Identification of EIV models with coloured input–output noise: combining PEM and covariance matching method

In this paper, a novel identification method for discrete-time linear systems when input–output observations are contaminated by coloured noise (errors-in-variables models) is proposed. To develop the new approach, modified prediction error and covariance matching methods are utilised. It is proved that the proposed approach leads to a consistent estimation. System identification through the proposed approach entails the existence of a flat frequency interval in power spectra of input and ratio of noise-free input to input signals which is a somewhat mild assumption. Two Monte Carlo simulations are provided to explain the efficiency, numerical complexity and the application of the proposed method.     

Joint input–output identification of unstable systems with kernel regularization

This paper discusses closed-loop identification of unstable systems. In particular, we first apply the joint input–output identification method and then convert the identification problem of unstable systems into that of stable systems, which can be tackled by using kernel-based regularization methods.We propose to identify two transfer functions by kernel regularization, the one from the reference signal to the input, and the one from the reference signal to the output. Since these transfer functions are stable, kernel regularization methods can construct their accurate models. Then the model of unstable system is constructed by ratio of these functions. The effectiveness of the proposed method is demonstrated by a numerical example and a practical experiment with a DC motor.     

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.     

Predictor–observer-based control of systems with multiple input/output delays

This paper deals with the control of single-input–single-output linear time-delayed systems, when there are different delays in the output/input transfer function. The process can be disturbed and unstable. A new control structure is proposed, solving the problem in several steps. First, by using a stable predictor/observer the plant is stabilized, regardless the delays. On the stable plant, the multidelay plant model is considered as a single delay plant with additional disturbances. The problem of disturbance rejection is solved by using a disturbance observer approach. Finally, output tracking is achieved by a two degrees of freedom controller.     

Fault detection of discrete-time switched systems with distributed delays: input–output approach

This article is concerned with the ?_∞ fault detection of discrete-time switched systems with distributed delays. By using the input–output approach combining with the small-scale gain theorem, a sufficient condition is established in terms of linear matrix inequality, which guarantees the fault detection system to be exponentially stable with an ?_∞ performance. Then, a solvability condition for the desired fault detection filter is also proposed. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed theory.     

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.     

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.     

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.     

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.     

The model matching problem for a class of polynomial non-linear discrete input–output systems with cross-products. An algorithmic approach

In this paper we examine the model matching problem that concerns non-linear input–output discrete systems, containing products among delays of input and output signals, through a special factorisation. The algebraic framework of δε-operators and the star-product that we adopt describe these systems. Moreover, a certain procedure that resembles the Euclidean division allows us to discover the linear factors of those systems, with respect to the above mentioned operations. The entire approach is symbolically algorithmic and involves the use of suitable software.     

Classification of radar echoes with a textural–fuzzy approach: an application for the removal of ground clutter observed in Sétif (Algeria) and Bordeaux (France) sites

This work deals with the classification of radar echoes and the removal of clutter caused by the Earth’s surface. Two incoherent radar sites are considered, which are the regions of Sétif (Algeria) and Bordeaux (France) where different climates and landforms prevail. To perform this task, we used a combination of textural and fuzzy approaches. For the textural technique, we applied grey-level co-occurrence matrices that are widely used in the analysis of texture images. We have shown that among nine parameters, only energy and local homogeneity are considered to be effective in discriminating between precipitation echoes and clutter. Then, these parameters are used as inputs for the fuzzy system, while the two radar echo types are its output classes. Image processing done by using this approach has reduced ground echoes by more than 93.5% for Sétif and 92.3% for Bordeaux sites, while more than 97.6% of precipitation echoes are stored at both sites. In addition, over 96% of the anomalous propagations observed only in Bordeaux site are removed. The proposed approach gives a filtering average rate that is 94.5% higher than that obtained for the textural technique alone, which is 91.5%.