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In this paper, we propose a novel moving horizon estimation algorithm for discrete-time linear systems with a limited number of measurements. Motivated by the idea of the back-and-forth nudging algorithm, we design the back-and-forth nudging in time moving-horizon estimation method by deploying two moving horizon estimators that move backward and forward iteratively. Based on a finite number of measurements, the proposed algorithm can be used for moving-horizon state estimation with guaranteed convergence. By using the proposed method, we show that the norm of the state estimation error is upper bounded by a sequence that converges to its steady-state in finite-time (i.e., using a finite number of measurements), provided that suitable parameters are selected. The unbiasedness properties and comparison results with the conventional (forward-in-time) moving horizon estimation are discussed. The effectiveness of the proposed approach is validated through a numerical example. [ABSTRACT FROM AUTHOR]

The topology identification of sparse networks is crucial for network modeling in many fields. The variational Bayesian inference has been proved to be effective for solving this issue. However, since all the observed data are used to compute the posterior distributions of the global variables at each iteration of the classical variational inference, the computation complexity is too high to be suitable for large data sets, especially for large-scale networks, where more data is needed for the inference. In this paper, we derive an efficient algorithm to maximize a lower bound function in the Bayesian inference based on stochastic optimization, where only a part of data is used at each iteration. Compared with the traditional variational Bayesian inference approach, the proposed method can significantly decrease the computation so that it is more suitable for the network identification with large data sets. Several typical sparse networks are used to test the performance of the proposed method, and the results demonstrate its merits. [ABSTRACT FROM AUTHOR]

This paper develops a variational Bayesian approach for identifying ARX models with missing observations and varying time-delays. The outputs of the ARX models are subject to both slow sampling rates and communication delays. The unknown missing observations which are used in the variational Bayesian approach can be estimated by a modified Kalman filter, and based on the estimated missing observations and available data, the unknown parameters and the varying time-delays can be estimated by using the variational Bayesian approach. The simulation results demonstrate that the variational Bayesian method is effective. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution of higher order moment stability region for Markov jump systems with respect to cases of both known and unknown transition probabilities. By exploring the cumulant generating function, the original stochastic system with Markov jumping modes is transformed to a deterministic system. Then based on the estimation of matrix eigenvalues, the explicit solution for higher order moment stability region is expressed in terms of transition probabilities, operation modes, state transition matrix and its dimension, and the moment order. Several examples are presented to illustrate the effectiveness of the proposed method and its associated algorithm. [ABSTRACT FROM AUTHOR]

The finite impulse response (FIR) filter and infinite impulse response filter including the Kalman filter (KF) are generally considered as two different types of state estimation methods. In this paper, the sequential Bayesian philosophy is extended to a filter design using a fixed amount of most recent measurements, with the aim of exploiting the FIR structure and unifying some basic FIR filters with the KF. Specifically, the conditional mean and covariance of the posterior probability density functions are first derived to show the FIR counterpart of the KF. To remove the dependence on initial states, the corresponding likelihood is further maximized and realized iteratively. It shows that the maximum likelihood modification unifies the existing unbiased FIR filters by tuning a weighting matrix. Moreover, it converges to the Kalman estimate with the increase of horizon length, and can thus be considered as a link between the FIR filtering and the KF. Several important properties including stability and robustness against errors of noise statistics are illustrated. Finally, a moving target tracking example and an experiment with a three degrees-of-freedom helicopter system are introduced to demonstrate effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of state estimation incorporating infrequent, delayed and integral measurements. In chemical process, there often exist two types of measurements. On one hand, the measurements for process variables such as flow rates and pressures are sampled frequently and are available nearly instantaneously. On the other hand, the measurements for quality variables such as concentration are sampled infrequently and are available with a delay due to long analysis time involved. Moreover, due to the interval time taken by chemical sample collection, the measurements for some quality variables have another important characteristic: it is a function of the states of the compositions over a period of time. This paper formulates the process with infrequent, delayed and integral measurements as an equivalent variable dimension system, whose measurements are both delay and integration free. Based on the new model, a variable dimension unscented Kalman filter (VD-UKF) is proposed to estimate the states. Furthermore, the stability of the proposed VD-UKF is analyzed. Compared with the existing results, the proposed stability condition is significantly relaxed and the invertibility condition of Jacobian matrices is no longer needed. Finally, a simulation example demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with moving horizon estimation for a class of constrained switching nonlinear systems, where the system mode is regarded as an unknown discrete state to be estimated together with the continuous state. In this work, we establish the observability framework of switching nonlinear systems by proposing a series of concepts about observability and analyzing the properties of such concepts. By fully applying the observability properties, we prove the stability of the proposed moving horizon estimators. Simulation results are reported to verify the derived results. [Copyright &y& Elsevier]

