Least-squares parameter estimation of linear systems with noisy input–output data

This paper studies the computational efficiency of the bias-eliminated least-squares (BELS) method recently proposed for estimating linear systems in the presence of input and output noises. It is found that the BELS method based on expanding the denominator polynomial of the system transfer function by two dimensions may involve some redundant computations due to its handling of an augmented system model in its estimation scheme. To improve the computational efficiency, a direct estimation scheme is proposed to identify the underlying noisy input–output system. Numerical results show that the computational cost can be considerably reduced using such a new estimation scheme.     

Robust fault detection in linear systems based on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers （FSO）. Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.     

Robust input–output linearisation using uncertainty and disturbance estimation

This article proposes a new approach to robustify an input–output linearisation controller. The robustification is achieved by estimating the uncertainties and external unmeasurable disturbances using a novel uncertainty and disturbance estimator. A significant feature of the proposed approach is that it does not need any information about the uncertainties. The stability of the system and the estimator is established. Effectiveness of the proposed approach is demonstrated through application to the wing rock motion control problem.     

Wavelet based non-parametric NARX models for nonlinear input–output system identification

Wavelet based non-parametric additive NARX models are proposed for nonlinear input–output system identification. By expanding each functional component of the non-parametric NARX model into wavelet multiresolution expansions, the non-parametric estimation problem becomes a linear-in-the-parameters problem, and least-squares-based methods such as the orthogonal forward regression (OFR) approach, coupled with model size determination criteria, can be used to select the model terms and estimate the parameters. Wavelet based additive models, combined with model order determination and variable selection approaches, are capable of handling problems of high dimensionality.     

Distributed fault diagnosis for continuous-time nonlinear systems: The input–output case

In this paper, some new results on distributed fault diagnosis of continuous-time nonlinear systems with partial state measurements are proposed. By exploiting an overlapping decomposition framework, the dynamics of a nonlinear uncertain large-scale dynamical system is described as the interconnections of several subsystems. Each subsystem is monitored by a Local Fault Diagnoser: a set of local estimators, based on the nominal local dynamic model and on an adaptive approximation of the interconnection and of the fault function, allows to derive a local fault decision. A consensus-based protocol is used in order to improve the detectability and the isolability of faults affecting variables shared among different subsystems because of the overlapping decomposition. A sufficient condition ensuring the convergence of the estimation errors is derived. Finally, possibly non-conservative time-varying threshold functions guaranteeing no false-positive alarms and theoretical results dealing with detectability and isolability sufficient conditions are presented.     

Distributed fault diagnosis for process and sensor faults in a class of interconnected input–output nonlinear discrete-time systems

This paper presents a distributed fault diagnosis scheme able to deal with process and sensor faults in an integrated way for a class of interconnected input–output nonlinear uncertain discrete-time systems. A robust distributed fault detection scheme is designed, where each interconnected subsystem is monitored by its respective fault detection agent, and according to the decisions of these agents, further information regarding the type of the fault can be deduced. As it is shown, a process fault occurring in one subsystem can only be detected by its corresponding detection agent whereas a sensor fault in a subsystem can be detected by either its corresponding detection agent or the detection agent of another subsystem that is affected by the subsystem where the sensor fault occurred. This discriminating factor is exploited for the derivation of a high-level isolation scheme. Moreover, process and sensor fault detectability conditions characterising quantitatively the class of detectable faults are derived. Finally, a simulation example is used to illustrate the effectiveness of the proposed distributed fault detection scheme.     

Minimal realisation of bilinear and quadratic input–output difference equations in state-space form

This article studies the realisability property of discrete-time bilinear and quadratic input–output (i/o) equations in the classical state-space form. Constraints on the parameters of the i/o model are suggested that lead to realisable models. Using new formulae for computing basis vectors of certain vector spaces of differential one-forms, we present in this article the complete list of the third- and fourth-order realisable i/o bilinear models, and a new realisable subclass of an arbitrary order is suggested. Moreover, we provide the sufficient conditions of the second- and third-order realisable i/o quadratic models, respectively. All the developed theory and algorithms are illustrated by means of several examples.     

An iterative algorithm for simulation error based identification of polynomial input–output models using multi-step prediction

Effective identification of polynomial input–output models for applications requiring long-range prediction or simulation performance relies on both careful model selection and accurate parameter estimation. The simulation error minimisation (SEM) approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short-term prediction capabilities but unsuitable long-term dynamics. However, SEM-based parameter estimation has been generally avoided due to excessive computational effort. This article extends to the nonlinear case a computationally efficient approach for this task, that was previously developed for linear models, based on the iterative estimation of predictors with increasing prediction horizon. Conditions for the applicability of the approach to various model classes are also discussed. Finally, some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input–output identification, as well as the improvements achievable by enforcing SEM parameter estimation. A benchmark for nonlinear identification is also analysed, with encouraging results.     

