Volumen 22 (2012): Heft 3 (September 2012)

The paper is devoted to the problem of observability and controllability analysis in nonlinear dynamic systems. Both continuous- and discrete-time systems described by nonlinear differential or difference equations, respectively, are considered. A new approach is developed to solve this problem whose features include (i) consideration of systems with non-differentiable nonlinearities and (ii) the use of relatively simple linear methods which may be supported by existing programming systems, e.g.,Matlab. Sufficient conditions are given for nonlinear unobservability/uncontrollability analysis. To apply these conditions, one isolates the linear part of the system which is checked to be unobservable/uncontrollable and, if the answer is positive, it is examined whether or not existing nonlinear terms violate the unobservability/uncontrollability property.

This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

Two description forms of a linear fractional-order discrete system are considered. The first one is by a fractional-order difference equation, whereas the second by a fractional-order state-space equation. In relation to the two above-mentioned description forms, stability domains are evaluated. Several simulations of stable, marginally stable and unstable unit step responses of fractional-order systems due to different values of system parameters are presented.

This paper deals with the stability study of the nonlinear Saint-Venant Partial Differential Equation (PDE). The proposed approach is based on the multi-model concept which takes into account some Linear Time Invariant (LTI) models defined around a set of operating points. This method allows describing the dynamics of this nonlinear system in an infinite dimensional space over a wide operating range. A stability analysis of the nonlinear Saint-Venant PDE is proposed both by using Linear Matrix Inequalities (LMIs) and an Internal Model Boundary Control (IMBC) structure. The method is applied both in simulations and real experiments through a microchannel, illustrating thus the theoretical results developed in the paper.

In this paper, stabilizing problems in control design are addressed for linear discrete-time systems, reflecting equality constraints tying together some state variables. Based on an enhanced representation of the bounded real lemma for discretetime systems, the existence of a state feedback control for such conditioned stabilization is proven, and an LMI-based design procedure is provided. The control law gain computation method used circumvents generally an ill-conditioned singular design task. The principle, when compared with previously published results, indicates that the proposed method outperforms the existing approaches, guarantees feasibility, and improves the steady-state accuracy of the control. Furthermore, better performance is achieved with essentially reduced design effort. The approach is illustrated on simulation examples, where the validity of the proposed method is demonstrated using one state equality constraint.

We investigate parametric interval linear systems of equations. The main result is a generalization of the Bauer–Skeel and the Hansen–Bliek–Rohn bounds for this case, comparing and refinement of both. We show that the latter bounds are not provable better, and that they are also sometimes too pessimistic. The presented form of both methods is suitable for combining them into one to get a more efficient algorithm. Some numerical experiments are carried out to illustrate performances of the methods.

Design of a state observer is an important issue in control systems and signal processing. It is well known that it is difficult to obtain the desired properties of state feedback control if some or all of the system states cannot be directly measured. Moreover, the existence of a lumped perturbation and/or a time delay usually reduces the system performance or even produces an instability in the closed-loop system. Therefore, in this paper, a new Variable Structure Observer (VSO) is proposed for a class of uncertain systems subjected to a time varying delay and a lumped perturbation. Based on the strictly positive real concept, the stability of the equivalent error system is verified. Based on the generalized matrix inverse approach, the global reaching condition of the sliding mode of the error system is guaranteed. Also, the proposed variable structure observer will be shown to possess the invariance property in relation to the lumped perturbation, as the traditional variable structure controller does. Furthermore, two illustrative examples with a series of computer simulation studies are given to demonstrate the effectiveness of the proposed design method.

In the reliability modeling field, we sometimes encounter systems with uncertain structures, and the use of fault trees and reliability diagrams is not possible. To overcome this problem, Bayesian approaches offer a considerable efficiency in this context. This paper introduces recent contributions in the field of reliability modeling with the Bayesian network approach. Bayesian reliability models are applied to systems with Weibull distribution of failure. To achieve the formulation of the reliability model, Bayesian estimation of Weibull parameters and the model’s goodness-of-fit are evoked. The advantages of this modelling approach are presented in the case of systems with an unknown reliability structure, those with a common cause of failures and redundant ones. Finally, we raise the issue of the use of BNs in the fault diagnosis area.

A new approach to control an omnidirectional mobile manipulator is developed. The robot is considered to be an individual agent aimed at performing robotic tasks described in terms of a displacement and a force interaction with the environment. A reactive architecture and impedance control are used to ensure reliable task execution in response to environment stimuli. The mechanical structure of our holonomic mobile manipulator is built of two joint manipulators mounted on a holonomic vehicle. The vehicle is equipped with three driven axles with two spherical orthogonal wheels. Taking into account the dynamical interaction between the base and the manipulator, one can define the dynamics of the mobile manipulator and design a nonlinear controller using the input-state linearization method. The control structure of the robot is built in order to demonstrate the main capabilities regarding navigation and obstacle avoidance. Several simulations were conducted to prove the effectiveness of this approach.

