Error Variance Constraints Research Articles

A variance-constrained method to encoding–decoding [formula omitted] state estimation for memristive neural networks with energy harvesting sensor

This paper considers the encoding–decoding-based H∞ state estimation issue under variance constraint for delayed memristive neural networks with energy harvesting sensor. In order to improve the transmission security, the encoding–decoding communication mechanism is introduced in the transmission channel, which can encode the transmitted data with limited bits. In addition, the energy level of the energy harvester is described by a random variable that obeys the specific probability distribution, in which the energy harvesting technology is used to provide the required energy and continuously maintain the operation of the sensor. The main objective is to present new encoding–decoding-based H∞ state estimation method such that, in the presence of time-delay and energy harvesting mechanism, the desirable H∞ performance requirement and the estimation error variance constraints are both ensured by providing some sufficient conditions. In the end, the feasibility of new encoding–decoding-based H∞ state estimation algorithm is demonstrated by a simulation experiment.

Variance-Constrained Filtering Fusion for Nonlinear Cyber-Physical Systems With the Denial-of-Service Attacks and Stochastic Communication Protocol

In this paper, a new filtering fusion problem is studied for nonlinear cyber-physical systems under error-variance constraints and denial-of-service attacks. To prevent data collision and reduce communication cost, the stochastic communication protocol is adopted in the sensor-to-filter channels to regulate the transmission order of sensors. Each sensor is allowed to enter the network according to the transmission priority decided by a set of independent and identically-distributed random variables. From the defenders' view, the occurrence of the denial-of-service attack is governed by the randomly Bernoulli-distributed sequence. At the local filtering stage, a set of variance-constrained local filters are designed where the upper bounds (on the filtering error covariances) are first acquired and later minimized by appropriately designing filter parameters. At the fusion stage, all local estimates and error covariances are combined to develop a variance-constrained fusion estimator under the federated fusion rule. Furthermore, the performance of the fusion estimator is examined by studying the boundedness of the fused error covariance. A simulation example is finally presented to demonstrate the effectiveness of the proposed fusion estimator.

Protocol-based variance-constrained distributed secure filtering with measurement censoring

In this article, the variance-constrained distributed secure filtering issue based on communication protocol is investigated for time-varying stochastic systems with measurement censoring and cyber attacks over wireless sensor networks. In order to accurately characterise the measurement censoring property of real instruments, a two-sided censoring model is introduced for each sensor node, where the actual measurement value can be obtained only when the pre-set condition is satisfied. The DoS attack, occurring in a random way, is considered on the sensor-to-filter channel. The try-once-discard (TOD) protocol is employed to reduce the transmitted data and alleviate the burdens of shared communication networks, such that only one sensor node is granted to transmit the measurement data at each time instant. By the aid of the Lyapunov stability theory and recursive linear matrix inequality (RLMI) method, the sufficient condition is acquired to guarantee that the desired secure filter under cyber attacks ensures certain performance index and the filtering error variance constraint over a finite horizon. Finally, an illustrative example is provided to exhibit the effectiveness of the designed filtering algorithm.

Variance‐constrained resilient H∞ filtering for mobile robot localization under dynamic event‐triggered communication mechanism

AbstractThis paper is concerned with the mobile robot localization problem subject to filter gain uncertainty under dynamic event‐triggered communication mechanism, and meanwhile, the H∞ filtering performance and the error variance constraint are guaranteed. For saving the sensor energy, a dynamic event‐triggered communication mechanism is introduced to manage the transmission of the measurement data from the sensor to the filter. To characterize the possible fluctuations of the desired filter gain, a resilient filter is constructed for the mobile robot localization. The aim of this paper is to find a solution to the mobile robot localization problem by designing a nonlinear resilient filter such that the filtering error dynamics satisfies both the H∞ performance requirement and the error variance constraint over a finite time horizon simultaneously. By resorting to the Lyapunov theory and the stochastic analysis technique, the sufficient conditions are established to guarantee that the error dynamic system satisfies both the H∞ performance requirement and the error variance constraint. Then, a recursive linear matrix inequality (RLMI) approach is employed to design the desired filter. Based on the proposed filter design scheme, the corresponding localization algorithm is presented. Finally, an experiment is conducted in the simulation environment to verify the effectiveness of the proposed localization algorithm.

