Fuzzy Observer Research Articles

Command filter‐based adaptive robust prescribed performance formation control for nonlinear multi‐agent systems

SummaryThis paper investigates an observer‐based adaptive robust fuzzy formation tracking control method for nonlinear multi‐agent systems (MAS) with input delay. The considered nonlinear MAS contains the unknown nonlinear functions, that is, unmeasured states. The fuzzy logic systems (FLS) are used to approximate the unknown nonlinear functions, and then a fuzzy adaptive state observer is designed to estimate the unmeasured states. The Pade approximation approach is introduced to solve the input delay issue. By combining command filtering and backstepping recursive control techniques, a robust adaptive prescribed performance formation output feedback tracking controller is designed. Moreover, the proposed controller can avoid the “explosion of complexity” and “singularity” problems in the backstepping design framework. Based on Lyapunov stability theory, it is proved that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (SGUUB), and the formation tracking errors do not exceed the prescribed performance bounds. Finally, the feasibility of the proposed control approach can be further verified through numerical and practical examples.

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.

Event-triggered control for switched systems with sensor faults via adaptive fuzzy observer

This article lays emphasis on a mode-dependent event-triggered controller (MDETC) scheme for a kind of nonlinear switched systems with delay and sensor faults, where the state of the system, sensor faults, and nonlinear term are all unknown. By utilizing a fuzzy logic method and constructing adaptive laws, an adaptive fuzzy observer is designed to simultaneously estimate the states and sensor faults. Meanwhile, a MDETC output feedback is designed for the adaptive fuzzy observer, which is practical and can reduce the conservatism of obtained result since the dwell time (DT) of the switching modes is independent of the triggering interval and the asynchronous phenomenon between system mode and controller mode is avoided. It is discovered that the switching has positive effects on the stability and the designed observer can estimate both the unknown states and sensor faults with arbitrary approximate bound. The effectiveness of the theoretical analysis is demonstrated through numerical simulations.

Intelligent fuzzy back-stepping observer design based induction motor robust nonlinear sensorless control

Introduction. The control algorithm of Induction Motor (IM) is massively dependent on its parameters; so, any variation in these parameters (especially in rotor resistance) gives unavoidably error propagates. To avoid this problem, researches give more than solution, they have proposed Variable Structure Control (VSC), adaptive observers such as Model Reference Adaptive System, Extended Luenberger Observer (ELO) and the Extended Kalman Filter (EKF), these solutions reduce the estimated errors in flux and speed. As novelty in this paper, the model speed observer uses the estimated currents and voltages as state variables; we develop this one by an error feedback corrector. The Indirect Rotor Field Oriented Control (IRFOC) uses the correct observed value of speed; in our research, we improve the observer’s labour by using back-stepping Sliding Mode (SM) control. Purpose. To generate the pulse-width modulation inverter pulses which reduce the error due of parameters variations in very fast way. Methods. We develop for reach this goal an exploration of two different linear observers used for a high performance VSC IM drive that is robust against speed and load torque variations. Firstly, we present a three levels inverter chosen to supply the IM; we present its modelling and method of control, ending by an experiment platform to show its output signal. A block diagram of IRFOC was presented; we analyse with mathematic equations the deferent stages of modelling, showed clearly the decoupling theory and the sensorless technique of control. The study described two kinds of observers, ELO and EKF, to estimate IM speed and torque. By the next of that, we optimize the step response using the fuzzy logic, which helps the system to generate the PI controller gains. Both of the two observers are forward by SM current controller, the convergence of SM-ELO and SM-EKF structures is guaranteed by minimizing the error between actual and observed currents to zero. Results. Several results are given to show the effectiveness of proposed schemes.

Output feedback containment fuzzy control for multi-agent systems with quantitative input and tunable reference signals

For multi-agent systems with quantitative input, we propose a novel containment control scheme to guarantee that the agents can enter a convex hull generated by the leader's signals after starting from any initial position. The problem with existing schemes is that the reference signals of the agents are affected by the communication topology such that the position of the reference signal cannot be changed when this communication topology is determined. To solve this problem, the proposed scheme can generate a flexible and adjustable reference signal for each agent. This has the advantage of reducing the probability of collisions among agents. Meanwhile, to address the situation where some agents cannot receive reference signals, we design an estimator to generate an adjustable estimation signal for each specific agent to ensure that all agents continue moving within the convex hull. In addition, by combining the fuzzy observer with the command filter design method, we devise a novel controller design scheme for quantitative input, which ensures that all signals in closed-loop multi-agent systems are uniformly and ultimately bounded. Finally, the simulation results demonstrate the feasibility and superiority of the proposed scheme for controlling multi-agent systems.

