Estimation Error System Research Articles

Reliable Finite‐Time Control for Nonlinear Chaotic Semi‐Markov Jump Systems With Incomplete Transition Rates

ABSTRACTThis article studies the finite‐time control problem for a class of nonlinear chaotic semi‐Markov jump systems with incomplete transition rates described by the T‐S fuzzy model approach. As a means to depict the dynamical properties pertaining to the examined system, parametric uncertainties, faults, external disturbances and input saturation are taken into consideration. The foremost objective of this study is to come up with a composite control mechanism that effectively rejects and attenuates the repercussions of faults and disturbances. In particular, we primarily built a disturbance observer in order to obtain a precise estimation of the external disturbances. After which, the fault diagnosis observer is designated to effectively estimate the faults. Specifically, a composite reliable control mechanism is developed by fusing the output of the constructed observers with the mode‐dependent fuzzy‐rule based state feedback controller. By employing suitable Lyapunov functions in conjunction with the linear matrix inequality technique, a set of mode‐dependent conditions is derived to ensure the finite‐time stochastic boundedness of the underlying closed‐loop and estimation error systems. Following this, the anticipated controller and observer gain matrices are elicited by resolving the established linear matrix inequalities. Thereafter, intending to ascertain the efficacy and usefulness of accrued theoretical findings, simulation results performed on Chua's circuit system is endowed.

Adaptive event-triggered stochastic estimator-based sampled-data fuzzy control for fractional-order permanent magnet synchronous generator-based wind energy systems

This study aims to develop an adaptive event-triggered estimation sampled-data control method for a fractional-order permanent magnet synchronous generator (PMSG)-based wind energy system (WES) using the Takagi–Sugeno (T–S) fuzzy approach. Unlike existing PMSG-based WES control schemes, we propose an aperiodic event-triggered communication scheme with an adaptive mechanism to reduce data transmission. To address the challenge of limited communication resources, we introduce an adaptive event-triggered (AET) estimation method with aperiodic sampling, significantly reducing communication overhead while maintaining stable WES performance. This method employs transmission techniques based on absolute errors, resulting in high data transmission efficiency. First, the fractional-order model for the PMSG-based WES is represented using linear sub-models through the T–S fuzzy approach. Next, a fuzzy aperiodic AET mechanism is proposed for the PMSG model with augmented estimation error systems. Then, the fractional Lyapunov function theory is employed to derive linear matrix inequalities (LMIs), ensuring bounded mean-square stability for the PMSG-based WES with the augmented estimation error systems. Additionally, the desired estimator control gains are determined through solvable LMIs. Finally, simulation studies are presented to demonstrate the superiority and feasibility of the proposed control scheme.

Secure virtual coupling control of connected train platoons under cyber attacks

Virtual coupling of automated trains has emerged as a promising technology to enhance the operational efficiency and line capacity of railway transportation systems. However, the vulnerability of such systems to malicious cyber attacks poses a significant threat to their stability, reliability and applicability. This article addresses the challenge of ensuring secure virtual coupling control of connected train platoons subject to various cyber attacks, including false data injection attacks, denial-of-service attacks, and replay attacks. First, based on the low-dimensional and noisy sensor measurements, novel set-valued observers are designed for each follower train to estimate their inaccessible full longitudinal motion states despite uncertainties and unknown attacks and noises. Then, distributed secure attack-compensation-based virtual coupling control laws are developed to ensure the platoon's stability and resilience against cyber attacks. Additionally, formal stability analysis of the resultant estimation error system and platoon tracking error system is provided. Furthermore, two algorithms are presented to elaborate the offline observer and controller design process as well as their online implementation. Finally, based on the data of a realistic urban rail transit line, simulation experiments are conducted to validate the efficacy of the proposed theoretical findings.

The Dynamic Event-Based Non-Fragile H∞ State Estimation for Discrete Nonlinear Systems with Dynamical Bias and Fading Measurement

The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused by unknown inputs is represented by a dynamic equation with bounded noise. Subsequently, the augmentation technique is employed and the dynamic event-triggered mechanism is introduced in the sensor-to-estimator channel to determine whether data should be transmitted or not, thereby conserving resources. Furthermore, an augmented state-dependent non-fragile state estimator is constructed considering gain perturbation of the estimator and fading measurements during network transmission. Sufficient conditions are provided based on Lyapunov stability and matrix analysis techniques to ensure exponential mean-square stability of the estimation error system while satisfying the H∞ disturbance fading level. The desired estimator gain matrix can be obtained by solving the linear matrix inequality (LMI). Finally, an example is presented to illustrate the effectiveness of the proposed method for designing estimators.

