Robust Estimation Problem Research Articles

Dynamic event‐triggered fault estimation and accommodation for networked systems based on intermediate variable

AbstractIn this paper, the problem of robust fault estimation and fault‐tolerant control is considered for networked systems with external disturbances. By introducing an intermediate variable containing the system state information and fault information, the observer to accurately estimate the fault and system state is proposed. The gain matrices of fault estimation observer, fault‐tolerant controller and dynamic event‐triggered mechanism(ETM) are calculated simultaneously by solving a convex optimization problem. Compared with the existing results, the proposed fault estimation strategy does not match observer matching conditions. Furthermore, the introduction of dynamic ETM can effectively reduce the burden of the network with limited bandwidth resources. Finally, two simulation examples show the effectiveness of the proposed method.

A membership function-dependent L∞ performance based output interval estimation method for discrete-time Takagi–Sugeno fuzzy systems applied to fault detection

In the design process of traditional L∞ methods, a common performance index is often considered in different fuzzy rules. This may introduce a certain conservatism when most of the whole fuzzy system operates under a certain fuzzy rule or a few fuzzy rules. Therefore, this paper focuses on robust interval estimation problems for discrete-time Takagi–Sugeno fuzzy systems, and a new membership function-dependent L∞ performance index is proposed. The proposed L∞ performance can ensure better results in practical engineering applications by using the priori knowledge that the model works most of the time on some specific fuzzy systems to design performance index. By means of fuzzy basis-dependent Lyapunov functions, a membership function-dependent L∞ performance based interval estimation strategy applied to fault detection is presented. Through simulation analysis, the L∞ index in this paper is better than the conventional one and a tighter interval estimation is obtained leading to more accurate and faster fault detection effects. Meanwhile, the simulation results of this method also reflect the membership function-dependent property well.

Feasible operation region estimation of virtual power plant considering heterogeneity and uncertainty of distributed energy resources

The concept of the virtual power plant (VPP) has attracted extensive attention due to its distinguished capability of integrating various types of distributed energy resources (DERs). Defining the feasible operation region (FOR) is a crucial prerequisite for VPP's participation in the provision of power system services. However, considering the heterogeneity and uncertainty of DERs, it is always a challenging task to calculate the accurate FOR of VPP. In this paper, we propose a novel internal resource aggregation approach to estimate the FOR of VPP. The design of the proposed aggregation model consists of two stages. In the first stage, all the operational constraints of various DERs at the same node are expressed with a unified polytope form, and then these constraints are aggregated into one single polytope operation constraint by the computational geometry method. In the second stage, based on the aggregated polytope operation constraint at each node, combined with the dynamic line rating (DLR) and network constraints, a data-driven distributionally robust FOR estimation problem is formulated to determine the boundaries of the FOR. Numerical experiments have been conducted to validate the feasibility and superiority of the proposed approach and its applicability in handling multi-period FOR estimation.

Distributionally robust parameter estimation for nonlinear fed-batch switched time-delay system with moment constraints of uncertain measured output data

<p>In this paper, we investigated a nonlinear continuous-time switched time-delay (NCTSTD) system for glycerol fed-batch bioconversion to 1, 3-propanediol with unknown time-delay and system parameters. The measured output data was uncertain, while the first moment information about its distribution was available. Our goal was to identify these unknown quantities under the environment of uncertain measurement output data. A distributionally robust parameter estimation problem (i.e., a bi-level parameter estimation (BLPE) problem) subject to the NCTSTD system was presented, where the expectation of the discrepancy between the output of the NCTSTD system and the uncertain measured output data with respect to its probability distributions was included in the cost functional. By applying the duality theory, the BLPE problem was transformed into a single-level parameter estimation (SLPE) problem with non-smooth term approximated by a smoothing technique and its error analysis was given. Then, the gradients of the cost function of the SLPE problem were derived. A hybrid optimization algorithm was proposed for solving the SLPE problem. The paper concluded by presenting the simulation results.</p>

Intermediate observers based robust fault estimation for multi-agent systems under communication constraints via switching scheme

This paper addresses the problem of robust fault estimation for multi-agent systems (MASs) under communication constraints. Taking into account the possible data packet loss (DPL) in the information interaction of each subsystem, MASs are remodelled as switching systems by introducing a variable sampling strategy. Then, using the local information among agents, a novel intermediate observer design method based on switching scheme is proposed to estimate faults of MASs. Combining Lyapunov’s criterion and linear matrix inequality, sufficient conditions for the intermediate observer to be exponentially stable and have H ∞ performance against bounded disturbances and the DPL are given. Finally, some simulations are provided to verify the effectiveness of the proposed method.