Robust fuzzy adaptive stabilization for uncertain nonlinear systems with quantized input and output constraints

In this paper, we study the problem of robust fuzzy adaptive output feedback stabilization for a class of nonlinear systems with quantized input and output constraints. The system under consideration has these characteristics: unknown state mismatch uncertainties and unknown disturbances, and unknown measurement noises. By employing the output filtering transformation, the fuzzy logic system (FLS) approximator, the backstepping, and the high gain observer technique, a non-fragile robust fuzzy adaptive observer and a hyperbolic tangent adaptive controller are presented to guarantee that the closed-loop system is ultimately uniformly bounded and the output is constricted in a prescribed performance curve. The effectiveness of the scheme is verified by numerical simulations.

Finite-time adaptive optimal control of uncertain strict-feedback nonlinear systems based on fuzzy observer and reinforcement learning

This paper proposes an adaptive optimal control strategy of finite-time control for high-order uncertain strict-feedback nonlinear systems. Firstly, a reinforcement learning (RL) based an optimal control scheme is employed to design a optimal controller, to achieve global optimisation. Additionally, considering the unmeasurable states, we construct a fuzzy observer and utilise fuzzy logic systems to approximate the unknown functions. Meanwhile, the inclusion of command filtering and time-based control simplifies the controller design and enhances the system's response rapidity. Finally, the effectiveness and feasibility of the proposed approach are validated through a numerical simulation and a single link-robot system simulation.

Observer-Based Adaptive Fuzzy Consensus Control of Nonlinear Multiagent Systems Encountering Deception Attacks

This paper investigates the fuzzy adaptive output- feedback consensus control problem for nonlinear multi-agent systems (MASs) with network communication encountering deception attacks. Fuzzy logic systems (FLSs) are used to approximate unknown nonlinear functions, and a novel fuzzy state observer is established to estimate the states of encountered deception attacks. For the case of unknown time-varying gains caused by deception attacks, a projection operator-based compensation mechanism is designed. Consequently, under the framework of adaptive backstepping, a novel adaptive fuzzy output- feedback consensus control method is proposed. The proposed control method can not only ensure that all signals remain bounded, but also make all followers maintain consensus with the trajectory of the leader. Finally, the simulation results are given to confirm the effectiveness of the proposed control scheme.

Event-triggered prescribed time adaptive fuzzy output-feedback control for nonlinear systems subject to bounded disturbances via command filtering

The issue of prescribed time adaptive fuzzy output-feedback event-triggered control strategy subject to bounded disturbances is considered in this paper. For the unmeasured states, an adaptive fuzzy observer is designed to estimate them. Then, a novel event-triggering condition involving a decreasing function containing the error between the system states is designed by synthesising the backstepping design framework and command filtered technique. The developed prescribed finite time control approach ensures that all signals of the closed-loop system are bounded and the tracking error remains within the predefined bound in the prescribed time. Meanwhile, Zeno phenomenon can be avoided. Finally, a mass-spring-damper system is taken as an example for simulation.

Security-based distributed fuzzy funnel cooperative control for uncertain nonlinear multi-agent systems against DoS attacks

This article focuses on the distributed funnel cooperative control of nonlinear multi-agent systems suffering denial-of-service (DoS) attacks, which aim to disrupt communication links between agents and can lead to discontinuities in system outputs. First, an actual measurement model of output signals is given, and a fuzzy switching observer is designed by utilizing the practical output model to obtain the unknown states. Second, a funnel-based tracking control strategy is presented by skillfully blinding the funnel function and backstepping technique to defend against DoS attacks. A crucial stability criterion is established by combining an improved average dwell time (ADT) approach and Lyapunov stability theory that integrates the constraints imposed by DoS attacks. In particular, based on an appropriate error transformation, the developed control law has a simpler structure than existing barrier function methods to solve performance constraints. It guarantees that the output of each follower agent yi is able to track the reference signal yd, and synchronization errors ϵi=∑s=1Mai,s(yi−ys)+bi(yi−yd) are consistently confined within a prearranged performance funnel Fϕ, (that is, (t,ϵi(t))∈Fϕ,∀t). Ultimately, a simulation example is presented to prove the validity of the established solution.

