Fuzzy State Estimation Research Articles

Attack-resilient asynchronous state estimation of interval type-2 fuzzy systems under stochastic protocols

This article addresses the state estimator design issue of interval type-2 (IT2) fuzzy systems under deception attacks. The permission of sensors to access the network is determined by a stochastic protocol obeying Markov scheduling rules. An attack-resilient IT2 fuzzy state estimator is proposed to mitigate the adverse effect of deception attacks on estimation performance. By using the known bounds of system membership functions and introducing two new weighting functions, the MFs of fuzzy state estimator are reconstructed. A hidden Markov model is employed to describe the asynchronous behaviour of scheduling rules between the sensor and the estimator. Sufficient conditions are derived to ensure the ultimate boundedness of estimation error. Finally, a numerical example demonstrates the applicability of the proposed attack-resilient asynchronous state estimation method.

Adaptive fuzzy finite-time event-triggered formation control for unmanned surface vehicle systems

This paper studies the finite-time event-triggered fuzzy formation control problem for multiple unmanned surface vehicle (USV) system. The fuzzy state estimator is designed by intermittent output signal to estimate unmeasurable velocity and yaw velocity of the USV. The dual-channel event-triggered mechanisms (ETMs) are designed to reduce the updating times from sensor-to-actuator and controller-to-actuator channels, respectively. Based on the designed fuzzy state estimator and ETMs, a finite-time fuzzy adaptive output feedback formation control is formulated. It is proved that the controlled USV system is semi-global practically finite-time stable. Moreover, the outputs of the followers are able to track the output of the leader. Finally, the simulation and comparison results are provided to demonstrate the feasibility of the presented formation control algorithm.

Supervisory Control of Fuzzy Discrete Event Systems Under Partial Observation

Supervisory control of fuzzy discrete event systems under partial observation is investigated in the paper. Without loss of generality, we consider fuzzy discrete event systems with constraints where a fuzzy discrete event system is modeled by a fuzzy automaton. Sequences of events that can be generated by the system are regarded as constraints and are modeled by a crisp automaton. A supervisor is designed to control the fuzzy discrete event system so that the supervised system is prevented from entering a pre-specified set of illegal/unsafe fuzzy states. A necessary and sufficient condition for the existence of a supervisor is obtained. When the condition is satisfied, an online supervisor can be designed. Fuzzy state estimation problem is first solved, as the supervisor is fuzzy-state-estimate-based. A method is developed to estimate fuzzy state iteratively after observation of each new event. We show that the supervisor so developed ensures the safety of the system and is least restrictive among all possible safe supervisors. Potential of the theoretical results for real-world applications is illustrated through an example of HIV/AIDS treatment decision-making.

Finite-Time Dissipative Fuzzy State Estimation for Jump Systems With Mixed Cyber Attacks: A Probabilistic Event-Triggered Approach.

This article addresses the finite-time dissipative fuzzy state estimation for Markov jump systems under mixed cyber attacks. A probabilistic event-triggered mechanism (PETM) is proposed to reduce the unwanted network traffic by using the statistic information of network-induced delays. The dual asynchronizations characterized by asynchronous modes and mismatched premise variables are tackled simultaneously. Under the PETM, Takagi-Sugeno (T-S) fuzzy state estimators are first constructed based on the imperfect measurements subject to mixed cyber attacks and exogenous disturbances. Less conservative criteria relying on both fuzzy rules and jumping modes are established to achieve the strictly (Q,S,R) - ϑ -dissipative finite-time state estimation performance. Furthermore, a synthesis algorithm is derived to calculate the fuzzy state estimator gains by virtue of an improved matrix decoupling technique. Finally, two examples are utilized to validate the effectiveness and advantage of the proposed results.

Enhanced Fuzzy State Estimation of Discrete-Time Nonlinear Circuits via Two Relaxed Measures

This brief gives an enhanced result for fuzzy state estimation of discrete-time nonlinear circuits by developing two new technical measures of relaxations. Firstly, a novel balanced matrix method is proposed in which all the involved free matrices are with arbitrary variable orders, and thus a lot of freedom can be introduced into different switching modes for reducing the conservatism caused by existing those free matrices with fixed orders in the recent result. Secondly, an important property is employed in order to further relax the conservatism caused by the mismatch of adjacent normalized fuzzy weighting functions. Therefore, the scope of application of fuzzy state estimation can be enlarged by a large margin and much better estimation performance is obtained than before. Finally, the superiority of the developed approach is tested and verified based on the common benchmark example applied in the literature.

