Fuzzy Observer Research Articles

Piecewise Attack Strategy Design for T–S Fuzzy Cyber–Physical Systems

This article is concerned with the problem of the stealth attack strategy design for T–S fuzzy cyber–physical systems (CPSs). Virtual systems that reflect the attacker’s target are established, in which the parameter matrices of virtual systems rely on the different regions where the premise variables (PVs) of the T–S fuzzy CPS and the piecewise fuzzy observer are located at different past instants. Unlike the existing attack policies, a piecewise attack strategy is designed based on the established virtual systems, while the existing ones are required to be nonpiecewise. Furthermore, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{-}/H_{\infty }$ </tex-math></inline-formula> scheme is applied to maximize the impact of the attack on the estimation performance (EP) of the observer while avoiding detected by the detector. A simulation example is applied to verify the effectiveness and advantages of the designed attack scheme.

Fuzzy model based fault estimation and fault tolerant control for flexible spacecraft with unmeasurable vibration modes

This paper investigates the problem of anti-disturbance fault estimation and attitude tracking fault tolerant control for a flexible spacecraft subject to actuator faults, external disturbances, input saturation, and configuration misalignment. Different form the traditional methods, both the nonlinear dynamics subsystem and attitude control system are reconstructed into Takagi–Sugeno fuzzy models, where partial nonlinear term is remained to assist the design of fuzzy controller. A fuzzy fault estimation observer with proportional–integral adaptive laws is first designed. Without measuring any dynamic information of flexible appendages, estimated values of unknown actuator faults and vibration disturbances of flexible appendages can be obtained simultaneously. This is the most important advantage of the proposed fault estimation scheme over the previous methods. Then, a fuzzy sliding mode fault tolerant control scheme, based on fewer fuzzy rules and less computational burden, is developed under the framework of feedback linearisation and feedforward compensation. The actuator faults and vibration disturbances are counteracted in real time. Regional pole placement and virtual controller with input saturation are adopted to tune the control input and avoid the radical control torque scheduling. Finally, numerical simulations are given to illustrate the validity of the proposed fault estimation and fault tolerant control strategies.

Cascade Takagi–Sugeno fuzzy observer design for nonlinear uncertain systems with unknown inputs: A sliding mode approach

This article investigates the design of Takagi–Sugeno (TS) fuzzy model-based observers for nonlinear systems with parametric uncertainties and unknown inputs. To address this challenging problem, two observers are constructed in cascade. Based on the sliding mode technique, the first observer allows to examine a new system whose both state and output equations are subject to uncertainties but without unknown inputs. The second Luenberger-type observer is designed for the new system where the effects of uncertainties on the estimation error can be canceled. The TS fuzzy observer design is recast as optimization problems under linear matrix inequalities, which can be effectively solved using convex optimization technique. The new cascade observer structure enables a simultaneous estimation of the system states, the unknown inputs and the uncertainties of the original nonlinear system. The effectiveness and advantage of the proposed estimation method is demonstrated via two numerical examples including a nonlinear vehicle application.

State estimation and fuzzy sliding mode control of nonlinear Markovian jump systems via adaptive neural network

This paper deals with the problem of Takagi-Sugeno fuzzy model-based state estimation and sliding mode control for nonlinear systems through an adaptive neural network, in which the system parameters follow the Markovian switching rules. In order to deal with the unknown local nonlinearity, a multi-layer neural network is used for the nonlinear function approximation. First, a Lebesgue fuzzy observer with adaptive compensator is designed based on state-dependent fuzzy rules. Second, an integral sliding surface is proposed, based on which the obtained sliding mode dynamics has good property of sliding mode manifold. Third, an H∞ performance with stochastic stability of the sliding mode dynamics and error dynamics are developed in the form of linear matrix inequality. Moreover, reachability of sliding surface in finite-time and maintenance of sliding motion are realized by constructing a fuzzy sliding mode controller. Finally, a simulation study is added to show the validity of the proposed results on the robot manipulator model.

Convergence in measure of intuitionistic fuzzy observables

The aim of this paper is to define a convergence in measure m, where m is an intuitionistic fuzzy state. We prove a version of weak law of large numbers for a sequence of independent intuitionistic fuzzy observables, too.

