Fuzzy Observer Research Articles

Adaptive Fuzzy Output-Feedback Decentralized Control for Fractional-Order Nonlinear Large-Scale Systems

This article studies the adaptive fuzzy output-feedback decentralized control problem for the fractional-order nonlinear large-scale systems. Since the considered strict-feedback systems contain unknown nonlinear functions and unmeasurable states, the fuzzy-logic systems (FLSs) are used to model unknown fractional-order subsystems, and a fuzzy decentralized state observer is established to obtain the unavailable states. By introducing the dynamic surface control (DSC) design technique into the adaptive backstepping control algorithm and constructing the fractional-order Lyapunov functions, an adaptive fuzzy output-feedback decentralized control scheme is developed. It is proved that the decentralized controlled system is stable and that the tracking and observer errors are able to converge to a neighborhood of zero. A simulation example is given to confirm the validity of the proposed control scheme.

A Cyclic-Small-Gain-Based Adaptive Fuzzy Control of Interconnected Systems

This article investigates a novel adaptive fuzzy decentralized output-feedback control method for a class of uncertain large-scale interconnected nonlinear systems with unknown dynamics and immeasurable states. By employing fuzzy logic systems, the unknown nonlinear dynamics are estimated. Moreover, the immeasurable states are approximated by constructing a fuzzy decentralized state observer. Based on the Lyapunov stability theory and decentralized backstepping technique, the Lyapunov functions are constructed in a recursive way for each subsystem. In the last step of our process, an overall Lyapunov function is proposed to realize the control objective. Differing from other works, the interconnection influence of the large-scale system is compensated with a more relaxed assumption by introducing the cyclic-small-gain condition. Under the proposed control method, the closed-loop system is capable of being semiglobally uniformly ultimately bounded. Furthermore, the observer and stabilizing errors are able to be bounded by an arbitrarily small residual set around the origin. Finally, a simulation with comparison is provided to illustrate the viability of the presented control scheme.

Saturation-Tolerant Prescribed Control for a Class of MIMO Nonlinear Systems.

This article proposes a saturation-tolerant prescribed control (SPC) for a class of multiinput and multioutput (MIMO) nonlinear systems simultaneously considering user-specified performance, unmeasurable system states, and actuator faults. To simplify the control design and decrease the conservatism, tunnel prescribed performance (TPP) is proposed not only with concise form but also smaller overshoot performance. By introducing non-negative modified signals into TPP as saturation-tolerant prescribed performance (SPP), we propose SPC to guarantee tracking errors not to violate SPP constraints despite the existence of saturation and actuator faults. Namely, SPP possesses the ability of enlarging or recovering the performance boundaries flexibly when saturations occur or disappear with the help of these non-negative signals. A novel auxiliary system is then constructed for these signals, which bridges the associations between input saturation errors and performance constraints. Considering nonlinearities and uncertainties in systems, a fuzzy state observer is utilized to approximate the unmeasurable system states under saturations and unknown actuator faults. Dynamic surface control is employed to avoid tedious computations incurred by the backstepping procedures. Furthermore, the closed-loop state errors are guaranteed to a small neighborhood around the equilibrium in finite time and evolved within SPP constraints although input saturations and actuator faults occur. Finally, comparative simulations are presented to demonstrate the feasibility and effectiveness of the proposed control scheme.

Adaptive Fuzzy Output-Feedback Predefined-Time Control of Nonlinear Switched Systems With Admissible Edge-Dependent Average Dwell Time

This article investigates the adaptive fuzzy output-feedback predefined-time control of nonlinear switched systems with an admissible edge-dependent average dwell time. Different from most of the existing results on neural or fuzzy adaptive finite/fixed-time tracking control of switched systems, where the tracking error goes to a small neighborhood of the origin within finite time, the proposed one can ensure the output tracking error to reach user-defined accuracy within predefined time, which can be arbitrarily preassigned by the designers. Technically, based on the mode-dependent fuzzy state observer, an adaptive output-feedback predefined-time controller is constructed by incorporating a new state-scale transformation function into the barrier Lyapunov function, ensuring predefined transient behavior and tracking accuracy. Besides, by extending the adaptive control problem to the admissible edge-dependent average dwell time framework, the proposed adaptive control scheme can guarantee that all the closed-loop signals are bounded under switching signals with an admissible edge-dependent average dwell time property. It is less conservative than the average dwell time and mode-dependent average dwell time. Finally, two illustrative examples validate the performance of the method presented.