This paper presents a new algorithm for fuzzy c-regression model clustering. The proposed methodology is based on adding a second regularization term in the objective function of a Fuzzy C-Regression Model (FCRM) clustering algorithm in order to take into account noisy data. In addition, a new error measure is used in the objective function of the FCRM algorithm, replacing the one used in this type of algorithm. Then, particle swarm optimization is employed to finally tune parameters of the obtained fuzzy model. The orthogonal least squares method is used to identify the unknown parameters of the local linear model. Finally, validation results of two examples are given to demonstrate the effectiveness and practicality of the proposed algorithm.

The paper presents a new (to the best of the authors’ knowledge) estimator of probability called the “Eph √ 2 completeness estimator” along with a theoretical derivation of its optimality. The estimator is especially suitable for a small number of sample items, which is the feature of many real problems characterized by data insufficiency. The control parameter of the estimator is not assumed in an a priori, subjective way, but was determined on the basis of an optimization criterion (the least absolute errors).The estimator was compared with the universally used frequency estimator of probability and with Cestnik’s m-estimator with respect to accuracy. The comparison was realized both theoretically and experimentally. The results show the superiority of the Eph √ 2 completeness estimator over the frequency estimator for the probability interval p_h ∈ (0.1, 0.9). The frequency estimator is better for p_h ∈ [0, 0.1] and p_h ∈ [0.9, 1].

Meta-learning is becoming more and more important in current and future research concentrated around broadly defined data mining or computational intelligence. It can solve problems that cannot be solved by any single, specialized algorithm. The overall characteristic of each meta-learning algorithm mainly depends on two elements: the learning machine space and the supervisory procedure. The former restricts the space of all possible learning machines to a subspace to be browsed by a meta-learning algorithm. The latter determines the order of selected learning machines with a module responsible for machine complexity evaluation, organizes tests and performs analysis of results. In this article we present a framework for meta-learning search that can be seen as a method of sophisticated description and evaluation of functional search spaces of learning machine configurations used in meta-learning. Machine spaces will be defined by specially defined graphs where vertices are specialized machine configuration generators. By using such graphs the learning machine space may be modeled in a much more flexible way, depending on the characteristics of the problem considered and a priori knowledge. The presented method of search space description is used together with an advanced algorithm which orders test tasks according to their complexities.

The increased production of Reactive Oxygen Species (ROS) in plant leaf tissues is a hallmark of a plant’s reaction to various environmental stresses. This paper describes an automatic segmentation method for scanned images of cucurbits leaves stained to visualise ROS accumulation sites featured by specific colour hues and intensities. The leaves placed separately in the scanner view field on a colour background are extracted by thresholding in the RGB colour space, then cleaned from petioles to obtain a leaf blade mask. The second stage of the method consists in the classification of within mask pixels in a hue-saturation plane using two classes, determined by leaf regions with and without colour products of the ROS reaction. At this stage a two-layer, hybrid artificial neural network is applied with the first layer as a self-organising Kohonen type network and a linear perceptron output layer (counter propagation network type). The WTA-based, fast competitive learning of the first layer was improved to increase clustering reliability. Widrow–Hoff supervised training used at the output layer utilises manually labelled patterns prepared from training images. The generalisation ability of the network model has been verified by K-fold cross-validation. The method significantly accelerates the measurement of leaf regions containing the ROS reaction colour products and improves measurement accuracy.

Developing a model based digital human meridian system is one of the interesting ways of understanding and improving acupuncture treatment, safety analysis for acupuncture operation, doctor training, or treatment scheme evaluation. In accomplishing this task, how to construct a proper model to describe the behavior of human meridian systems is one of the very important issues. From experiments, it has been found that the hysteresis phenomenon occurs in the relations between stimulation input and the corresponding response of meridian systems. Therefore, the modeling of hysteresis in a human meridian system is an unavoidable task for the construction of model based digital human meridian systems. As hysteresis is a nonsmooth, nonlinear and dynamic system with a multi-valued mapping, the conventional identification method is difficult to be employed to model its behavior directly. In this paper, a neural network based identification method of hysteresis occurring in human meridian systems is presented. In this modeling scheme, an expanded input space is constructed to transform the multi-valued mapping of hysteresis into a one-to-one mapping. For this purpose, a modified hysteretic operator is proposed to handle the extremum-missing problem. Then, based on the constructed expanded input space with the modified hysteretic operator, the so-called Extreme Learning Machine (ELM) neural network is utilized to model hysteresis inherent in human meridian systems. As hysteresis in meridian system is a dynamic system, a dynamic ELMneural network is developed. In the proposed dynamic ELMneural network, the output state of each hidden neuron is fed back to its own input to describe the dynamic behavior of hysteresis. The training of the recurrent ELM neural network is based on the least-squares algorithm with QR decomposition.