Relaxed Fault Estimation of Discrete-Time Nonlinear System Based on a New Multi-Instant Real-Time Scheduling Fuzzy Observer

Relaxed fault estimation (FE) criteria of a class of discrete-time nonlinear plants are proposed based on a new multi-instant real-time scheduling fuzzy FE observer. Compared with the existing methods given in the recent literature, the newly developed fuzzy observer is capable of providing much freedom for reducing the conservatism of designing feasible FE criteria. At each sampling point, the information of adjacent groups of normalized fuzzy weighting functions can be updated and utilized for deciding the activated mode of our developed fuzzy FE observer. Based on this, an exclusive pair of gain matrices can be given by introducing a set of well-designed free matrices into the designed FE criteria for every activated mode. Moreover, it can be found that the proposed result will include the previous one as a special case if all of those free matrices are removed. Finally, the well-known nonlinear truck–trailer plant with actuator fault is utilized to validate the superiority of our approach over the existing ones reported in the literature.

Fault-Tolerant Control of Nonlinear Systems With Actuator and Sensor Faults Based on T–S Fuzzy Model and Fuzzy Observer

In this work, we study simultaneous reconstructions of sensor fault and actuator fault, as well as fault-tolerant control (FTC) for nonlinear systems approximated by the T–S fuzzy model. By making the sensor fault as part of the state, a rectangular singular system is firstly given, based on which, a proportional-integral observer (PIO) is synthesized to realize the reconstructions of sensor and actuator faults simultaneously. With the support of these estimation information, an FTC scheme is well provided to maintain the stability of the closed-loop system even in the occurrence of faults. Furthermore, by resorting to linear matrix inequalities (LMIs), the stability criteria are formulated via the fuzzy Lyapunov function method. Finally, the performance of the theoretical result is verified through two real dynamics.

Distributed Output Feedback Funnel Control for Uncertain Nonlinear Multiagent Systems

Adaptive output-feedback consensus with funnel performance is studied for nonlinear uncertain multiagent systems (MASs). The nonlinear MASs contain unknown dynamics and only an output variable can be measured. The other states are not measured directly and are reconstructed via fuzzy state observers. The presence of output feedback makes the proposed design significantly different from the existing literature on control with funnel performance. In particular, appropriate adaptive laws must be defined to handle the presence of uncertain dynamics and local output information from a few neighboring nodes. Interestingly, with a suitable error transformation, it is shown that the proposed control law has a simpler structure than barrier function methods proposed in the literature to handle funnel-like performance. With respect to this point, simulation studies illustrate that the proposed method can dramatically reduce the control effort while satisfying transient and steady-state performance imposed by the funnel.

Adaptive Fuzzy Event-Triggered Tracking Control for Nonstrict Nonlinear Systems

This article addresses adaptive fuzzy event-triggered controller design for nonstrict nonlinear systems. First, for estimating the unmeasurable states, the high-gain fuzzy state observer is designed. By using backstepping technique, the adaptive fuzzy controller is designed. A new switching threshold event-triggered mechanism is given to decide when the controller needs to be updated and the Zeno behavior is avoided. Stability analysis shows that the tracking error can be arbitrarily small and all variables of the closed-loop system remain bounded. At last, the effectiveness of our control strategy is illustrated through simulation.

Filter-Based Event-Triggered Adaptive Fuzzy Control for Discrete-Time MIMO Nonlinear Systems With Unknown Control Gains

In this article, an event-triggered output feedback adaptive fuzzy control scheme is developed for a class of uncertain discrete-time multiinput–multioutput (MIMO) nonlinear systems with immeasurable states and unknown control gains. Due to the existence of unmeasured states, a set of fuzzy filters are designed, then a filter-based event-triggered adaptive fuzzy control scheme is developed for discrete-time MIMO nonlinear systems. To solve the problem of state estimation caused by the coupling of control input and unknown control gains, a fuzzy filters-based state observer is developed by combining filter states. And then, a parameterized state observer is constructed to effectively estimate immeasurable state signals by the combination of the fuzzy filter states and the gradient-based fuzzy parameter updating law. Based on filter states and estimation states, an event-based adaptive fuzzy control scheme is proposed by novel intermediate errors and backstepping. To overcome the causal problem caused by the low-triangular structure, the variable substitution and a predictor are, respectively, employed to forecast the future state and reference signals. A series of stability analyses illustrates that the proposed scheme achieves immeasurable state estimations, guarantees the ultimately uniformly boundedness of the closed-loop system, and obtains the good tracking performance, while reducing communication occupancy. Finally, simulation studies on a numerical and a practical example are conducted to demonstrate the effectiveness of the proposed scheme.

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.