Dynamic Event-Triggered Antidisturbance Control for Flexible Spacecraft Systems

This study develops a dynamic event-triggered anti-disturbance (DETAD) controller to solve attitude control problem for flexible spacecraft systems with multiple disturbances. The disturbances involve two aspects: one belongs to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> space, and the other is described by an exogenous nonlinear system. Two sets of Takagi–Sugeno (T–S) fuzzy models are employed to model the flexible spacecraft systems and an exogenous nonlinear system, respectively. Moreover, a flexible vibration observer (FVO) is introduced to estimate the flexible modes. And a fuzzy disturbance observer (FDO) is designed to estimate the T–S fuzzy modeling disturbance in the case of the unmeasurable premise variables. By utilizing the estimations of two observers, a DETAD controller is constructed, where a dynamic event-triggered mechanism is implemented to reduce communication transmission. Additionally, new sufficient conditions for the closed-loop system to be asymptotically stable with strict dissipative performance are formed using linear matrix inequality techniques. Simulations are also provided to verify the advantages of the proposed scheme for flexible spacecraft systems subject to different types of disturbances.

Observer-Based Event-Triggered Adaptive Fuzzy Control for Fractional-Order Time-Varying Delayed MIMO Systems Against Actuator Faults

This article presents the observer-based event-triggered adaptive hybrid fuzzy dynamic surface control strategy for a category of uncertain nonstrict-feedback fractional-order nonlinear multi-input multi-output systems, including unknown time-varying delays and actuator faults. First, an adaptive hybrid fuzzy state observer and a serial-parallel estimation system are constructed to estimate the unmeasured system states and incorporate them into the control design scheme, respectively, where some appropriate fuzzy logic systems are introduced to approximate the unknown nonlinear functions. According to the dynamic surface control technique, the designed adaptive fuzzy control approach can surmount the deficiency of “complexity explosion.” Then, an observer-based adaptive event-triggered control algorithm is developed by constructing the Lyapunov–Krasovskii functionals and estimating the compounded disturbances. Furthermore, it is proved that under the drive of the reference signals, all the signals in the closed-loop system are semiglobally uniformly ultimately bounded and Zeno behavior can be successfully excluded. Finally, an example with numerical simulations is utilized to exhibit the applicability of the obtained observer-based event-triggered adaptive fuzzy control approach.

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.

Disturbance observer-based nonfragile fuzzy tracking control of a spacecraft

This paper deals with the nonfragile fuzzy tracking control technique of a spacecraft subject to external disturbances and control gain uncertainties. First, the Takagi–Sugeno (T–S) fuzzy model of the tracking error dynamics is newly derived. Unlike the existing studies, we assume that the controller output is norm bounded and its gain matrix is perturbed because of the aging of the actuator. Next, a fuzzy disturbance observer (DOB) estimating the external disturbance is constructed to enhance the robustness of the control system. Then, a fuzzy controller feeding back the estimated disturbance is designed to attenuate external disturbances. In addition, we establish the linear matrix inequality (LMI) conditions, by which both the H∞ disturbance attenuating performance and the asymptotic stabilization are guaranteed. From the solution to the LMI conditions, we obtain the controller and DOB gain matrices. Finally, a simulation example validates the disturbance estimation and tracking performance of the proposed method.

