Robust synchronization for 2-D discrete-time coupled dynamical networks

This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Model based fault detection for two-dimensional systems

Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for one dimensional (1-D) systems, where variables vary only with time. The existing FDI strategies are mainly focussed on 1-D systems and can generally be classified as model based and process history data based methods. In many industrial systems, the state variables change with space and time (e.g., sheet forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems represent a great challenge in both theoretical development and applications and only limited research results are available. In this thesis, model based fault detection strategies for 2-D systems have been investigated based on the F-M and the Roesser models. A dead-beat observer based fault detection has been available for the F-M model. In this work, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems but strict conditions are required in order for an observer and a residual generator to exist. These strict conditions may not be satisfied for some systems. The effect of process noises are also not considered in the observer based fault detection approaches for 2-D systems. To overcome the disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation error variances. Based on the state estimate from the Kalman filter, a residual is generated reflecting fault information. A model is formulated for the relation of the residual with faults over a moving evaluation window. Simulations are performed on two F-M models and results indicate that faults can be detected effectively and efficiently using the Kalman filter based fault detection. In the observer based and Kalman filter based fault detection approaches, the residual signals are used to determine whether a fault occurs. For systems with complicated fault information and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component analysis (DPCA). Based on historical data, the reference residuals are first generated using either the observer or the Kalman filter based approach. Based on the residual time-lagged data matrices for the reference data, the principal components are calculated and the threshold value obtained. In online applications, the T2 value of the residual signals are compared with the threshold value to determine fault occurrence. Simulation results show that applying DPCA to evaluation of 2-D residuals is effective.Doctoral These

On the connection between discrete linear repetitive processes and 2-D discrete linear systems

A direct method is developed that reduces a polynomial system matrix describinga discrete linear repetitive process to a 2-D singular state-space form such that all the relevant properties, including the zero structure of the system matrix, are retained. It is shown that the transformation linking the original polynomial system matrix with its associated 2-D singular form is zero coprime system equivalence. The exact nature of the resulting system matrix in singular form and the transformation involved are established

Stabilization of Linear Systems with Structured Perturbations

The problem of stabilization of linear systems with bounded structured uncertainties are considered in this paper. Two notions of stability, denoted quadratic stability (Q-stability) and μ-stability, are considered, and corresponding notions of stabilizability and detectability are defined. In both cases, the output feedback stabilization problem is reduced via a separation argument to two simpler problems: full information (FI) and full control (FC). The set of all stabilizing controllers can be parametrized as a linear fractional transformation (LFT) on a free stable parameter. For Q-stability, stabilizability and detectability can in turn be characterized by Linear Matrix Inequalities (LMIs), and the FI and FC Q-stabilization problems can be solved using the corresponding LMIs. In the standard one-dimensional case the results in this paper reduce to well-known results on controller parametrization using state-space methods, although the development here relies more heavily on elegant LFT machinery and avoids the need for coprime factorizations

Two-dimensional block Kalman filtering for image restoration

Includes bibliographical references.This paper is concerned with developing an efficient two-dimensional (2-D) block Kalman filtering for digital image restoration. A new 2-D multiinput, multioutput (MIMO) state-space structure for modeling the image generation process is introduced. This structure is derived by arranging a vector autoregressive (AR) model with a causal quarter-plane region of support in block form. This model takes into account the correlations of the image data in successive neighboring blocks and, as a result, reduces the edge effects prominent in the available Kalman strip filtering techniques. The degradation model for an infinite extent Linear space invariant (LSI) blur and white Gaussian (WG) noise is also modeled by an MIMO block state-space equation stemmed from a single-input single-output (SISO) 2-D state-space structure. The image generation model and the degradation model are combined to yield a composite block-state dynamic structure. The block Kalman filtering equations are obtained for this dynamic structure and then used to compute the suboptimal filter estimates of a noisy and blurred image

Equivalence of robust stabilization and robust performance via feedback

One approach to robust control for linear plants with structured uncertainty as well as for linear parameter-varying (LPV) plants (where the controller has on-line access to the varying plant parameters) is through linear-fractional-transformation (LFT) models. Control issues to be addressed by controller design in this formalism include robust stability and robust performance. Here robust performance is defined as the achievement of a uniform specified $L^{2}$-gain tolerance for a disturbance-to-error map combined with robust stability. By setting the disturbance and error channels equal to zero, it is clear that any criterion for robust performance also produces a criterion for robust stability. Counter-intuitively, as a consequence of the so-called Main Loop Theorem, application of a result on robust stability to a feedback configuration with an artificial full-block uncertainty operator added in feedback connection between the error and disturbance signals produces a result on robust performance. The main result here is that this performance-to-stabilization reduction principle must be handled with care for the case of dynamic feedback compensation: casual application of this principle leads to the solution of a physically uninteresting problem, where the controller is assumed to have access to the states in the artificially-added feedback loop. Application of the principle using a known more refined dynamic-control robust stability criterion, where the user is allowed to specify controller partial-state dimensions, leads to correct robust-performance results. These latter results involve rank conditions in addition to Linear Matrix Inequality (LMI) conditions.Comment: 20 page

Computational and algebraic aspects of two-dimensional, linear, multivariable control systems

There are at present a large number of theoretical and algorithmic results relating to one-variable polynomial matrices arising from one-dimensional multivariable systems. In recent years many of the theoretical results have been extended to two-variable polynomial matrices arising from two-dimensional multi variable systems, such as delay-differential or partial differential systems. However there has been no major attempt to extend the algorithmic results associated with single variable polynomial matrices to two-variable or multivariable polynomial matrices. This thesis investigates further some of the extensions of the algebra of one-dimensional multivariable systems to two-dimensional multivariable systems. [Continues.