STATE ESTIMATION FOR A CLASS OF FRACTIONAL-ORDER UNCERTAIN NONLINEAR SYSTEMS

The robust state estimation problem for a class of fractional-order uncertain non- linear systems is investigated in this paper. The class of fractional-order uncertain nonlinear systems is more general than the existing one in the literature. For the first time, a method based on a new fractional-order state observer is proposed to give robust state estimation of the fractional-order uncertain nonlinear systems. A new condition for the existence of the fractional-order observer in terms of an optimization problem is proposed. The effectiveness of the proposed method is demonstrated through two examples.

On scaling robust feedback control and state estimation problems in power networks

Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of scalability and sensitivity. In particular, Lyapunov-based approaches rely on forming semi-definite programs (SDPs) that are (i) not scalable and (ii) extremely sensitive to the choice of the bounding scalar that ensures the strict feasibility of the linear matrix inequalities (LMIs). This paper addresses these two issues by employing a celebrated non-Lyapunov approach (NLA) from the control theory literature. In lieu of linearized models of power grids, we focus on (the more representative) nonlinear differential algebraic equation (DAE) models and showcase the simplicity, scalability, and parameter-resiliency of NLA. For some power systems, the approach is nearly fifty times faster than solving SDPs via standard solvers with almost no impact on the performance. The case studies also demonstrate that NLA can be applied to more realistic scenarios in which (i) only partial state data is available and (ii) sparsity structures are imposed on the feedback gain. The paper also showcases that virtually no degradation in state estimation quality is experienced when applying NLA.

Robust fault estimation for T‐S fuzzy systems with intermittently sampled data based on finite information learning observer

SummaryIn this article, we study the problem of robust fault estimation for a class of T‐S fuzzy systems with time delays and external disturbances based on the finite information learning observer. The learning observer with intermittent sampling is constructed and the change rate of output estimation error is introduced to estimate the system fault effectively. At the same time, by introducing a generalized inverse matrix to the designed observer, a sufficient condition for the stability of the error estimation system is given by using fuzzy Lyapunov function, which not only solves the problem of system fault and external disturbance estimation, but also reduces the conservatism of the obtained conclusion. Finally, the results described by LMI are solved numerically and simulated to demonstrate the effectiveness of the proposed method.

Distributed Observer-Based Robust Fault Estimation Design for Discrete-Time Interconnected Systems With Disturbances.

This article focuses on the distributed robust fault estimation problem for a kind of discrete-time interconnected systems with input and output disturbances. For each subsystem, by letting the fault as a special state, an augmented system is constructed. Particularly, the dimensions of system matrices after augmentation are lower than some existing related results, which may help to reduce calculation amount, especially, for linear matrix inequality-based conditions. Then, a distributed fault estimation observer design scheme that utilizes the associated information among subsystems is presented to not only reconstruct faults, but also suppress disturbances in the sense of robust H∞ optimization. Besides, to improve the fault estimation performance, a common Lyapunov matrix-based multiconstrained design method is first given to solve the observer gain, which is further extended to the different Lyapunov matrices-based multiconstrained calculation method. Thus, the conservatism is reduced. Finally, simulation experiments are shown to verify the validity of our distributed fault estimation scheme.

Robust and scalable distributed recursive least squares

We consider a problem of robust estimation over a network in an errors-in-variables context. Each agent measures noisy samples of a local pair of signals related by a linear regression defined by a common unknown parameter, and the agents must cooperate to find the unknown parameter in presence of uncertainty affecting both the regressor and the regressand variables. We propose a recursive least squares estimation method providing global exponential convergence to the unknown parameter in absence of uncertainty, and robust stability of the estimate, formalized in terms of input-to-state stability, in presence of uncertainty affecting all the variables. The result relies on a cooperative excitation assumption that is proved to be strictly weaker than persistency of excitation of each local data set. The proposed estimator is validated on an adaptive road pricing application.

Distributed robust‐multivariate‐observer‐based FDI attacks estimation for nonlinear multi‐agent systems with directed graphs

AbstractThis article investigates the distributed robust estimation problem for false data injection (FDI) attacks in nonlinear multi‐agent systems with directed graphs. To approximate the realistic attack scenario, the case where both the actuator network channel and sensor network channel suffering from FDIs are considered, and the attack signals contain time‐varying circumstances. A novel distributed robust‐multivariate‐observer (DRMO) strategy is developed such that the online estimation of FDI attack dynamics can be realized with the partially unknown nonlinear dynamics, attack transient increments, and disturbances impact being eliminated. The designed DRMO scheme only depends on the received compromised/uncompromised measurement output information on the account that whole state information cannot be measured directly. Finally, two simulation examples, including a network of four one‐link flexible joint manipulator systems with comparisons to existing methods, are given to show the effectiveness of the proposed scheme.

Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss.

Under the influence of multiple types of noises, missing measurement, one-step measurement delay and packet loss, the robust Kalman estimation problem is studied for the multi-sensor descriptor system (MSDS) in this paper. Moreover, the established MSDS model describes uncertain-variance noises, multiplicative noises, time delay and packet loss phenomena. Different types of noises and packet loss make it more difficult to build the estimators of MSDS. Firstly, MSDS is transformed to the new system model by applying the singular value decomposition (SVD) method, augmented state and fictitious noise approach. Furthermore, the robust Kalman estimator is constructed for the newly deduced augmented system based on the min-max robust estimation principle and Kalman filter theory. In addition, the given estimator consists of four parts, which are the usual Kalman filter, predictor, smoother and white noise deconvolution estimator. Then, the robust fusion Kalman estimator is obtained for MSDS according to the relation of augmented state and the original system state. Simultaneously, the robustness is demonstrated for the actual Kalman estimator of MSDS by using the mathematical induction method and Lyapunov's equation. Furthermore, the error variance of the obtained Kalman estimator is guaranteed to the upper bound for all admissible uncertain noise variance. Finally, the simulation example of a circuit system is examined to illustrate the performance and effectiveness of the robust estimators.

Event-Triggered Robust Fusion Estimation for Multi-Sensor Time-Delay Systems with Packet Drops

This paper investigates the robust fusion estimation problem for multi-sensor systems with communication constraints, parameter uncertainty, d-step state delays, and deterministic control inputs. The multi-sensor system consists of a fusion center and some sensor nodes with computational capabilities, between which there are random packet drops. The state augmentation method is utilized to transform a time-delay system into a non-time-delay one. The robust state estimation algorithm is derived based on the sensitivity penalty for each sensor node to reduce the impact of modelling errors, and modelling errors here are not limited to a unique form, which implies that the fusion estimator applies to a wide range of situations. An event-triggered transmission strategy has been adopted to effectively alleviate the communication burden from the sensor node to the fusion center. Moreover, the fusion estimator handles packet drops arising from unreliable channels, and the corresponding pseudo-cross-covariance matrix is provided. Some conditions are given to ensure that the estimation error of the robust fusion estimator is uniformly bounded. Two sets of numerical simulations are provided to illustrate the effectiveness of the derived fusion estimator.

A diffusion strategy for robust distributed estimation based on streaming graph signals

The problem of robust distributed estimation over dynamic and streaming graph signals is investigated in this paper. Existing works related to distributed estimation over dynamic and streaming graph signals are mainly derived from the Mean-Square-Error criterion, and they are vulnerable to non-Gaussian noise. Therefore, a new kind of diffusion Mixture correntropy (d-MC) algorithm is developed to deal with the disadvantage in this paper. Incorporating the diffusion strategy and a novel cost function, the proposed algorithm could accurately estimate the graph filter parameter with the dynamic and streaming graph signals, and achieve desirable performance under both Gaussian and impulsive noise environment. Besides, the theoretical analysis results of mean and mean-square stability are derived. Simulations on various case studies indicate the desirable performance of proposed d-MC algorithm by comparing it to other benchmarks.

RegCloser: a robust regression approach to closing genome gaps

BackgroundClosing gaps in draft genomes leads to more complete and continuous genome assemblies. The ubiquitous genomic repeats are challenges to the existing gap-closing methods, based on either the k-mer representation by the de Bruijn graph or the overlap-layout-consensus paradigm. Besides, chimeric reads will cause erroneous k-mers in the former and false overlaps of reads in the latter.ResultsWe propose a novel local assembly approach to gap closing, called RegCloser. It represents read coordinates and their overlaps respectively by parameters and observations in a linear regression model. The optimal overlap is searched only in the restricted range consistent with insert sizes. Under this linear regression framework, the local DNA assembly becomes a robust parameter estimation problem. We solved the problem by a customized robust regression procedure that resists the influence of false overlaps by optimizing a convex global Huber loss function. The global optimum is obtained by iteratively solving the sparse system of linear equations. On both simulated and real datasets, RegCloser outperformed other popular methods in accurately resolving the copy number of tandem repeats, and achieved superior completeness and contiguity. Applying RegCloser to a plateau zokor draft genome that had been improved by long reads further increased contig N50 to 3-fold long. We also tested the robust regression approach on layout generation of long reads.ConclusionsRegCloser is a competitive gap-closing tool. The software is available at https://github.com/csh3/RegCloser. The robust regression approach has a prospect to be incorporated into the layout module of long read assemblers.