Observer‐based active fault‐tolerant control for a class of pure‐feedback switched nonlinear systems

SummaryAn active fault‐tolerant control (FTC) strategy for a class of switched nonlinear systems in pure‐feedback form by using average dwell time method is investigated in this article. The unknown functions in the system are approximated directly by fuzzy logic systems. A fuzzy state observer is designed to estimate the unavailable states, based on which, a fault detection project is designed. In fault‐free case, all the signals in the closed‐loop system are proved to be bounded under the control of the designed input. The fault estimation and FTC projects will be activated after a fault has been detected. In addition, the active FTC is constructed in the framework of backstepping design technique. The proposed controller guarantee that all the closed‐loop signals remain bounded under a class of switching signals with average dwell time. The simulation results show the effectiveness of the proposed method.

Adaptive PID Fault-Tolerant Tracking Controller for Takagi-Sugeno Fuzzy Systems with Actuator Faults: Application to Single-Link Flexible Joint Robot

This paper considers the problem of Fault Tolerant Tracking Control (FTTC) strategy design for nonlinear systems using Takagi-Sugeno (T-S) fuzzy models with measurable premise variables affected by actuator faults subject to unknown bounded disturbances (UBD). Firstly, the Adaptive Fuzzy Observer (AFO) is proposed to estimate the faults. Based on the information provided by this observer, an active fault tolerant tracking controller described by an adaptive Proportional-Integral-Derivative (PID) structure has been developed to compensate for the actuator fault effects and to guarantee the trajectory tracking of desired outputs to the reference model despite the presence of actuator faults. The stability and the trajectory tracking performances of the proposed approach are analyzed based on the Lyapunov theory. Sufficient conditions can be obtained and solved for the design of the controller, and the observer gains using Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed technique is illustrated by using a single-link flexible joint robot.

Relaxed observer-based stabilization and dissipativity conditions of T-S fuzzy systems with nonhomogeneous Markov jumps via non-PDC scheme

This paper aims to design a robust observer-based dissipative controller for discrete-time Takagi–Sugeno (T-S) fuzzy systems with nonhomogeneous Markov jumps through a non-parallel distributed compensation (non-PDC) scheme. Based on a mode-dependent nonquadratic Lyapunov function, the final form of the stabilization conditions is expressed as linear matrix inequalities in a less conservative manner. To be specific, this paper proposes a decoupling technique that can address the inherent nonconvex terms by extracting them from the stabilization conditions, where all slack variables are set to be fuzzy-basis-dependent for less conservative performance. Furthermore, the proposed stabilization method adopts a one-step design strategy that simultaneously designs the fuzzy observer and control gains without any iteration procedures by employing a positive tuning parameter. In particular, the time-varying transition probabilities included in the stabilization conditions are effectively removed using a modified relaxation technique that can avoid excessive use of free weighting matrices. Finally, based on four examples, the validity of the proposed method is verified through comparison with other studies.

Finite-time attack detection for nonlinear complex cyber-physical networks under false data injection attacks

This paper investigates the problem of finite-time attack detection for nonlinear complex cyber-physical networks under false data injection (FDI) attacks. Firstly, a Takagi-Sugeno (T-S) fuzzy model is used to approximate nonlinear complex cyber-physical networks in which the measurement channels are injected by FDI attacks. Secondly, based on adding a power integrator technique, a finite-time fuzzy observer is designed to achieve the rapid state observation of complex cyber-physical networks within a finite time by adjusting the observer parameters. Then, an attack detection mechanism consisting of the finite-time fuzzy observer and an attack detector is developed to detect FDI attacks, which can trigger an alarm within a finite time when FDI attacks occur. Finally, simulation results are given to show the effectiveness and superiority of the proposed method.

Adaptive Fuzzy Output-Feedback Control for Switched Uncertain Nonlinear Systems With Full-State Constraints.

This article investigates an adaptive fuzzy tracking control approach via output feedback for a class of switched uncertain nonlinear systems with full-state constraints under arbitrary switchings. The adaptive observer and controller are designed based on fuzzy approximation. The main characteristic of discussed systems is that the state variables are not available for measurement and need to be kept within the constraint set. In order to estimate the unmeasured states, the adaptive fuzzy state observer is constructed. To guarantee that all the states do not violate the time-varying bounds, the tangent barrier Lyapunov functions (BLF-Tans) are selected in the design procedure. Based on the common Lyapunov function method, the stability of considered systems is analyzed. It is demonstrated that all the signals in the resulting system are bounded, and all the states are limited in their constrained sets. Furthermore, the simulation example is used to validate the effectiveness of the presented control strategy.