Fuzzy disturbance observer-based fuzzy swing suppression control of a ‘mooring-heavy lift crane-cargo’ coupled system

In this paper, an adaptive fuzzy disturbance observer (FDO)-based control is proposed for the swing suppression of the mooring-heavy lift crane (HLC)-cargo system in the presence of a wave disturbance. First, the dynamic model of the HLC system is determined by employing the Lagrangian method, and the wave force is modeled as an exosystem with unknown terms based on the Jonswap spectrum. Then, based on the HLC model and the wave force exosystem, an FDO is established to determine the wave disturbances, and a fuzzy approximator is developed to estimate the unknown terms. A novel disturbance estimation error observer is first developed to facilitate the parameter adaptive updating law. Subsequently, by augmenting the HLC system and disturbance estimation error system, an FDO-based fuzzy antiswing control method is proposed in terms of the linear matrix inequality technique to suppress the swing. The closed-loop system stability is examined by using the Lyapunov method. Finally, the effectiveness of the proposed method is validated by numerical simulation.

Mittag-Leffler function based security control for fractional-order complex network system subject to deception attacks via Observer-based AETS and its applications

The goal of this paper is to investigate the security control for uncertain fractional-order delayed complex network systems under deception attacks using the Mittag-Leffler function and observer-based adaptive event-triggered scheme (AETS) with the fractional commensurate order in q ∈ (0, 1). The adaptive event-triggering scheme is used during the data transmission process from the sensors to the observer, where the triggering threshold can be dynamically modified to reduce resource waste. We make a novel model for the estimation error system that takes into account both the effects of the adaptive event-triggered scheme and the effects of deception attacks. A sufficient condition is obtained to guarantee the stochastic mean-square stability of the augmented error system using the Mittag-Leffler (M-L) functions and the Lyapunov functional method and by using the singular value decomposition (SVD) and linear matrix inequality (LMI) techniques, the co-design problem of desired observer and controller gains is found, and it is shown that the solution ensures the stability of a closed-loop uncertain fractional-order complex networked system. At the end of this study, two numerical examples and diesel engine system model are given to show that the above findings are correct.

State estimation for proportional delayed complex-valued memristive neural networks

The paper addresses the issue of state estimation for a kind of complex-valued memristive neural networks (CVMNNs) accompanied by proportional delays, without applying regular split method of CVMNNs. By virtue of constructing pertinent Lyapunov functional (LF), and deploying matrix inequality techniques, various delay-dependent principles for scrutinizing the asymptotical stability of the estimation error system of the CVMNNs are constituted by linear matrix inequalities (LMIs) with CV variables. Examples are portrayed to manifest the validity and accuracy of the raised principles, and demonstrated applications in image security.

Distributed State Estimation for Mixed Delays System Over Sensor Networks With Multichannel Random Attacks and Markov Switching Topology.

This article deals with the distributed state estimation for mixed delays system under unknown attacks. A new multichannel random attack model is established for the first time, where network attacks are considered to exist in three channels: the target-to-sensor channel, the senor-to-sensor channel, and the sensor-to-estimator channel. In the above model, transmitted packets are allowed to be attacked multiple times simultaneously, and when they are successfully attacked, the transmitted information is modified. Besides, the topology of the sensor network is considered to change dynamically according to the Markov chain. Based on the newly established distributed estimation model, the estimation error system is proven to be asymptotically mean-square stable under a given H∞ antidisturbance index by using a Lyapunov theory and a stochastic analysis technique; then, the estimator parameter matrices are solved utilizing a linearization method. Finally, several simulation examples are listed to testify the effectiveness of the designed algorithm.

Moving horizon estimation for localization of mobile robots with measurement outliers

This paper investigates the moving horizon estimation (MHE) problem of mobile robots with measurement outliers. To deal with measurement outliers, the Euclidean distance of measurement error is introduced to detect and remove abnormal data. Then, we use dimension expansion methods to preprocess the data of heterogeneous sensors, such as UWB and IMU. An MHE-based method is proposed that deals with the localization of mobile robots with measurement outliers in the presence of bounded noise. An MHE-based estimator is obtained by solving a regularized least-squares problem. We analyze the convergence of the estimation error system using the properties of norm inequalities, and an upper bound is derived for the estimation error system by using norm inequality. Finally, simulation and experiment examples are given to verify the effectiveness and applicability of the proposed approach.