A prescribed time attitude control method based on thrust vector control (TVC) nozzle for solid propulsion satellite

With the development of on-orbit missions, solid propulsion technology is applied to the rapid orbital maneuver of satellites. During solid propulsion maneuver, the position change of the mass center caused by the fuel consumption and the installation error of thruster have brought serious attitude disturbances. For this problem, a novel prescribed time attitude control method is proposed in this paper. Firstly, a dynamics model of the solid propulsion micro-satellite is established, while the thrust direction is adjusted by the thrust vector control (TVC) nozzle. Then, a constraint boundary function is constructed to characterize the strict fixation of the thruster operating time and an adaptive fuzzy observer is developed to quickly estimate the lumped model uncertainties. Using the backstepping method, a novel prescribed time attitude control strategy regardless of initial conditions is designed. Simulation results show that the designed controller can achieve the prescribed time convergence of satellite attitude during solid propulsion orbital maneuver, effectively.

Adaptive finite‐time control of multi‐agent systems with partial state constraints and input saturation via event‐triggered strategy

AbstractThis paper focuses on the finite‐time control problem of multi‐agent systems with input saturation, unknown nonlinear dynamics, external disturbances and partial state constraints via output feedback. Fuzzy logic system and fuzzy state observer are introduced to approximate the uncertain nonlinearities and estimate the unmeasurable states, respectively. The partial state constraints are dealt with by using the barrier Lyapunov function, so that all states of the system do not exceed the preset boundary values. In order to reduce the computational complexity of the virtual controller and save communication resources, a first‐order filter and an event‐triggered mechanism are introduced, respectively. It is proved that the Zeno behavior does not occur via the proposed event‐triggered controller. By stability analysis, the finite‐time convergence of tracking error to a small neighborhood of the origin is proven. The effectiveness of the theoretical results is verified by examples.

Event-triggered fuzzy finite-time reliable control for dynamic positioning of nonlinear unmanned marine vehicles

This paper studies the fuzzy finite-time reliable dynamic positioning (DP) control for nonlinear unmanned marine vehicles. Firstly, the motion dynamics of nonlinear unmanned marine vehicles is modeled by the Takagi-Sugeno (T-S) fuzzy system. Secondly, a fuzzy state observer is designed to estimate the immeasurable position and velocity of unmanned marine vehicles. In order to decrease the frequency of data transmission of actuators and sensors, a dynamic event-triggered mechanism is presented based on unmanned marine vehicles information and the estimation error. Then, a fuzzy event-triggered reliable output feedback control method is presented by finite-time theory to tackle the actuator faults problem occurring in unmanned marine vehicles. The sufficient finite-time stable conditions in the form of LMIs are established via constructing finite-time Lyapunov-Krasovskii functional. Ultimately, the computer simulation results and comparisons with the existing control methods verify the advantages of the presented control method.

Distributed finite-time performance-prescribed time-varying formation control of autonomous surface vehicles with saturated inputs

This paper studies a time-varying formation control problem of a swarm of autonomous surface vehicles (ASVs) with prescribed constraints. Every ASV suffers from unavailable velocities, saturated inputs, internal uncertainties, and external disturbances. A distributed finite-time performance-prescribed time-varying formation control method is proposed for ASVs. Specifically, an adaptive fuzzy state observer (AFSO) is firstly proposed to recover the unavailable velocity by using saturated inputs and estimated disturbances from the fuzzy logic system. Secondly, a tunnel prescribed performance (TPP) function is designed to limit tracking errors with a concise form and smaller overshoot. At the kinematic level, with TPP-based error transformation, a C1 finite-time time-varying guidance law is proposed by using the smooth switch functions and recovered velocities. Next, a finite-time command filter based on Levant differentiator is presented to smooth the guidance signals. At the kinetic level, a C1 finite-time saturated control law is developed with the estimated velocities and disturbances. Then, it proves that tracking errors of the proposed closed-loop system converge into a small neighborhood around the equilibrium within finite time while evolving under TPP constraints regardless of saturated inputs. Finally, comparison results are provided to demonstrate the effectiveness of the proposed distributed finite-time performance-prescribed time-varying formation control method.