Event-triggered H∞ state estimation for time-varying neural networks with variance-constraint and fading measurements

This paper addresses the event-triggered H∞ state estimation problem for a class of discrete recurrent neural networks subject to variance-constraint and fading measurements. The phenomena of fading measurements are described by introducing a set of mutually independent random variables, which reflect that each sensor has individual missing probability. In addition, for the purpose of energy saving, an event-triggered H∞ state estimation scheme is used for time-varying neural networks to determine whether the measurement output is transmitted to the estimator or not. Some sufficient conditions are obtained to guarantee that the estimation error system satisfies both estimation error variance constraint and prescribed H∞ performance requirement. Finally, the feasibility of the proposed event-triggered H∞ state estimation method is verified by a numerical example.

Reconstruction of a directed acyclic graph with intervention.

Identification of causal relations among variables is central to many scientific investigations, as in regulatory network analysis of gene interactions and brain network analysis of effective connectivity of causal relations between regions of interest. Statistically, causal relations are often modeled by a directed acyclic graph (DAG), and hence that reconstruction of a DAG's structure leads to the discovery of causal relations. Yet, reconstruction of a DAG's structure from observational data is impossible because a DAG Gaussian model is usually not identifiable with unequal error variances. In this article, we reconstruct a DAG's structure with the help of interventional data. Particularly, we construct a constrained likelihood to regularize intervention in addition to adjacency matrices to identify a DAG's structure, subject to an error variance constraint to further reinforce the model identifiability. Theoretically, we show that the proposed constrained likelihood leads to identifiable models, thus correct reconstruction of a DAG's structure through parameter estimation even with unequal error variances. Computationally, we design efficient algorithms for the proposed method. In simulations, we show that the proposed method enables to produce a higher accuracy of reconstruction with the help of interventional observations.

Variance-constrained resilient H_{infty } state estimation for time-varying neural networks with randomly varying nonlinearities and missing measurements

This paper addresses the resilient H_{infty } state estimation problem under variance constraint for discrete uncertain time-varying recurrent neural networks with randomly varying nonlinearities and missing measurements. The phenomena of missing measurements and randomly varying nonlinearities are described by introducing some Bernoulli distributed random variables, in which the occurrence probabilities are known a priori. Besides, the multiplicative noise is employed to characterize the estimator gain perturbation. Our main purpose is to design a time-varying state estimator such that, for all missing measurements, randomly varying nonlinearities and estimator gain perturbation, both the estimation error variance constraint and the prescribed H_{infty } performance requirement are met simultaneously by providing some sufficient criteria. Finally, the feasibility of the proposed variance-constrained resilient H_{infty } state estimation method is verified by some simulations.

Variance-Constrained Recursive State Estimation for Time-Varying Complex Networks With Quantized Measurements and Uncertain Inner Coupling.

In this paper, a new recursive state estimation problem is discussed for a class of discrete time-varying stochastic complex networks with uncertain inner coupling and signal quantization under the error-variance constraints. The coupling strengths are allowed to be varying within certain intervals, and the measurement signals are subject to the quantization effects before being transmitted to the remote estimator. The focus of the conducted topic is on the design of a variance-constrained state estimation algorithm with the aim to ensure a locally minimized upper bound on the estimation error covariance at every sampling instant. Furthermore, the boundedness of the resulting estimation error is analyzed, and a sufficient criterion is established to ensure the desired exponential boundedness of the state estimation error in the mean square sense. Finally, some simulations are proposed with comparisons to illustrate the validity of the newly developed variance-constrained estimation method.

Variance-constrained H∞ state estimation for time-varying multi-rate systems with redundant channels: The finite-horizon case

This paper deals with the H∞ state estimation problem for a class of networked multi-rate time-varying systems with estimation error variance constraint. The redundant channel transmission scheme is employed to reduce the packet dropout rate and improve the quality of the data delivery. By utilizing the lifting technique, an augmented estimation error system is established with a uniform sampling rate. The objective of this paper is to design a time-varying state estimator such that, in the simultaneous presence of the asynchronous sampling, probabilistic packet dropouts as well as stochastic noises, the error dynamics of the state estimation satisfies both the prescribed H∞ performance requirement and the prescribed estimation error variance constraints. Through intensive stochastic analysis, sufficient conditions are established to ensure the existence of the desired estimator whose parameters are determined by solving a set of recursive linear matrix inequalities. A numerical example is presented to show the validity of the proposed estimation strategy.

Resilient State Estimation for 2-D Time-Varying Systems With Redundant Channels: A Variance-Constrained Approach.

This paper investigates the state estimation problem for a class of 2-D time-varying systems with error variance constraints, where the implemented estimator gain is subject to stochastic perturbations. Redundant channels are utilized as a protocol to strengthen the transmission reliability and the channels' packet dropout rates are described by mutually uncorrelated Bernoulli distributions. The objective of the addressed problem is to design a resilient estimator such that an upper bound on the estimation error variance is first guaranteed and then minimized at each time step, where the considered gain perturbations are characterized by their statistical properties. By employing the induction method and the variance-constrained approach, an upper bound on the estimation error variance is first constructed by means of the solutions to two Riccati-like difference equations and, subsequently, a locally minimal upper bound is achieved by appropriately designing the gain parameter. Then, an effective algorithm is proposed for designing the desired estimator, which is in a recursive form suitable for online applications. Finally, a numerical simulation is provided to demonstrate the usefulness of the proposed estimation scheme.

