Volumen 26 (2016): Heft 3 (September 2016)

The paper is concerned with time-delay linear fractional systems with multiple delays in the state. A formula for the solution of the discussed systems is presented and derived using the Laplace transform. Definitions of relative controllability with and without constraints for linear fractional systems with delays in the state are formulated. Relative controllability, both with and without constraints imposed on control values, is discussed. Various types of necessary and sufficient conditions for relative controllability and relative U-controllability are established and proved. Numerical examples illustrate the obtained theoretical results.

The Weierstrass–Kronecker theorem on the decomposition of the regular pencil is extended to fractional descriptor continuous-time linear systems described by the Caputo–Fabrizio derivative. A method for computing solutions of continuous-time systems is presented. Necessary and sufficient conditions for the positivity and stability of these systems are established. The discussion is illustrated with a numerical example.

This paper presents a new formulation for set-membership parameter estimation of fractional systems. In such a context, the error between the measured data and the output model is supposed to be unknown but bounded with a priori known bounds. The bounded error is specified over measurement noise, rather than over an equation error, which is mainly motivated by experimental considerations. The proposed approach is based on the optimal bounding ellipsoid algorithm for linear output-error fractional models. A numerical example is presented to show effectiveness and discuss results.

The finite element method (FEM) is applied to obtain numerical solutions to a recently derived nonlinear equation for the shallow water wave problem. A weak formulation and the Petrov–Galerkin method are used. It is shown that the FEM gives a reasonable description of the wave dynamics of soliton waves governed by extended KdV equations. Some new results for several cases of bottom shapes are presented. The numerical scheme presented here is suitable for taking into account stochastic effects, which will be discussed in a subsequent paper.

We propose a new observer where the model, decomposed in generalized canonical form of regulation described by Fliess, is dissociated from the part assuring error correction. The obtained stable exact estimates give direct access to state variables in the form of successive derivatives. The dynamic response of the observer converges exponentially, as long as the nonlinearities are locally of Lipschitz type. In this case, we demonstrate that a quadratic Lyapunov function provides a number of inequalities which guarantee at least local stability. A synthesis of gains is proposed, independent of the observation time scale. Simulations of a Düffing system and a Lorenz strange attractor illustrate theoretical developments.

The paper presents a new method for diagnosis of a process fault which takes the form of an abrupt change in some real parameter of a time-continuous linear system. The abrupt fault in the process real parameter is reflected in step changes in many parameters of the input/output model as well as in step changes in canonical state variables of the system. Detection of these state changes will enable localization of the faulty parameter in the system. For detecting state changes, a special type of exact state observer will be used. The canonical state will be represented by the derivatives of the measured output signal. Hence the exact state observer will play the role of virtual sensors for reconstruction of the derivatives of the output signal. For designing the exact state observer, the model parameters before and after the moment of fault occurrence must be known. To this end, a special identification method with modulating functions will be used. A novel concept presented in this paper concerns the structure of the observer. It will take the form of a double moving window observer which consists of two signal processing windows, each of width T. These windows are coupled to each other with a common edge. The right-hand side edge of the left-side moving window in the interval [t − 2T, t − T ] is connected to the left-hand side edge of the right-side window which operates in the interval [t − T, t]. The double observer uses different measurements of input/output signals in both the windows, and for each current time t simultaneously reconstructs two values of the state—the final value of the state in the left-side window z_T (t − T) and the initial value of the state z₀(t − T) in the right-side window. If the process parameters are constant, the values of both the states on the common joint edge are the same. If an abrupt change (fault) in some parameter at the moment t_A = t − T occurs in the system, then step changes in some variables of the canonical state vector will also occur and the difference between the states will be detected. This will enable localization of the faulty parameter in the system.

For many practical weakly nonlinear systems we have their approximated linear model. Its parameters are known or can be determined by one of typical identification procedures. The model obtained using these methods well describes the main features of the system’s dynamics. However, usually it has a low accuracy, which can be a result of the omission of many secondary phenomena in its description. In this paper we propose a new approach to the modelling of weakly nonlinear dynamic systems. In this approach we assume that the model of the weakly nonlinear system is composed of two parts: a linear term and a separate nonlinear correction term. The elements of the correction term are described by fuzzy rules which are designed in such a way as to minimize the inaccuracy resulting from the use of an approximate linear model. This gives us very rich possibilities for exploring and interpreting the operation of the modelled system. An important advantage of the proposed approach is a set of new interpretability criteria of the knowledge represented by fuzzy rules. Taking them into account in the process of automatic model selection allows us to reach a compromise between the accuracy of modelling and the readability of fuzzy rules.

Inverse three-dimensional heat conduction problems devoted to heating source localization are ill posed. Identification can be performed using an iterative regularization method based on the conjugate gradient algorithm. Such a method is usually implemented off-line, taking into account observations (temperature measurements, for example). However, in a practical context, if the source has to be located as fast as possible (e.g., for diagnosis), the observation horizon has to be reduced. To this end, several configurations are detailed and effects of noisy observations are investigated.