Integrated State/Fault Estimation and Fault-Tolerant Control Design for Switched T–S Fuzzy Systems With Sensor and Actuator Faults

This article proposes an integrated design approach addressing the state/fault estimation (SFE) and fault-tolerant control (FTC) issues for switched T–S fuzzy systems with sensor and actuator faults and external disturbances. A switched fuzzy observer is developed to simultaneously estimate the system states and the sensor and actuator faults from measurement outputs affected by sensor faults. Based on this observer, a switched fuzzy FTC is designed to stabilize the closed-loop system and compensate for the effects of different considered faults, taking into account the presence of external disturbances. The mutual coupling between the estimation unit (SFE) and the control unit (FTC) supports the integrated design of these two units instead of the separated one. However, the separated design is the most adopted in the literature because the integrated design leads to complex stability conditions in the form of bilinear matrix inequalities. This work focuses on the integrated design considering the different interactions between the observer and the controller and thus ensuring good performance in terms of estimation, control, robustness, and fault compensation. For this purpose, a two-step integrated design strategy and a single-step integrated design strategy are proposed to formalize the integrated SFE and FTC design as linear matrix inequalities instead of bilinear ones. These strategies are based on the mode-dependent average dwell time concept, the piecewise Lyapunov function technique, and the robust <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> approach. The applicability and efficiency of the developed results are illustrated by studying a numerical example and a single-link robotic manipulator.

Further Studies on State Estimation of Discrete-Time Nonlinear Circuits Based on a Switching-Type Multi-Instant Fuzzy Observer

This brief proposes further studies on fuzzy state estimation of discrete-time nonlinear circuits. In order to give a less conservative result over the most recent one, a new switching-type multi-instant fuzzy observer is introduced and thus different groups of gain matrices can be dispatched in the light of the updated mode about the normalized fuzzy weighting functions. For each possible mode, its corresponding gain matrices are deduced by using a new time-varying balanced matrix method. Compared with the existing time-invariant balanced matrix method, much more freedom can be provided with the aid of the powerful analysis tool of multi-instant homogenous polynomials. As a result, the conservatism is reduced and better performance of fuzzy state estimation is capable of being obtained in this brief. Finally, two advantages of our proposed results are validated via the benchmark example of this field.

A technique for designing nano-scale circuits using a fuzzy logic and nature-inspired fish swarm optimization algorithm

Recent breakthroughs in quantum processing software and hardware have shown substantial development toward operational results. We anticipate quantum computing to have significant applications in some domains ranging from machine learning and optimization to drug development in the future. Quantum computing and designing have gotten a lot of interest from investigators. Physical design is one of the two main stages in designing nano-scale circuits that receive a list of circuit nodes as input and produce the final arrangement in a particular technology. However, it has encountered several design issues and execution limits in the long term. Moreover, designing nano-scale circuits is an NP-hard problem in terms of cost, delay, and energy consumption. This paper has provided a new method for solving the optimal design of nano-scale circuits using a fuzzy-based Fish Swarm Algorithm (FSA). The FSA represents fish, hunting, and fish behavior to get the best results. It has a quick integration speed, a powerful global search capacity, and a significant shortcoming. In our proposed method, the fuzzy observer is responsible for detecting the system's state within the defined area and maintaining the state within it. The proposed method has been evaluated against some benchmarks, and cost, delay, energy, and area characteristics have been reduced. Simulation outcomes demonstrated the suggested method's correct performance in terms of "energy," "cost", "area", and "delay" where the suggested technique outperforms others (GA, PSO, FSA and ACO).

Extended Kalman filter and Takagi-Sugeno fuzzy observer for a strip winding system

This paper proposes two nonlinear estimation approaches, namely based on Extended Kalman Filter (EKF) and a Takagi-Sugeno Fuzzy Observer with 32 rules (TSFO-32), for a Strip Winding System (SWS) characterized by variable reference input, variable moment of inertia with constant increasing tendency and variable parameters. The SWS is a complex and nonlinear mechatronic system viewed as a controlled process, which wraps a strip with constant linear velocity on a reel, and the variable radius modifies both the angular velocity and the moment of inertia. The motivation of using EKF is the zero stationary error at low speeds. The motivation of using TSFO-32 is that once the Takagi-Sugeno fuzzy models are obtained, various analysis and design tools initially developed for linear systems, which facilitate the observation and/or synthesis of the controller for complex nonlinear systems, can be adapted appropriately and used in these nonlinear systems. Therefore, these tools simplify the design as well-established approaches and algorithms are available. The fuzzy control system stability and observer design conditions are derived and expressed as linear matrix inequalities. The efficiency of TSFO-32 is discussed in this paper in terms of setting a certain convergence rate. The performance of the two nonlinear estimation approaches is validated by means of digital simulations conducted for three values of the moment of inertia.