State Estimation for Recurrent Neural Networks With Intermittent Transmission.

This work addresses the state estimation problem for recurrent neural networks over capacity-constrained communication channels. The intermittent transmission protocol is used to reduce the communication load, where a stochastic variable with a given distribution is used to describe the transmission interval. A corresponding transmission interval-dependent estimator is designed, and an estimation error system based on it is also derived, whose mean-square stability is proved by constructing an interval-dependent function. By analyzing the performance in each transmission interval, sufficient conditions of the mean-square stability and the strict (Q,S,R) - γ -dissipativity are established for the estimation error system. Finally, the correctness and the superiority of the developed result are illustrated by a numerical example.

Secure state estimation for affine T-S fuzzy systems under sparse sensor attacks

This paper is concerned with the secure state estimation problem of affine T-S fuzzy systems under sparse sensor attacks. The objective is to construct a bank of fuzzy state estimators with an adaptive switching mechanism to ensure the attacked sensor measurements be isolated, and the estimation error system is asymptotic stable with a guaranteed H∞ performance. The case of unmeasurable plant premise variables is considered, which leads to the estimator implementation according to estimators’ state-space partitions may not be always synchronous with the plant. By constructing piecewise Lyapunov functions and employing the S-procedure and matrices decoupled techniques, the constructed state estimators synthesis conditions are derived in linear matrix inequalities (LMIs) form. Compared with existing methods, the proposed approach avoids restrictions on the structure of Lyapunov matrices and derives less conservative estimator design conditions. Finally, the effectiveness and superiorities of the proposed method is verified with a numerical example.

Dynamic event-triggered fault detection for multi time scale systems: Application to grid connected converters

This paper deals with the fault detection problem for multi time scale systems. To save network resources, a novel dynamic event-triggered protocol with more generality and higher flexibility of parameters is proposed. The main novelties are condensed as follows, firstly, a modified fault detection observer and a quadratic residual evaluation function are synthetically designed; secondly, the sufficient condition is proved to guarantee that the estimation error system is asymptotically stable and satisfies the specified H∞ performance index; finally, a Lyapunov function is designed to composite the multi time scale perturbation parameter and the influence of the dynamic event-triggered scheme. Finally, a practical experiment on a type of grid connected converters is given to verify the proposed approach.

Event‐triggered H∞$$ {H}_{\infty } $$ performance state estimation for neural networks with time‐varying delay

The issue of event‐triggered performance state estimation for neural networks with time‐varying delays is addressed in this paper. An innovative event‐triggered approach is presented, designed to strike a harmonious equilibrium between the state estimator's performance and the communication bandwidth of the network. The proposed approach captures the relationship between the time‐varying delay and system states by employing a delay derivative‐dependent integral inequality with matrices that account for delay derivatives. This novel formulation ensures the asymptotic stability of the estimation error system, thereby fulfilling the performance requirement. The desired event‐triggered estimators are then obtained through the use of linear matrix inequalities. The effectiveness of this approach is demonstrated through a numerical example.

Finite‐dimensional, output‐predictor‐based, adaptive observer for heat PDEs with sensor delay

SummaryWe are considering the problem of designing observers for heat partial differential equations (PDEs) that are subject to sensor delay and parameter uncertainty. In order to get finite‐dimensional observers, described by ordinary differential equations (ODE), we develop a design method based on the modal decomposition approach. The approach is extended so that both parameter uncertainty and sensor delay effects are compensated for. To cope more effectively with sensor delay, an output predictor is designed and the online provided output predictions are substituted to the future output values in the observer. To compensate for parameter uncertainty, we design a parameter estimator providing online parameter estimates, which are substituted to the unknown parameters in the observer. The parameter estimator design is made decoupled from the observer gain design by using an appropriate decoupling transformation. Using an analysis of the small‐gain‐theorem type, the whole (state and parameter) estimation error system is shown to be exponentially stable, under well‐defined conditions on the observer dimension, the sensor delay, and signal persistent excitation (PE).