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.

Relaxed Conditions of Observer Design of Discrete-Time Takagi–Sugeno Fuzzy Systems via a New Multi-Instant Gain-Scheduling Scheme

A novel multi-instant gain-scheduling scheme is proposed in order to further improve the state estimation performance of discrete-time Takagi–Sugeno fuzzy systems in this article. Different from those existing methods, the enabled working pattern at each sampling instant can be determined in cycle according to utilization of the updated information of adjacent normalized fuzzy weighting functions in depth, and then the featured time-varying free matrices are introduced for each working pattern, which can remove those existing constraints on traditional free matrices. Consequently, the conservatism can be reduced significantly and it does broaden the range of application for observer-based fuzzy state estimation. Despite the fact that the quantity of the free matrices becomes much bigger than before, it needs to be pointed out that the actual computational complexity only increases by a small amount through depressing the number of cycles. Given that the developed designing process belongs to an offline computation, it is an acceptable tradeoff between the increasement of computational burdens and the reduction of conservatism. In the end, the effectiveness of the developed method is illustrated through the detailed analysis of numerical simulations.

Observer-Based Multi-Instant Fuzzy State Estimation of Discrete-Time Nonlinear Circuits via a New Slack Variables Technique

This brief investigates the problem of relaxed observer-based multi-instant fuzzy state estimation of discrete-time nonlinear circuits. In contrast with the recent result whose observer gain matrices may be too many to be applied in practice, there is only an unique group of observer gain matrices required in this study while the conservatism can be reduced markedly by developing a new slack variables technique. The proposed slack variables technique is constructed on the basis of multi-instant homogenous polynomials so that much more recessive algebraic properties of the normalized fuzzy weighting functions can be excavated in order to remove those redundant positive definite constraints which bring about conservatism. Especially, those previous slack variables techniques belong to special cases of ours. Finally, a benchmark example is given to validate the progressiveness of the developed result.

Formula omitted] fuzzy state estimation for delayed genetic regulatory networks with random gain fluctuations and reaction-diffusion

In this paper, the problem of H∞ state estimation for reaction-diffusion genetic regulatory networks under Dirichlet boundary conditions is investigated, where the random gain fluctuations and time-varying delays are taken into consideration. With regard to the existence of disturbance, the H∞ performance index is introduced to evaluate the capacity of resisting disturbance of the system. Furthermore, the fuzzy-model-based approach is adopted to deal with the nonlinearity of the aforementioned system. The primary objective of the study is to devise a fuzzy state estimator to approximate the concentrations of proteins and mRNAs, such that the states of the error system satisfying H∞ performance index converge to zero asymptotically. Afterwards, the stability conditions are deduced by virtue of the Lyapunov theory, and the estimator gains are obtained through an effective decoupling method. Ultimately, an example is provided to illustrate the feasibility and validity of the proposed method.

Adaptive disturbance observer-based event-triggered fuzzy control for nonlinear system

This paper investigates the issue of tracking control of nonlinear system with external disturbance, an event-triggered fuzzy backstepping sliding-mode control strategy is proposed. Firstly, a fuzzy state estimator is designed to estimate the unmeasurable state, and a sliding-mode disturbance observer is presented on the estimation error. In which, consider the conservativeness of the observer parameter, a parameter adaptation law with a double nested structure is proposed to mitigate chattering problems caused by parameter conservativeness. Then an event-triggered mechanism along with backstepping control and sliding-mode strategy is designed to achieve tracking control and save the network resources, and the Zeno phenomenon can be avoided. Furthermore, the backstepping law combines with Lyapunov theory is used to prove that the tracking error can converge to a small bounded set and all the signals of closed-loop plant are bounded. Finally, simulation results are carried out to illustrate the potential of designed approaches.

Fuzzy Finite Memory State Estimation for Electro-Hydraulic Active Suspension Systems

This paper presents a novel nonlinear estimator called the fuzzy finite memory (FFM) state estimator for electro-hydraulic active suspension systems, based on fuzzy techniques and finite impulse response. The Takagi-Sugeno fuzzy model is introduced to effectively describe highly nonlinear suspension systems with electro-hydraulic actuator dynamics. Compared with the conventional state estimator, which has an infinite memory structure and requires whole data from the initial to current time, the proposed fuzzy state estimator with a finite memory structure guarantees robustness against external disturbances and modeling uncertainty. The simulation results verify that the developed fuzzy finite memory state estimator is more robust under external disturbances and modeling uncertainties than the existing infinite impulse response nonlinear estimator.