Abstract: In industrial process control engineering, using routine operating data obtained from closed-loop operation of a process for model identification would be extremely valuable in applications such as control performance monitoring, root cause diagnosis, and controller retuning. However, the conditions for closed-loop identifiability using routine operating data are still largely unknown or untried. In this paper, criteria for closed-loop identification of an autoregressive, moving average process with exogenous input (ARMAX) regulated with an arbitrary, rational, polynomial controller are derived. The theoretical criteria that are developed for the closed-loop identification of an ARMAX process are compared with Monte Carlo simulations and previous theoretical results. It is shown that the newly-proposed theoretical results are in agreement with the simulation results. [Copyright &y& Elsevier]

Abstract: Conventional Bayesian methods commonly assume that the evidences are temporally independent. This condition, however, does not hold for most engineering problems. With the evidence transition information being considered, the temporal information can be synthesized within the Bayesian framework to improve diagnosis performance. In this paper, the important evidence dependency problem is solved by a data-driven Bayesian approach with consideration of evidence transition probability. The applications in a simulated distillation column and a pilot scale process are presented to demonstrate the data dependency handling ability of the proposed control loop performance diagnosis approach. [Copyright &y& Elsevier]

Abstract: In this paper, robust optimal filtering is addressed for continuous-time stochastic systems with polytopic parameter uncertainty. A new robust stability condition is presented. A continuous-time robust optimal filter is obtained by solving a sufficient linear matrix inequality condition characterizing a solution of a robust minimum variance filtering problem which takes into account the polytopic type of model uncertainties. The proposed approach is demonstrated through numerical examples. [Copyright &y& Elsevier]

This paper presents a novel reduced-order algorithm for identifying rational models. From the Arnoldi process, an orthonormal basis of the Krylov subspace is constructed. Based on the Krylov subspace, a high-order cost function is transformed into a low-order one, thereby significantly reducing the computational efforts. This algorithm can be considered as a reduced-order least squares (LS) algorithm or an extension of the traditional gradient iterative (GI) algorithm for different Krylov subspaces, and it presents several advantages over the traditional LS and GI algorithms. The simulated numerical results/figures are consistent with the analytically derived results in terms of the feasibility and effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

As a recursive state estimation algorithm, the Kalman filter (KF) assumes initial state distribution is known a priori , while in practice the initial distribution is commonly treated as design parameters. In this paper, we will answer three questions concerning initialization: (1) At each time step, how does the KF respond to measurements, control signals, and more importantly, initial states? (2) What is the price (in terms of accuracy) one has to pay if inaccurate initial states are used? and (3) Can we find a better strategy rather than through guessing to improve the performance of KF in the initial estimation phase when the initial condition is unknown? To these ends, the classical recursive KF is first transformed into an equivalent but batch form, from which the responses of the KF to measurements, control signal, and initial state can be clearly separated and observed. Based on this, we isolate the initial distribution by dividing the original state into two parts and reconstructing a new state-space model. An initialization algorithm is then proposed by employing the Bayesian inference technique to estimate all the unknown variables simultaneously. By analyzing its performance, an improved version is further developed. Two simulation examples demonstrate that the proposed initialization approaches can be considered as competitive alternatives of various existing initialization methods when initial condition is unknown. [ABSTRACT FROM AUTHOR]