Event-Based Variance-Constrained ${\mathcal {H}}_{\infty }$ Filtering for Stochastic Parameter Systems Over Sensor Networks With Successive Missing Measurements.

This paper is concerned with the distributed filtering problem for a class of discrete time-varying stochastic parameter systems with error variance constraints over a sensor network where the sensor outputs are subject to successive missing measurements. The phenomenon of the successive missing measurements for each sensor is modeled via a sequence of mutually independent random variables obeying the Bernoulli binary distribution law. To reduce the frequency of unnecessary data transmission and alleviate the communication burden, an event-triggered mechanism is introduced for the sensor node such that only some vitally important data is transmitted to its neighboring sensors when specific events occur. The objective of the problem addressed is to design a time-varying filter such that both the requirements and the variance constraints are guaranteed over a given finite-horizon against the random parameter matrices, successive missing measurements, and stochastic noises. By recurring to stochastic analysis techniques, sufficient conditions are established to ensure the existence of the time-varying filters whose gain matrices are then explicitly characterized in term of the solutions to a series of recursive matrix inequalities. A numerical simulation example is provided to illustrate the effectiveness of the developed event-triggered distributed filter design strategy.

Robust filtering for a class of nonlinear stochastic systems with probability constraints

This paper is concerned with the probability-constrained filtering problem for a class of time-varying nonlinear stochastic systems with estimation error variance constraint. The stochastic nonlinearity considered is quite general that is capable of describing several well-studied stochastic nonlinear systems. The second-order statistics of the noise sequence are unknown but belong to certain known convex set. The purpose of this paper is to design a filter guaranteeing a minimized upper-bound on the estimation error variance. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time. Then, under the probability constraints, a minimax estimation problem is proposed for determining the suboptimal filter structure that minimizes the worst-case performance on the estimation error variance with respect to the uncertain second-order statistics. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed method.

Error variance-constrained ℋ∞ filtering for a class of nonlinear stochastic systems with degraded measurements: the finite horizon case

This article is concerned with the robust ℋ∞ filtering problem for a class of time-varying nonlinear stochastic systems with error variance constraint. The stochastic nonlinearities considered are quite general, which contain several well-studied stochastic nonlinear systems as special cases. The purpose of the filtering problem is to design a filter which is capable of achieving the pre-specified ℋ∞ performance and meanwhile guaranteeing a minimised upper-bounded on the filtering error variance. By means of the adjoint system method, a necessary and sufficient condition for satisfying the ℋ∞ constraint is first given, expressed as a forward Riccati-like difference equation. Then an upper-bound on the variance of filtering error system is given, guaranteeing the error variance is not more than a certain value at each sampling instant. The existence condition for the desired filter is established, in terms of the feasibility of a set of difference Riccati-like equations, which can be solved forward in time, hence is suitable for online computation. A numerical example is presented finally to show the effectiveness and applicability of the proposed method.

분산 제약을 갖는 비선형 시스템의 최적 퍼지 필터

본 논문에서는 추정 분산 제약을 갖는 비선형 이산시간에 대한 최적의 퍼지 필터에 대한 내용을 다루고자 한다. 필터를 설계할 때, 추정오차의 분산값은 필터의 성능이 결정하는 변수중 하나다. 이런 분산값에 더욱 강인한 필터를 설계하고자, 분산 제약 조건을 주어 필터를 설계하고자 한다. 먼저, 비선형 모델을 Tagaki-Sugeno 퍼지 모델을 이용하여 선형 모델로 변형한 후, 이 모델을 기반으로 선형 필터를 디자인한다. 이때 필터설계 과정 중 필터의 각 파라미터값을 구하기 위해 상태 추정오차 값은 평균제곱에 제한되며, 상태오차의 정상상태 분산값은 각각의 미리 정한 상한 제한 값 보다 작은 조건에서 필터를 설계하여 선형행렬부등식과 대수 이차 행렬부등식을 이용하여 파라미터값을 구한다. 이렇게 설계된 퍼지 필터는 트럭트레일러 시뮬레이션을 통해 설계 과정과 성능을 보여준다. In this paper, we consider the optimal fuzzy filter of nonlinear discrete-time with estimation error variance constraint. First, the Takagi and Sugeno(T-S) fuzzy model is employed to approximate the nonlinear system. Next, the error state is mean square bounded, and the steady state variance of the estimation error of each state is not more than the individual predefined value. It is shown that, the addressed problem can be carried out by solving linear matrix inequality(LMI) and some algebraic quadratic matrix inequalities. Finally, some examples are provided to illustrate the design procedure and expected performance through simulations.