Stability and performance analysis of linear positive systems with delays using input–output methods

It is known that input–output approaches based on scaled small-gain theorems with constant D-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where input–output approaches provide, in general, sufficient conditions only. Using these results, we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral time-invariant/-varying delays and linear difference equations. In particular, we give a simple proof for the characterisation of diagonal Riccati stability for systems with discrete-delays and generalise this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the input–output framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the L ₁-, L ₂- and L _∞-gains. It is also flexible enough to be used for design purposes.     

A modified super-efficiency measure based on simultaneous input–output projection in data envelopment analysis

Super-efficiency data envelopment analysis (SE-DEA) models have been developed and applied in many situations. However, under the condition of variable returns to scale (VRS), infeasibility of the SE-DEA model may occur and restrict its application. A modified SE-DEA measure based on simultaneous input–output projection is proposed as a way to systematically characterize the super-efficiency in both inputs and outputs. The modified measure overcomes the infeasibility problem while providing ease of computation and interpretation. The practicability of the proposed measure in real applications and its comparison to other super-efficiency measures are illustrated empirically using an example.     

A method for solving systems of linear interval equations applied to the Leontief input–output model of economics

A new approach to solving systems of linear interval equations based on the generalized procedure of interval extension is proposed. This procedure is based on the treatment of interval zero as an interval centered around zero, and for this reason it is called the “interval extended zero” method. Since the “interval extended zero” method provides a fuzzy solution to interval equations, its interval representations are proposed. It is shown that they may be naturally treated as modified operations of interval division. These operations are used for the modified interval extensions of known numerical methods for solving systems of linear equations and finally for solving systems of linear interval equations. Using a well known example, it is shown that the solution obtained by the proposed method can be treated as an inner interval approximation of the united solution and an outer interval approximation of the tolerable solution, and lies within the range of possible AE-solutions between the extreme tolerable and united solutions. Generally, we can say that the proposed method provides the results which can be treated as approximate formal solutions sometimes referred to as algebraic solutions. Seven known examples are used to illustrate the method’s efficacy and advantages in comparison with known methods providing formal (algebraic) solutions to systems of linear interval equations. It is shown that a new method provides results which are close to the so-called maximal inner solutions (the corresponding method was developed by Kupriyanova, Zyuzin and Markov) and the algebraic solutions obtained by the subdifferential Newton method proposed by Shary. It is important that the proposed method makes it possible to avoid inverted interval solutions. The influence of the system’s size and number of zero entries on the results is analyzed by applying the proposed method to the Leontief input–output model of economics.     

Optimal digital controller and observer design for multiple time-delay transfer function matrices with multiple input–output time delays

In this article, we address the optimal digital design methodology for multiple time-delay transfer function matrices with multiple input–output time delays. In our approach, the multiple time-delay analogue transfer function matrix with multiple input–output time delays is minimally realised using a continuous-time state-space model. For deriving an explicit form of the optimal digital controller, the realised continuous-time multiple input–output time-delay system is discretised, and an extended high-order discrete-time state-space model is constructed for discrete-time LQR design. To derive a low-order optimal digital observer for the multiple input–output time-delay system, the multiple time-delay state obtained from the multiple time-delay outputs is discretised. Then, the well-known duality concept is employed to design an optimal digital observer using the low-order discretised multiple input time-delay system together with the newly discretised multiple time-delay state. The proposed approach is restricted to multiple time-delay systems where multiple time delays arise only in the input and output, and not in the state.     

H∞ output tracking control of uncertain and disturbed nonlinear systems based on neural network model

The work presented in this paper seeks to address the tracking problem for uncertain continuous nonlinear systems with external disturbances. The objective is to obtain a model that uses a reference-based output feedback tracking control law. The control scheme is based on neural networks and a linear difference inclusion (LDI) model, and a PDC structure and H_∞ performance criterion are used to attenuate external disturbances. The stability of the whole closed-loop model is investigated using the well-known quadratic Lyapunov function. The key principles of the proposed approach are as follows: neural networks are first used to approximate nonlinearities, to enable a nonlinear system to then be represented as a linearised LDI model. An LMI (linear matrix inequality) formula is obtained for uncertain and disturbed linear systems. This formula enables a solution to be obtained through an interior point optimisation method for some nonlinear output tracking control problems. Finally, simulations and comparisons are provided on two practical examples to illustrate the validity and effectiveness of the proposed method.     

