, some sufficient conditions are derived to gurantee the asymptotic stability of the overall system subjected to unknown disturbances using the Lyapunov–Krasovskii functional (LKF) stability theory and linear matrix inequalities (LMIs). The fuzzy state feedback controller and observer gains are designed using the LMI and matrix decomposition approaches. Simulation results illustrate the effectiveness and feasibility of the proposed scheme with comparative study.