Relaxed Multi-Instant Fuzzy State Estimation Design of Discrete-Time Nonlinear Systems and its Application: A Deep Division Approach

The problem of relaxed state estimation design of multi-instant fuzzy switching observer for discrete-time nonlinear systems is studied by proposing a deep division approach. Firstly,both the enhancement factor and the attenuation factor for each normalized fuzzy weighting function are for the first time introduced synchronously in order to derive much finer subdivisions of the whole spanning space constituted by all the normalized fuzzy weighting functions. Consequently, a more advanced ranking-based switching mechanism can be proposed over the previous results. Secondly, a new multi-instant fuzzy switching observer with different gain matrices for each finer subdivision is designed with the help of the given switching mechanism and thus much more freedom can be brought for reducing the conservatism of existing designs of fuzzy observers. More importantly, it is worth noting that the calculation of all the involved gain matrices belongs to a feasible off-line process. Finally, two simulation examples including tunnel diode circuits are provided to validate the progressiveness of the proposed deep division approach.

Distributed adaptive output consensus tracking of nonlinear multi-agent systems via state observer and command filtered backstepping

This paper investigates the adaptive fuzzy output consensus tracking control for nonlinear multi-agent systems in the presence of input saturation. The interaction among the agents is described by a directed graph. Firstly, a local fuzzy state estimator is proposed to reconstruct the unmeasured state of each agent. Then, a novel command filtered backstepping based distributed adaptive control law is designed, where theunknown nonlinear dynamics are approximated by using the fuzzy logic system. The proposed control law can guarantee that the output consensus tracking errors converge into a sufficiently small neighborhood of the origin and all signals in the closed-loop system are bounded although the input saturation exists. Simulation results show the effectiveness of the proposed design.

Hybrid Fuzzy Adaptive Fault-Tolerant Control for a Class of Uncertain Nonlinear Systems With Unmeasured States

In this paper, a hybrid adaptive output feedback fault-tolerant control is investigated for a class of uncertain nonlinear systems with unmeasured states. The generalized fuzzy hyperbolic model is used to approximate the unknown nonlinear functions, and the fuzzy state estimator (FSE) is established for estimating the unmeasured states. Based on the backstepping and dynamic surface control technique, a novel adaptive control method is proposed by introducing the prediction errors between FSE and serial–parallel estimation model. It is proved that all the variables of the closed-loop systems are semi-globally uniformly ultimately bounded by Lyapunov approach, and the tracking errors can converge to a small neighborhood. Two simulation examples are used to illustrate the effectiveness of the proposed control method.

State Estimate-Based Robust Adaptive Control of a Linked Mass-Spring System With Nonlinear Friction

This paper aims to develop a state estimate-based friction fuzzy modeling and robust adaptive control techniques for controlling a class of multiple degrees of freedom (MDOF) mechanical systems. A fuzzy state estimator is proposed to estimate the state variables for friction modeling. Under some conditions, it is shown that such a state estimator guarantees the uniformly ultimate boundedness (UUB) of the estimate error. Based on system input–output data and our proposed state estimator, a robust adaptive fuzzy output-feedback control scheme is presented to control multiple degrees of freedom system with friction. The adaptive fuzzy output-feedback controller can guarantee the uniformly ultimate boundedness of the tracking error of the closed-loop system. A typical mass-spring system is employed in our simulation studies. The results demonstrate that our proposed techniques in this paper have good potential in controlling nonlinear systems with uncertain friction.

Triangular and Trapezoidal Fuzzy State Estimation with Uncertainty on Measurements

In this paper, a new method for uncertainty analysis in fuzzy state estimation is proposed. The uncertainty is expressed in measurements. Uncertainties in measurements are modelled with different fuzzy membership functions (triangular and trapezoidal). To find the fuzzy distribution of any state variable, the problem is formulated as a constrained linear programming (LP) optimization. The viability of the proposed method would be verified with the ones obtained from the weighted least squares (WLS) and the fuzzy state estimation (FSE) in the 6-bus system and in the IEEE-14 and 30 bus system.