This paper proposes a reliability-based economic model predictive control (MPC) strategy for the management of generalised flow-based networks, integrating some ideas on network service reliability, dynamic safety stock planning, and degradation of equipment health. The proposed strategy is based on a single-layer economic optimisation problem with dynamic constraints, which includes two enhancements with respect to existing approaches. The first enhancement considers chance-constraint programming to compute an optimal inventory replenishment policy based on a desired risk acceptability level, leading to dynamical allocation of safety stocks in flow-based networks to satisfy non-stationary flow demands. The second enhancement computes a smart distribution of the control effort and maximises actuators’ availability by estimating their degradation and reliability. The proposed approach is illustrated with an application of water transport networks using the Barcelona network as the case study considered.

The aim of this paper is to introduce a strategy to find a minimal set of test nodes for diagnostics of complex analog systems with single parametric faults using the support vector machine (SVM) classifier as a fault locator. The results of diagnostics of a video amplifier and a low-pass filter using tabu search along with genetic algorithms (GAs) as node selectors in conjunction with the SVM fault classifier are presented. General principles of the diagnostic procedure are first introduced, and then the proposed approach is discussed in detail. Diagnostic results confirm the usefulness of the method and its computational requirements. Conclusions on its wider applicability are provided as well.

Typical monocular localization schemes involve a search for matches between reprojected 3D world points and 2D image features in order to estimate the absolute scale transformation between the camera and the world. Successfully calculating such transformation implies the existence of a good number of 3D points uniformly distributed as reprojected pixels around the image plane. This paper presents a method to control the march of a humanoid robot towards directions that are favorable for visual based localization. To this end, orthogonal diagonalization is performed on the covariance matrices of both sets of 3D world points and their 2D image reprojections. Experiments with the NAO humanoid platform show that our method provides persistence of localization, as the robot tends to walk towards directions that are desirable for successful localization. Additional tests demonstrate how the proposed approach can be incorporated into a control scheme that considers reaching a target position.

Earliest deadline first (EDF) and fixed priority (FP) are the most commonly used and studied scheduling algorithms for real-time systems. This paper focuses on combining the EDF and FP strategies in one system. We provide a new sufficient schedulability analysis for real-time hybrid task systems which are scheduled by EDF and FP. The proposed analysis has a polynomial time complexity and no restrictions on task parameters, where the relative deadline of each task could be less than, equal to, or greater than its period. By extensive experiments, we show that our proposed analysis significantly improves the acceptance ratio compared with the existing results of the sufficient schedulability test for hybrid scheduling systems.

In this work we consider a problem of scheduling preemptable, independent jobs, characterized by the fact that their processing speeds depend on the amounts of a continuous, renewable resource allocated to jobs at a time. Jobs are scheduled on parallel, identical machines, with the criterion of minimization of the schedule length. Since two categories of resources occur in the problem: discrete (set of machines) and continuous, it is generally called a discrete-continuous scheduling problem. The model studied in this paper allows the total available amount of the continuous resource to vary over time, which is a practically important generalization that has not been considered yet for discrete-continuous scheduling problems. For this model we give some properties of optimal schedules on a basis of which we propose a general methodology for solving the considered class of problems. The methodology uses a two-phase approach in which, firstly, an assignment of machines to jobs is defined and, secondly, for this assignment an optimal continuous resource allocation is found by solving an appropriate mathematical programming problem. In the approach various cases are considered, following from assumptions made on the form of the processing speed functions of jobs. For each case an iterative algorithm is designed, leading to an optimal solution in a finite number of steps.

Peer-to-peer (P2P) networks offer a cost-effective and easily deployable framework for sharing content. However, P2P file-sharing applications face a fundamental problem of unfairness. Pricing is regarded as an effective way to provide incentives to peers to cooperate. In this paper we propose a pricing scheme to achieve reasonable resource allocation in P2P file-sharing networks, and give an interpretation for the utility maximization problem and its sub-problems from an economic point of view. We also deduce the exact expression of optimal resource allocation for each peer, and confirm it with both simulation and optimization software. In order to realize the optimum in a decentralized architecture, we present a novel price-based algorithm and discuss its stability based on Lyapunov stability theory. Simulation results confirm that the proposed algorithm can attain an optimum within reasonable convergence times.

This study provides a proof that the limit of a distance-based inconsistency reduction process is a matrix induced by the vector of geometric means of rows when a distance-based inconsistent pairwise comparisons matrix is transformed into a consistent PC matrix by stepwise inconsistency reduction in triads. The distance-based inconsistency indicator was defined by Koczkodaj (1993) for pairwise comparisons. Its convergence was analyzed in 1996 (regretfully, with an incomplete proof) and finally completed in 2010. However, there was no interpretation provided for the limit of convergence despite its considerable importance. This study also demonstrates that the vector of geometric means and the right principal eigenvector are linearly independent for the pairwise comparisons matrix size greater than three, although both vectors are identical (when normalized) for a consistent PC matrix of any size.