Distributed State Estimation Under Jointly Connected Switching Networks: Continuous-Time Linear Systems and Discrete-Time Linear Systems

In this paper, we address the distributed state estimation problem for both continuous-time linear time-invariant (LTI) systems and discrete-time LTI systems under switching networks. The observed system is jointly observable, i.e., each agent can only access a part of the measurement output of the observed system and cannot recover the full state by itself. The full state estimation has to be achieved by network communication of neighboring agents. In contrast to existing works, the salient feature of this work is that the developed approach can deal with the jointly connected switching network and thus is more resilient to unreliable communication. First, we propose a new observability decomposition method for linear systems in modal canonical form. Then, we design distributed observers for both the continuous-time and the discrete-time system. Based on the common Lyapunov function approach, we show that the switched estimation error system is asymptotically stable and thus, the full state estimation can be achieved under jointly connected switching networks.

Estimator-based event-triggered output synchronization for heterogeneous multi-agent systems under denial-of-service attacks and actuator faults

This paper studies the output synchronization problem with an event-triggered communication scheme for a class of heterogeneous multi-agent systems under denial-of-service (DoS) attacks and actuator faults. DoS attacks may render the followers incapable of acquiring the leader's states and actuator faults may cause the actuators to not perform the control operation well. Comparing with the previous studies adopting the continuous communication mechanism, a novel switching estimator with an event-triggered communication strategy is designed to estimate the leader's states for each follower. By using the Lyapunov stability theory and the average dwell time method, sufficient conditions for the upper bound of the frequency of DoS attacks are derived. The estimation error system is proved to be exponentially stable. Besides, in order to compensate for actuator faults, a distributed adaptive fault-tolerant controller is proposed. The conditions for the stability of the output regulation error when the systems suffer from DoS attacks and actuator faults are given. A simulation example is proposed to prove the effectiveness of the main results.

Nonfragile state estimation for semi-Markovian switching CVNs with general uncertain transition rates: An event-triggered scheme

This paper tackles the problem of nonfragile state estimation for semi-Markovian switching complex-valued networks with time-varying delay. The concerned transition rates of the semi-Markov process are uncertain, including both the completely unknown ones and the inaccurately known ones with known bounds. To reduce the communication burden, a particular event-triggered generator is constructed, which depends on the latest available measurement output and a predefined positive threshold. Combining the stochastic analysis method with the Lyapunov stability theory, some less conservative criteria are obtained to ascertain the global asymptotic stability of the estimation error system in the mean-square sense. In addition, by solving some matrix inequalities, the desired nonfragile estimator gains are explicitly designed. Finally, a numerical example with simulations is given to illustrate effectiveness of the established estimation scheme.

Combined finite‐time state feedback for high‐speed train systems with time‐varying delays and disturbances

AbstractIn this paper, finite‐time state estimation and control problems are considered for high‐speed train systems. First of all, dynamic error systems of the high‐speed trains are modeled as nonlinear systems with time‐varying delays and disturbances. Secondly, finite‐time state estimators and finite‐time controllers are designed for dynamic error systems, a combined finite‐time state feedback structure is obtained. Then based on the Lyapunov stability theory and the finite‐time stability theory, finite‐time bounded conditions of high‐speed train dynamic error systems and estimation error systems are obtained. Finally, the feasibility of designed control method is proved by a example.

State estimation for discrete-time fractional-order neural networks with time-varying delays and uncertainties

In this paper, the state estimation issue for a class of discrete-time fractional-order neural networks (DFNNs) with time-varying delays and uncertainties is investigated. Based on the theoretical results of Mittag-Leffler function and Caputo fractional difference, a novel discrete-time inequality is established, which has generality compared with the previous results. By designing suitable estimator, exploiting Lyapunov method and combining inequality we establish, sufficient conditions ensuring the global asymptotical stability of estimation error system are obtained through linear matrix inequalities (LMIs). Moreover, we further discuss the case of DFNNs without uncertainties. In the end, numerical examples are utilized to validate availability of our theoretical results.

Exponentially finite-time dissipative discrete state estimator for delayed competitive neural networks via semi-discretization approach

This article is concerned with the investigation of finite-time boundedness and exponential (Q,S,R)-dissipative performance for a class of discretized competitive neural networks (CNNs) with time-varying delays. Initially, by employing the semi-discretization technique, a discrete analog of the continuous-time CNNs is formulated, which preserves the dynamical behaviors of their continuous-time counterpart. An appropriate state estimator is developed for the discretized CNNs so that the dynamics of the associated estimation error system attain finite-time exponential (Q,S,R)-dissipative performance. Further, to obtain a tighter summation bound, two novel weighted summation inequalities are proposed, which linearize the quadratic summable terms occurring in the finite difference of the considered Lyapunov–Krasovskii functional. Finally, to refine our prediction, an illustrative example is provided that demonstrates the sustainability and merits of the proposed method.