Robust State Estimation for T–S Fuzzy Markov Jump Systems

The problem of robust state estimation for a class of uncertain nonlinear systems with Markov jump is investigated. The uncertain nonlinear system under consideration is represented by the Takagi–Sugeno (T–S) fuzzy model because it is difficult to describe. Firstly, different from the traditional T–S fuzzy modeling method, the deviation of the linear system approaching a nonlinear system is considered, which is represented as a model error in system modeling. Secondly, through a robust state estimation method based on the sensitivity penalty, we develop a robust state estimator for linear subsystems, and the fuzzy robust state estimator is obtained by fuzzy rules. Thirdly, the stability and boundedness of the fuzzy robust state estimator are proved under the assumption conditions to ensure the reliability of the obtained estimator. Finally, some numerical examples are given to verify the effectiveness of the fuzzy robust state estimator.

A New Method of Fault Estimation Observer Design for T-S Fuzzy Singular Systems With Disturbances Using Dissipativity Theory

This brief dedicates to addressing the robust fault estimation (FE) problem for a class of T-S fuzzy singular systems (TSFSSs) subject to faults and disturbances. A dissipativity-based FE observer design scheme is proposed to realize fault reconstruction, by which the FE performance can be improved in contrast to the existing one. With the help of the Lyapunov approach, dissipativity theory and matrix transformation technique, a brand-new condition is established to ensure observation error dynamics to be strictly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\mathscr {Q}, \mathscr {U}, \mathscr {R})-\iota -$ </tex-math></inline-formula> dissipative. It is worth mentioning that different from some previous studies, our method can solve observer gains simultaneously in a strict linear matrix inequality (LMI) framework rather than determine some of them artificially. Moreover, to bring extra degrees of freedom, slack scalars and matrices are added in FE observer design. The superiority of our method is fully illustrated via simulations.

Robust integrated sequential covariance intersection fusion Kalman filters and their convergence and stability for networked sensor systems with five uncertainties

AbstractFor networked sensor systems (NSSs) with hard and soft sensors including five uncertainties, two universal approaches of solving the robust fusion estimation problems are presented. It includes an integrated sequential covariance intersection (SCI) fusion minimax robust Kalman filtering approach with cross‐covariance information and a generalized Lyapunov equation approach with four pairs of Lyapunov equations. Applying them, the robust local and SCI fused time‐varying and steady‐state Kalman filters are presented in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds. The equivalent batch SCI fusers are also presented. Their robustness and accuracy relations are proved, and the sensitivity of the SCI fuser with respect to the fused orders of sensors is analyzed. Applying the dynamic error system analysis method and the dynamic variance error system analysis method, a new convergence and absolute asymptotic stability theory of robust fusion Kalman filtering is presented. The classical Kalman filtering convergence and stability theory is developed. Compared with the original covariance intersection fuser, they significantly reduced the computational complexity and burden. Compared with the optimal and conservative SCI fusers, they significantly improved the robust accuracies. They are suitable to deal with asynchronous or random delayed data and are suitable for real‐time applications. A simulation applied to the two‐mass spring damper mechanical system shows their effectiveness.

Non-asymptotic and robust estimation for a class of nonlinear fractional-order systems

This paper aims to deal with the non-asymptotic and robust estimation problem for nonlinear fractional-order systems. The motivation starts with a physical system which develops into a group of system models including linear and nonlinear, commensurate and noncommensurate, integer-order and noninteger-order ones. Different from the existing modulating functions method, the proposed method breaks through the limitation of transforming the original system into the input–output differential equation, which makes the estimation for more types of systems possible. By introducing a new class of fractional order modulating functions, the state is exactly expressed by algebraic integral formulas without knowing the initial conditions of the studied system, despite the corrupting noises in the output measurement. Finally, it is illustrated in the simulation examples that the proposed estimator not only proves to be effective in the state estimation of noninteger-order systems, but also shows its advantages in that of integer-order systems compared to the high-gain observer.

Robust Estimation for Discrete-Time Markovian Jump Linear Systems in a Data Fusion Scenario

This paper considers the problem of robust recursive estimation for discrete-time Markovian jump linear systems in both weighted and probabilistic data fusion scenarios. The problem is stated in terms of the optimization of an appropriate quadratic functional in a data fusion scenario. The estimates presented here were developed based on systems with more than one measurement equation. Numerical examples are presented to verify the effectiveness of proposed algorithms.