Finite-Time Dynamic Event-Triggered Fuzzy Output Fault-Tolerant Control for Interval Type-2 Fuzzy Systems

The finite-time dynamic event-triggered fuzzy output feedback fault-tolerant control problem is studied in this article for the interval type-2 (IT2) Takagi–Sugeno fuzzy system with parameter uncertainties and actuator faults. A fuzzy state observer is first developed to solve the immeasurable state problem. Second, by using the sampled estimating states and measured output signals, a dynamic event-triggered mechanism is formulated via integrating sensor-to-observer with observer-to-controller. Third, an observer-based finite-time event-triggered fuzzy fault-tolerant controller is synthesized via the nonparallel distribution compensation design principle. Consequently, the finite-time stable conditions of the addressed IT2 fuzzy system are established by constructing an appropriate Lyapunov function. Furthermore, an output feedback control design algorithm of solving control and observer gains is given in terms of the established sufficient finite-time stable conditions. Finally, a practical example of a nonlinear tunnel diode circuit system is provided to verify the effectiveness of the proposed IT2 fuzzy control scheme.

Stability analysis with general fuzzy measure: An application to social security organizations.

An effective method for evaluating the efficiency of peer decision-making units (DMUs) is data envelope analysis (DEA). In engineering sciences and real-world management problems, uncertainty in input and output data always exists. To achieve reliable results, uncertainties must be taken into account. In this research, a General Fuzzy (GF) approach is designed to cope with uncertainty in the presence of fuzzy observations for categorizing and specifying stability radius and alterations ranges of efficient and inefficient DMUs, which is applicable to real-world decision-making problems. For this purpose, a DEA sensitivity analysis model is presented, which will be modeled by fuzzy sets. Then, by applying the General Fuzzy (GF) approach, the fuzzy DEA sensitivity analysis model is transformed into the equivalent crisp form of fuzzy chance constraints according to specific confidence levels. Finally, a numerical example and a case study of branches of the social security organization are presented to illustrate sensitivity and stability analysis in the presence of fuzzy data. The obtained results provide the input and output changes of the evaluated units according to the attitude and preference of the decision maker with different confidence levels so that the data changes in the fuzzy environment do not change the units’ classification from efficient to inefficient and vice versa.

Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarization of the light

We investigate two aspects of the elementary example of POVMs on the Euclidean plane, namely their status as quantum observables and their role as quantizers in the integral quantization procedure. The compatibility of POVMs in the ensuing quantum formalism is discussed, and a Naimark dilation is found for the quantum operators. The relation with Toeplitz quantization is explained. A physical situation is discussed, where we describe the linear polarization of the light with the use of Stokes parameters. In particular, the case of sequential measurements in a real bidimensional Hilbert space is addressed. An interpretation of the Stokes parameters in the framework of unsharp or fuzzy observables is given. Finally, a necessary condition for the compatibility of two dichotomic fuzzy observables which provides a condition for the approximate joint measurement of two incompatible sharp observables is found.

Robust fuzzy observer‐based fault‐tolerant control: A homogeneous polynomial Lyapunov function approach

In this paper, a homogeneous polynomial Lyapunov function (HPLF) is employed in robust observer-based Integrated Fault-Tolerant Control (IFTC) of nonlinear systems modelled by the polynomial fuzzy model (PFM). This makes the design problem benefit from the conservative reduction property of polynomial Lyapunov functions (PLFs) and simultaneously avoid the emergence of non-convex terms due to differentiation of the polynomial Lyapunov matrix. As a result, the less conservative sum of square (SOS) conditions are obtained in the form of polynomial matrix inequalities (PMI), which are solved via SOSTOOLS. For the first time, a non-quadratic Lyapunov function is used to design a polynomial fuzzy unknown-input observer that estimates the system's states and actuator faults in the presence of model uncertainties and external disturbances. The effectiveness of the proposed approach in providing more relaxed and less conservative results along with the better fault tolerance is illustrated through three simulating examples and compared with the quadratic Lyapunov function (QLF) approach.