Observer-based preview control for T-S fuzzy systems

PurposeConsidering the unmeasurable states of the systems and the previewed reference signal, a novel fuzzy observer-based preview controller, which is a mixed controller of the fuzzy observer-based controller, fuzzy integrator and preview controller, is considered to address the tracking control problem.Design/methodology/approachThe authors employ an augmentation technique to construct an augmented error system for uncertain T-S fuzzy discrete-time systems with time-varying uncertainties. Additionally, the authors obtain the corresponding linear matrix inequality (LMI) conditions for designing the preview controller.FindingsThis paper discusses the preview tracking problem for nonlinear systems. First, considering the unmeasurable states of the systems and the previewed reference signal, a novel fuzzy observer-based preview controller, which is a mixed controller of the fuzzy observer-based controller, fuzzy integrator, and preview controller, is considered to address the tracking control problem. Then, using the fuzzy Lyapunov functional with the linear matrix inequality (LMI) technique, new sufficient conditions for the asymptotic stability of the augmented system are derived by applying the LMI technique. The preview controller and fuzzy observer can be designed in one step. Finally, a numerical example is used to illustrate the effectiveness of the results.Originality/valueAn augmented error system is successfully constructed by the state augmentation approach. A novel preview controller is designed to address the tracking control problem. The preview controller and fuzzy observer can be designed in one step.

Fuzzy observer design for sampled nonlinear systems with measurement uncertainty

AbstractIn this paper, novel fuzzy observers are designed for a class of nonlinear systems with sampled outputs and unknown measurement noises. Firstly, sufficient conditions are given to ensure that a sampled‐data nonlinear system is ultimately uniformly bounded (UUB). Secondly, an output filtering transformation is taken. Then, an augmented nonlinear system is obtained. The sampled output and the measurement noise are transformed into the state equation of the augmented nonlinear system. Thirdly, an augmented observer is constructed by applying a fuzzy logic system (FLS) to approximate the unknown measurement noise. Sufficient conditions are derived by using a suitable Lyapunov–Krasovskii generalized function, such that the observation error is UUB. Finally, the effectiveness of the proposed method is verified by a numerical simulation example.

Disturbance estimation-based resilient control design for interval type-2 fuzzy stochastic systems under multiple disturbance observer

This research endeavour's primary attention is on the problems of stabilization and multiple disturbance rejection for a class of interval type-2 fuzzy stochastic systems that are prone to parameter uncertainties and multiple disturbances. Specifically, the multiple disturbances are classified into two aspects: the first aspect is matched disturbances, which emanate from an exogenous system, while the second aspect is norm-bounded mismatched disturbances. Further, to provide a precise estimation of the matched disturbances, a fuzzy rule-based multiple disturbance observer is built. Based on the estimated information from the framed observer, a disturbance estimation-based resilient control is devised that can withstand the effects of disturbances. Besides, the footprints of mismatched kind of disturbances are handled by employing the ( Q , S , R ) − ς ~ dissipative performance. Moreover, to insure the attainment of the foremost objective of this analysis, a collection of suitable criteria has been developed by means of linear matrix inequalities with the satisfied disturbance attenuation index through Lyapunov's theory of stability. In addition, under the lighting of adequate conditions, the gain matrices of the configured controller and the framed observer can be determined. Finally, two simulation examples are supplied as a conclusion to the examination, each serving to illustrate the potency and viability of the designed control scheme and the presented theoretical findings.

Fixed-time fuzzy disturbance observer–based adaptive integral sliding-mode spacecraft attitude control under time-varying output constraints

This article proposes a fixed-time fuzzy disturbance observer–based adaptive integral sliding-mode spacecraft control scheme with consideration of input uncertainties and unknown nonlinearities. First, for the purpose of satisfying the time-varying output constraints and simplifying the computational process, an error transformation function is employed to convert the constrained spacecraft system into an unconstrained one. Second, to ensure superior transient-state performance, an improved sliding manifold integrated with a nonlinear function is designed. Then, for accurately estimating the external disturbances, a fixed-time fuzzy disturbance observer is proposed. Furthermore, the unknown nonlinearities and the input uncertainties are handled by several adaptive laws. The simulation results are presented to verify the superiority and effectiveness of the proposed fixed-time fuzzy disturbance observer–based adaptive integral sliding-mode control scheme.

Fuzzy Finite-Time ${H_\infty }$ Hybrid-Triggered Dynamic Positioning Control of Nonlinear Unmanned Marine Vehicles Under Cyber-Attacks

This paper studies the fuzzy finite-time <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> hybrid-triggered dynamic positioning (DP) control design issue of the nonlinear unmanned marine vehicles against cyber-attacks and ocean disturbances. The motion dynamics are firstly represented by the Takagi-Sugeno (T-S) fuzzy DP models. Secondly, for the purpose of obtaining the surge position, sway position, yaw angle and velocity of unmanned marine vehicles, a fuzzy state observer is proposed to estimate them. Then, a hybrid-triggered mechanism described by a Bernoulli variable is designed to save the communication resources. To overcome the impacts of cyber-attacks and ocean disturbances, a fuzzy <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> hybrid-triggered DP output feedback controller based on finite-time theory is developed. The stability criterions of the considered systems are formulated through establishing finite-time Lyapunov-Krasovskii functional. Finally, the simulation and comparison results validate the feasibility and superiority of the proposed scheme.