State Estimation over Customized Wireless Network

In this paper the state estimation techniques are investigated over customized wireless network for a continuous-time plant. It is assumed that the plant is connected to the controller over the proposed network. The feedback control over wireless networks includes limited bandwidth, time-varying and unknown delays with a high probability of data loss. Reasonably, some of these issues are deduced from the wireless networks structures. In order to deal with these problems the customized wireless network architecture is proposed for this Wireless Networked Control System (WNCS) and the problem of transmission delays and packet losses which induced by this scheme is studied. The time-varying delays of the TCP based shared network is estimated by fuzzy state estimation technique. Thereafter the kalman filtering is applied to address the problem of optimal filtering for this continuous-time plant with time-varying delays. The re-organized innovation analysis approach is applied to tackle the network induced time-varying delays. The simulation results show the applicability of the proposed approach.

An enhanced fuzzy H∞ estimator applied to low‐cost attitude‐heading reference system

PurposeThe purpose of this paper is to consider the process of design and implementation of an enhanced fuzzy H∞ (EFH∞) estimation algorithm to determine the attitude and heading angles of ground vehicles, which are frequently affected by considerable exogenous disturbances. To detect the changes of disturbances, a fuzzy system is designed based on expert knowledge and experiences of a navigation engineer. In the EFH∞ estimator, the intensity bounds of disturbances affecting the measurements are updated using a heuristic combination of three change‐detection indices. Performance of the proposed estimator is evaluated by Monte‐Carlo simulations and field tests of three kinds of vehicles using a manufactured attitude‐heading reference system (AHRS). In both simulations and real tests, the proposed estimator results in a superior performance compared to those of the recently developed and standard H∞ estimators.Design/methodology/approachDesign, implementation and real tests of the EFH∞ estimator are considered for an AHRS specialized for vehicular applications. In the AHRS, three‐axis accelerometers (TAA) and three‐axis magnetometers (TAM) may be affected by large disturbances due to non‐gravitational accelerations and local magnetic fields. Therefore, the design parameters of EFH∞ estimator including the theoretic bound of disturbance intensity and the attenuation level are adaptively tuned using a fuzzy combination of three change‐detection indices. Once a sensor is affected by an exogenous disturbance, the fuzzy system will increase the scale factor of the corresponding measurement disturbance to place more confidence on the data of the AHRS dynamics including measurements of gyros with respect to the data coming from the TAA and TAM.FindingsAn intelligent fault detector is proposed for considering changes of disturbances to adjust the upper bounds of the estimator's disturbances and the length of data to update the fuzzy system inputs. The EFH∞ estimator is suitable to attenuate the effects of disturbances changes on accurate estimation of the attitude and heading angles, intelligently.Originality/valueThe paper provides a fuzzy state estimator for adaptively adjusting the theoretic disturbance matrices according to the actual intensity of the disturbances affecting the AHRS dynamics and the measurement sensors.

Advanced control and management functionalities for multi‐microgrids

AbstractThis paper addresses the extension of the microgrid concept, following a massive integration of these active cells in power distribution networks, by adopting a coordinated management strategy together with distributed generation units directly connected to the medium voltage distribution network. In order to achieve this, a technical and commercial management scheme must be developed for coordinated control of a distribution system with multi‐microgrids, which should take into account the specific technical capabilities and characteristics of each type of generating source. In particular, tools for coordinated voltage support and frequency control, as well as for state estimation have been developed for this type of network. Concerning voltage support, a new methodology exploiting an optimization tool based on a meta‐heuristic approach was developed. For state estimation, two approaches were considered: multi‐microgrid state estimation and fuzzy state estimation. Regarding frequency control, the hierarchical structure of the multi‐microgrid is exploited to deal with the transition to islanded operation and load following in islanded operation. All these tools have proved to be efficient in managing the multi‐microgrid system in normal interconnected mode and, in case of the frequency control, in islanded operation. Copyright © 2010 John Wiley & Sons, Ltd.

A fuzzy state estimator based on uncertain measurements

A fuzzy linear state estimation model is employed, which is based on Tanaka’s fuzzy linear regression model, for modeling uncertainty in power system state estimation. The estimation process is based on uncertainty measurements as well as uncertainty parametric. The uncertain measurements and the parameters are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the estimated states. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the states, subject to double inequality constraints on each measurement. Linear programming technique is employed to obtain the middle and the symmetric spread for every state variable. The estimated middle corresponds to the value of the estimated state, while the symmetric spreads represent the tightest uncertainty interval around that estimated states. For illustrative purposes, the proposed formulation has been applied to various test systems such as, 4-bus, 6-bus, IEEE 30-bus, IEEE 39-bus, IEEE 57-bus and IEEE 118-bus. Furthermore, an assessment of the time convergence of the proposed method has been carried out to demonstrate the applicability of the proposed estimator as an on-line tool for estimating the uncertainty bounds in power system state estimation.