Dynamic visual tracking based on multiple feature matching and g–h filter

The area-based matching approach has been used extensively in many dynamic visual tracking systems to detect moving targets because it is computation efficient and does not require an object model. Unfortunately, area-based matching is sensitive to occlusion and illumination variation. In order to improve the robustness of visual tracking, two image cues, i.e., target template and target contour, are used in the proposed visual tracking algorithm. In particular, the target contour is represented by the active contour model that is used in combination with the fast greedy algorithm. However, to use the conventional active contour method, the initial contour needs to be provided manually. In order to facilitate the use of contour matching, a new approach that combines the adaptive background subtraction method with the border tracing technique was developed and is used to automatically generate the initial contour. In addition, a g–h filter is added to the visual loop to deal with the latency problem of visual feedback so that the performance of dynamic visual tracking can be improved. Experimental results demonstrate the effectiveness of the proposed approach.     

Input–output method to fault detection for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses

The fault detection (FD) problem for discrete-time fuzzy networked systems with time-varying delay and multiple packet losses is investigated in this paper. The communication links between the plant and the FD filter (FDF) are assumed to be imperfect, and the missing probability is governed by an individual random variable satisfying a certain probabilistic distribution over the interval [0 1]. The discrete-time delayed fuzzy networked system is first transformed into the form of interconnect ion of two subsystems by applying an input–output method and a two-term approximation approach, which are employed to approximate the time-varying delay. Our attention is focused on the design of fuzzy FDF (FFDF) such that, for all data missing conditions, the overall FD dynamics are input–output stable in mean square and preserves a guaranteed performance. Sufficient conditions are first established via H_∞ performance analysis for the existence of the desired FFDF; meanwhile, the corresponding solvability conditions for the desired FFDF gains are characterised in terms of the feasibility of a convex optimisation problem. Moreover, we show that the obtained criteria based on the input–output approach can also be established by applying the direct Lyapunov method to the original time-delay systems. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed approaches.     

Parallel eigenvalue calculation based on multiple shift–invert Lanczos and contour integral based spectral projection method

We discuss the possibility of using multiple shift–invert Lanczos and contour integral based spectral projection method to compute a relatively large number of eigenvalues of a large sparse and symmetric matrix on distributed memory parallel computers. The key to achieving high parallel efficiency in this type of computation is to divide the spectrum into several intervals in a way that leads to optimal use of computational resources. We discuss strategies for dividing the spectrum. Our strategies make use of an eigenvalue distribution profile that can be estimated through inertial counts and cubic spline fitting. Parallel sparse direct methods are used in both approaches. We use a simple cost model that describes the cost of computing k eigenvalues within a single interval in terms of the asymptotic cost of sparse matrix factorization and triangular substitutions. Several computational experiments are performed to demonstrate the effect of different spectrum division strategies on the overall performance of both multiple shift–invert Lanczos and the contour integral based method. We also show the parallel scalability of both approaches in the strong and weak scaling sense. In addition, we compare the performance of multiple shift–invert Lanczos and the contour integral based spectral projection method on a set of problems from density functional theory (DFT).     

ROI image retrieval based on multiple features of mean shift and expectation–maximisation

In this paper, a novel region of interest (ROI) query method is proposed for image retrieval by combining a mean shift tracking (MST) algorithm and an improved expectation–maximisation (EM)-like (IEML) method. In the proposed combination, the MST is used to seek the initial location of the target candidate model and then IEML is used to adaptively change the location and scale of the target candidate model to include the relevant region and exclude the irrelevant region as far as possible. In order to improve the performance and effectiveness using IEML to track the target candidate model, a new similarity measure is built based on spatial and colour features and a new image retrieval framework for this new environment is proposed. Extensive experiments confirm that compared with the latest developed approaches, such as the generalized Hough transform (GHT) and EM-like tracking methods, our method can provide a much better performance in effectiveness. On the other hand, for the IEML, the new similarity measure model also substantially decreases computational complexity and improves the precision tracking of the target candidate model. Compared with the conventional ROI-based image retrieval methods, the most significant highlight is that the proposed method can directly find the target candidate model in the candidate image without pre-segmentation in advance.     

A novel temporal protein complexes identification framework based on density–distance and heuristic algorithm

Neural Computing and Applications - The construction of dynamic protein–protein interaction networks is affected by cell tissue and its biological function, and the identification of protein...