In this paper the problem of accurate edge detection in images of heat-emitting specimens of metals is discussed. The images are provided by the computerized system for high temperature measurements of surface properties of metals and alloys. Subpixel edge detection is applied in the system considered in order to improve the accuracy of surface tension determination. A reconstructive method for subpixel edge detection is introduced. The method uses a Gaussian function in order to reconstruct the gradient function in the neighborhood of a coarse edge and to determine its subpixel position. Results of applying the proposed method in the measurement system considered are presented and compared with those obtained using different methods for subpixel edge detection.

This paper presents an application of methods from the machine learning domain to solving the task of DNA sequence recognition. We present an algorithm that learns to recognize groups of DNA sequences sharing common features such as sequence functionality. We demonstrate application of the algorithm to find splice sites, i.e., to properly detect donor and acceptor sequences. We compare the results with those of reference methods that have been designed and tuned to detect splice sites. We also show how to use the algorithm to find a human readable model of the IRE (Iron-Responsive Element) and to find IRE sequences. The method, although universal, yields results which are of quality comparable to those obtained by reference methods. In contrast to reference methods, this approach uses models that operate on sequence patterns, which facilitates interpretation of the results by humans.

The paper introduces a method of mathematical modeling of high scale road traffic networks, where a new special hypermatrix structure is intended to be used. The structure describes the inner–inner, inner–outer and outer–outer relations, and laws of a network area. The research examines the nonlinear equation system. The analysed model can be applied to the testing and planning of large-scale road traffic networks and the regulation of traffic systems. The elaborated model is in state space form, where the states are vehicle densities on a particular lane and the dynamics are described by a nonlinear state constrained positive system. This model can be used directly for simulation and analysis and as a starting point for investigating various control strategies. The stability of the traffic over the network can be analyzed by constructing a linear Lyapunov function and the associated theory. The model points out that in intersection control one must take the traffic density values of both the input and the output sections into account. Generally, the control of any domain has to take the density of input and output sections into consideration.

Recently, distributed computing system have been gaining much attention due to a growing demand for various kinds of effective computations in both industry and academia. In this paper, we focus on Peer-to-Peer (P2P) computing systems, also called public-resource computing systems or global computing systems. P2P computing systems, contrary to grids, use personal computers and other relatively simple electronic equipment (e.g., the PlayStation console) to process sophisticated computational projects. A significant example of the P2P computing idea is the BOINC (Berkeley Open Infrastructure for Network Computing) project. To improve the performance of the computing system, we propose to use the P2P approach to distribute results of computational projects, i.e., results are transmitted in the system like in P2P file sharing systems (e.g., BitTorrent). In this work, we concentrate on offline optimization of the P2P computing system including two elements: scheduling of computations and data distribution. The objective is to minimize the system OPEX cost related to data processing and data transmission. We formulate an Integer Linear Problem (ILP) to model the system and apply this formulation to obtain optimal results using the CPLEX solver. Next, we propose two heuristic algorithms that provide results very

Wireless Backbone Networks (WBNs) equipped with Multi-Radio Multi-Channel (MRMC) configurations do experience power control problems such as the inter-channel and co-channel interference, high energy consumption at multiple queues and unscalable network connectivity. Such network problems can be conveniently modelled using the theory of queue perturbation in the multiple queue systems and also as a weak coupling in a multiple channel wireless network. Consequently, this paper proposes a queue perturbation and weakly coupled based power control approach forWBNs. The ultimate objectives are to increase energy efficiency and the overall network capacity. In order to achieve this objective, a Markov chain model is first presented to describe the behaviour of the steady state probability distribution of the queue energy and buffer states. The singular perturbation parameter is approximated from the coefficients of the Taylor series expansion of the probability distribution. The impact of such queue perturbations on the transmission probability, given some transmission power values, is also analysed. Secondly, the inter-channel interference is modelled as a weakly coupled wireless system. Thirdly, Nash differential games are applied to derive optimal power control signals for each user subject to power constraints at each node. Finally, analytical models and numerical examples show the efficacy of the proposed model in solving power control problems in WBNs.

It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.