Variance-Constrained ${\cal H}_{\infty}$ Filtering for a Class of Nonlinear Time-Varying Systems With Multiple Missing Measurements: The Finite-Horizon Case

This paper is concerned with the robust H ∞ finite-horizon filtering problem for a class of uncertain nonlinear discrete time-varying stochastic systems with multiple missing measurements and error variance constraints. All the system parameters are time-varying and the uncertainty enters into the state matrix. The measurement missing phenomenon occurs in a random way, and the missing probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval . The stochastic nonlinearities under consideration here are described by statistical means which can cover several classes of well-studied nonlinearities. Sufficient conditions are derived for a finite-horizon filter to satisfy both the estimation error variance constraints and the prescribed H ∞ performance requirement. These conditions are expressed in terms of the feasibility of a series of recursive linear matrix inequalities (RLMIs). Simulation results demonstrate the effectiveness of the developed filter design scheme.

Robust H/sub /spl infin// filter design with variance constraints and parabolic pole assignment

In this letter, we consider a multiobjective filtering problem for uncertain linear continuous time-invariant systems subject to error variance constraints. A linear filter is used to estimate a linear combination of the system states. The problem addressed is the design of a filter such that, for all admissible parameter uncertainties, the following three objectives are simultaneously achieved: 1) the filtering process is P-stable, i.e., the poles of the filtering matrix are located inside a parabolic region; 2) the steady-state variance of the estimation error of each state is not more than the individual prespecified value; and 3) the transfer function from exogenous noise inputs to error state outputs meets the prespecified H/sub /spl infin// norm upper-bound constraint. An effective algebraic matrix inequality approach is developed to derive both the existence conditions and the explicit expression of the desired filters. An illustrative example is used to demonstrate the usefulness of the proposed design approach.

Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty

The robust H ∞ filtering problem with error variance constraints is considered for discrete time-varying systems subject to norm-bounded parameter uncertainties in both the state and the output matrices of the state–space model. Sufficient conditions for a finite-horizon filter to satisfy state estimation error variance constraints as well as prescribed H ∞ performance for all admissible perturbations are given in terms of two discrete Riccati difference equations, which are of a form suitable for recursive computation. The results are extended to cover the case of stationary filtering over an infinite-horizon for uncertain time-invariant systems.

Distance and prediction error variance constraints for ARMA model portfolios

Poskitt and Tremayne 74 (1987) present a posterior odds ratio ( R ) portfolio selection strategy for ARMA models. This paper makes the range of prediction error variances that are implicit in R more explicit. Model closeness is quantified using a distance function in a Hilbert space. The relationship between distance and the posterior odds ratio is demonstrated. This provides a distance interpretation of the posterior odds ratio. The distance function also makes it possible to develop a prediction error variance (p.e.v.) criterion for identifying models to include in an ARMA model portfolio. A simulation experiment shows that the p.e.v. criterion provides forecasters with both a measure for assessing the likelihood that the models in an ARMA model portfolio yield practically equivalent forecasts, and a measure for assessing the usefulness of alternative criteria for identifying the order of an ARMA model.

Robust filtering for bilinear uncertain stochastic discrete-time systems

This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic system is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prespecified value. It is shown that the design of the robust filters can be carried out by solving some algebraic quadratic matrix inequalities. In particular, we establish both the existence conditions and the explicit expression of desired robust filters. A numerical example is included to show the applicability of the present method.

Robust state estimation for perturbed systems with error variance and circular pole constraints: The discrete-time case

This paper is concerned with the problem of robust state estimation for linear perturbed discrete-time systems with error variance and circular pole constraints. The goal of this problem addressed is the design of a linear state estimator such that, for all admissible uncertainties in both state and output equations, the following two performance requirements are simultaneously satisfied: (1) the poles of the filtering matrix are all constrained to lie inside a prespecified circular region; and (2) the steady-state variance of the estimation error for each state is not more than the individual prespecified value. It is shown that this problem can be converted to an auxiliary matrix assignment problem and solved by using an algebraic matrix equation/inequality approach. Specifically, the conditions for the existence of desired estimators are obtained and the explicit expression of these estimators is also derived. The main results are then extended to the case when an H performance requirement is added. Finally, a numerical example is presented to demonstrate the significance of the proposed technique.