In this paper, a confidence set-membership filter based on the finite impulse response (FIR) structure is proposed for time-variant systems that are simultaneously subject to both the unknown but bounded noises and the Gaussian noises. At each step, the filter provides a confidence state set that includes the true state with an adjustable confidence level. The FIR structure improves the robustness and brings more degrees of freedom to the filter design. Multiple recent measurements within a moving horizon are fully utilized to construct and optimize each confidence state set. Under two different size criteria, an analytical solution and an LMI-based numerical solution for the filter gain are derived by minimizing the size of the confidence state set, respectively. Finally, an example is given to illustrate the effectiveness and superiority of the algorithms. [ABSTRACT FROM AUTHOR]

This paper targets the development of a data-driven framework for designing observers and controllers of close-loop systems with consideration of disturbances. Under this framework, both the design of the observer and optimization of the controller can be achieved by only using data. After parameterizing the feedback control systems subject to disturbances, the first step is to identify data-driven stable kernel and image representations (SKR and SIR) with the aid of time-series data. Then, SKR constructs a data-driven realization of a diagnostic observer. Through disturbance elimination and reference tracking, online optimization using SIR provides a data-driven solution to the model matching problem (MMP) whilst the controller is re-configured and optimized in real time. An example is used to demonstrate the effectiveness of the proposed data-driven designs. [ABSTRACT FROM AUTHOR]

This paper proposes a novel data-driven fault detection (FD) method for Lipschitz nonlinear systems. The proposed method is developed by considering that the sample size of training data is limited, while the global system nonlinearity is taken into account. It is a nonparametric approach and consists of two FD versions corresponding to open-loop and closed-loop systems, respectively. It achieves a tradeoff between approximation and estimation errors. By quantifying the unknown modeling error that is closely related to the threshold used in FD tasks, an upper bound is obtained so that trial-and-error for finding the threshold can be avoided. The effectiveness of the proposed data-driven schemes is illustrated by two simulation studies. [ABSTRACT FROM AUTHOR]

This paper defines a generalized probabilistic linear latent variable model (GPLLVM) that under specific restrictions reduces to various probabilistic linear models used for process monitoring. For the defined model, we rigorously derive the monitoring statistics and their respective null distributions. Monitoring statistics of the defined model also reduce to the monitoring statistics of various probabilistic models when restricted with the corresponding conditions. The paper presents insightful equivalence between the classical multivariate techniques for process monitoring and their probabilistic counterparts, which is obtained by restricting the generalized model. We also provide an estimation approach based on the expectation maximization algorithm (EM) for GPLLVM. The results presented in the paper are verified using numerical simulation examples. [ABSTRACT FROM AUTHOR]

Many multivariate statistical analysis methods and their corresponding probabilistic counterparts have been adopted to develop process monitoring models in recent decades. However, the insightful connections between them have rarely been studied. In this study, a generalized probabilistic monitoring model (GPMM) is developed with both random and sequential data. Since GPMM can be reduced to various probabilistic linear models under specific restrictions, it is adopted to analyze the connections between different monitoring methods. Using expectation maximization (EM) algorithm, the parameters of GPMM are estimated for both random and sequential cases. Based on the obtained model parameters, statistics are designed for monitoring different aspects of the process system. Besides, the distributions of these statistics are rigorously derived and proved, so that the control limits can be calculated accordingly. After that, contribution analysis methods are presented for identifying faulty variables once the process anomalies are detected. Finally, the equivalence between monitoring models based on classical multivariate methods and their corresponding probabilistic graphic models is further investigated. The conclusions of this study are verified using a numerical example and the Tennessee Eastman (TE) process. Experimental results illustrate that the proposed monitoring statistics are subject to their corresponding distributions, and they are equivalent to statistics in classical deterministic models under specific restrictions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the minimum variance unbiased (MVU) finite impulse response (FIR) filtering problem for linear system described by discrete time-variant state-space models. An MVU FIR filter is derived by minimizing the variance from the unbiased FIR (UFIR) filter. The relationship between the filter gains of MVU FIR, UFIR and optimal FIR (OFIR) filters is derived analytically, and the mean square errors (MSEs) of different FIR filters are compared to provide an insight into the estimation performance. Simulations provided verify that errors in the MVU FIR filter are in between the UFIR and OFIR filters. It is also shown that the MVU FIR filter can offer optimal estimates without a prior knowledge of the initial state, and exhibits better robustness against temporary modeling uncertainties than the Kalman filter. [ABSTRACT FROM AUTHOR]