Fuzzy adaptive observer–based resilient formation control for heterogeneous multiple unmanned aerial vehicles with false data injection attacks and prescribed performance

This paper addresses the resilient formation control problem for heterogeneous multiple unmanned aerial vehicles (multi-UAV) under false data injection (FDI) attacks and prescribed performance constraints. The case of both actuator and sensor attacks is considered simultaneously, and the multi-UAV can exchange the information through a directed communication network. A fuzzy adaptive observer (FAO) is first proposed to estimate the FDI attacks and the unmeasurable velocity information for each UAV. In order to transform the formation control of heterogeneous multi-UAV into a trajectory tracking control problem of individual UAVs, a bank of distributed estimators is designed to achieve the leader’s states by only using local information among neighboring UAVs. Then, by incorporating a novel tracking error transform method and fractional-order sliding mode control technique, a resilient prescribed performance tracking controller without velocity measurements is constructed. Furthermore, it is proved that all signals of the closed-loop formation control systems are uniformly ultimately bounded (UUB) stable under FDI attacks. Finally, the simulation results are given to verify the effectiveness and superiority of the proposed control strategy.

Fault estimation and fault tolerant control for interval type-2 Takagi–Sugeno fuzzy systems via membership-function-dependent approach

This paper investigates the fault estimation (FE)-based fault tolerant control (FTC) technique to achieve the desired control performance for the nonlinear systems suffering from uncertainties, external disturbance and actuator faults using the interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy model. In this work, an IT2 fuzzy observer is built to simultaneously estimate both the system states and actuator faults, upon which a fault tolerant controller is proposed to guarantee the asymptotical stability of the closed-loop system with a prescribed H_{infty } performance level. Considering the bidirectional robustness interactions between the observer and FTC system, an integrated design technique is developed to address observer and FTC units together in one step to realize the required robustness within the whole closed-loop FTC system. By utilizing Lyapunov stability theory combined with the matrix inequality convexification techniques, a membership-function-dependent (MFD) FTC strategy is proposed where the information of membership functions is taken into account in the analysis for relaxation of the stability conditions. Additionally, to offer greater design flexibility and lower implementation cost to the fault tolerant controller, the imperfect premise matching (IPM) scheme is adopted, such that the premise membership functions of the fault tolerant controller can be chosen differently from those of IT2 fuzzy model. Finally, simulation results are provided to validate the effectiveness of the proposed FTC strategy.

Observer-Based Finite-Time Inverse Optimal Output Regulation for Uncertain Nonlinear Systems

This paper deals with the finite-time inverse optimal output regulation problem for a class of uncertain nonlinear systems that are subjected to an exosystem. The nonlinear systems not only contain external disturbances in the exosystem but also take the unknown nonlinear functions and unmeasured states into account. The output regulation problem is first converted into a stabilization problem through the internal model. Then, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. An auxiliary system is constructed and, based on the auxiliary system, a fuzzy state observer is designed to estimate the unmeasured states. Furthermore, a novel adaptive fuzzy finite-time inverse optimal output feedback controller and adaptive law are designed by combining backstepping technology, adaptive control technology, finite-time stability theory, and the inverse optimal control method. The control algorithm ensures that all the signals of the closed-loop system are semiglobally practical finite-time stable (SGPFS), so the newly well-defined cost function that is connected with the auxiliary system can be minimized. Finally, the validity of the approach is confirmed by virtue of the simulation results.

Reinforcement learning‐based optimized output feedback control of nonlinear strict‐feedback systems with event sampled states

SummaryThis article focuses on the event‐triggered optimized output feedback control problem for nonlinear strict‐feedback systems. First, a fuzzy state observer is designed to estimate the unmeasurable states. Then, the fuzzy‐based reinforcement learning is performed under critic‐actor architecture to realize the optimized control. In addition, a novel event‐triggered mechanism is developed for the system states to greatly economize communication resources. By means of the Lyapunov stability theory, it can be proved that all signals of the closed‐loop system are bounded, and the Zeno behavior can be successfully avoided. Lastly, an inverted pendulum example is provided to confirm the effectiveness of the derived algorithm.