Adaptive Fuzzy Output Feedback Fault-Tolerant Control for Active Suspension Systems

In this paper, a novel adaptive fuzzy output feedback fault-tolerant control (FTC) method is proposed for active suspension systems. The quarter active suspension systems studied in this paper contains electromagnetic actuator faults and unavailable state variables, such as the velocity of active suspensions and the electric current intensity of electromagnetic actuators. First, the complex spring nonlinear dynamics are approximated by fuzzy logic systems (FLSs), and the unmeasurable states are estimated by a fuzzy state observer. Based on an adaptive backstepping technique along with specific Lyapunov functions, a novel adaptive fuzzy output feedback FTC design is presented. To eliminate the need for knowing efficiency indexes, a fault compensation strategy is also developed by utilizing parameter estimation technique. In the presence of electromagnetic actuator failure, all vertical vibration states of the active suspension system remain stabilized. Eventually, the feasibility of the proposed control algorithm is evaluated through random road surface and bump road surface tests.

Adaptive Fuzzy Tracking Control for Switched Nonlinear Systems Under FDI Attacks and Input Saturation: A Flexible Transient Performance Approach.

The present study proposes an adaptive fuzzy tracking control strategy for switched nonlinear systems, capable of effectively addressing false data injection (FDI) attacks and input saturation, while achieving flexible prescribed performance control as well as semi-global uniform ultimate boundness for the resultant system. Compared to the previous work, the provided control strategy exhibits two notable strengths: 1) it introduces a novel modified fixed-time pregiven performance function to effectively balance input saturation and output constraint and 2) the detrimental impacts resulting from FDI attacks are successfully mitigated by implementing the fuzzy logic systems approximation technique in the backstepping procedure. A set of switching fuzzy observers are established to estimate the unobservable states while a first-order differential filter is utilized to handle the complexity explosion problem. Finally, the mass-spring-damper system is given to substantiate the developed approach.

On Another Type of Convergence for Intuitionistic Fuzzy Observables

The convergence theorems play an important role in the theory of probability and statistics and in its application. In recent times, we studied three types of convergence of intuitionistic fuzzy observables, i.e., convergence in distribution, convergence in measure and almost everywhere convergence. In connection with this, some limit theorems, such as the central limit theorem, the weak law of large numbers, the Fisher–Tippet–Gnedenko theorem, the strong law of large numbers and its modification, have been proved. In 1997, B. Riečan studied an almost uniform convergence on D-posets, and he showed the connection between almost everywhere convergence in the Kolmogorov probability space and almost uniform convergence in D-posets. In 1999, M. Jurečková followed on from his research, and she proved the Egorov’s theorem for observables in MV-algebra using results from D-posets. Later, in 2017, the authors R. Bartková, B. Riečan and A. Tirpáková studied an almost uniform convergence and the Egorov’s theorem for fuzzy observables in the fuzzy quantum space. As the intuitionistic fuzzy sets introduced by K. T. Atanassov are an extension of the fuzzy sets introduced by L. Zadeh, it is interesting to study an almost uniform convergence on the family of the intuitionistic fuzzy sets. The aim of this contribution is to define an almost uniform convergence for intuitionistic fuzzy observables. We show the connection between the almost everywhere convergence and almost uniform convergence of a sequence of intuitionistic fuzzy observables, and we formulate a version of Egorov’s theorem for the case of intuitionistic fuzzy observables. We use the embedding of the intuitionistic fuzzy space into the suitable MV-algebra introduced by B. Riečan. We formulate the connection between the almost uniform convergence of functions of several intuitionistic fuzzy observables and almost uniform convergence of random variables in the Kolmogorov probability space too.

Advanced nonlinear fuzzy observer and robust control design for systems subject to cyber-physical attacks

Advanced nonlinear fuzzy observer and robust control design for systems subject to cyber-physical attacks

Event-triggered prescribed performance adaptive secure control for nonlinear cyber physical systems under denial-of-service attacks

For a class of nonlinear cyber physical systems (CPSs) under intermittent denial-of-service attacks (DoS), this paper investigates a novel adaptive security control scheme. A switched fuzzy observer is designed to estimate unmeasurable states. In addition, the relative threshold-based event-triggered approach is introduced to reduce the released data, and the dynamic surface control technique is used to remove the ‘explosion of terms’ problem. Meanwhile, an observer-based adaptive event-triggered prescribed performance controller is constructed, which ensures that all closed-loop signals remain bounded and system output approaches a designed performance bound within a predefined finite time. Simultaneously, the Zeno behavior can be thoroughly eliminated. Finally, a numerical simulation is used to demonstrate the validity of the results.