Volumen 24 (2014): Heft 4 (December 2014)

In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo’s fixed point theorem. Examples are included to verify the result.

In a Hilbert space setting, necessary and sufficient conditions for the minimum norm solution u to the equation Su = Rz to be continuously dependent on z are given. These conditions are used to study the continuity of minimum energy and linear-quadratic control problems for infinite dimensional linear systems with fixed endpoints.

Necessary and sufficient conditions for the positivity and reachability of fractional descriptor positive discrete-time linear systems are established. The minimum energy control problem for descriptor positive systems is formulated and solved. Sufficient conditions for the existence of a solution to the minimum energy control problem are given. A procedure for computation of optimal input sequences and a minimal value of the performance index is proposed and illustrated by a numerical example.

Remarkable improvements in the stability properties of discrete system zeros may be achieved by using a new design of the fractional-order hold (FROH) circuit. This paper first analyzes asymptotic behaviors of the limiting zeros, as the sampling period T tends to zero, of the sampled-data models on the basis of the normal form representation for continuous-time systems with a new hold proposed. Further, we also give the approximate expression of limiting zeros of the resulting sampled-data system as power series with respect to a sampling period up to the third order term when the relative degree of the continuous-time system is equal to three, and the corresponding stability of the discretization zeros is discussed for fast sampling rates. Of particular interest are the stability conditions of sampling zeros in the case of a new FROH even though the relative degree of a continuous-time system is greater than two, whereas the conventional FROH fails to do so. An insightful interpretation of the obtained sampled-data model can be made in terms of minimal intersample ripple by design, where multirate sampled systems have a poor intersample behavior. Our results provide a more accurate approximation for asymptotic zeros, and certain known results on asymptotic behavior of limiting zeros are shown to be particular cases of the ideas presented here.

The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.

The maximal value of the error is the most important criterion in system design. It is also the most difficult one. For that reason there exist many other criteria. The extreme value of the error represents the attainable accuracy which can be obtained and the corresponding extreme time gives information about how fast the transients are. The extreme values of the error and the corresponding time are treated here as functions of the roots of the characteristic equation. The proposed analytical formulae allow designing systems with prescribed dynamic properties.

This paper examines the problem of designing a robust H_∞ fuzzy controller with D-stability constraints for a class of nonlinear dynamic systems which is described by a Takagi-Sugeno (TS) fuzzy model. Fuzzy modelling is a multi-model approach in which simple sub-models are combined to determine the global behavior of the system. Based on a linear matrix inequality (LMI) approach, we develop a robust H_∞ fuzzy controller that guarantees (i) the L₂-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, and (ii) the closed-loop poles of each local system to be within a specified stability region. Sufficient conditions for the controller are given in terms of LMIs. Finally, to show the effectiveness of the designed approach, an example is provided to illustrate the use of the proposed methodology.

The paper considers the problem of active fault diagnosis for discrete-time stochastic systems over an infinite time horizon. It is assumed that the switching between a fault-free and finitely many faulty conditions can be modelled by a finite-state Markov chain and the continuous dynamics of the observed system can be described for the fault-free and each faulty condition by non-linear non-Gaussian models with a fully observed continuous state. The design of an optimal active fault detector that generates decisions and inputs improving the quality of detection is formulated as a dynamic optimization problem. As the optimal solution obtained by dynamic programming requires solving the Bellman functional equation, approximate techniques are employed to obtain a suboptimal active fault detector.

This paper considers the problem of attitude sensor fault diagnosis in a quadrotor helicopter. The proposed approach is composed of two stages. The first one is the modelling of the system attitude dynamics taking into account the induced communication constraints. Then a robust fault detection and evaluation scheme is proposed using a post-filter designed under a particular design objective. This approach is compared with previous results based on the standard Kalman filter and gives better results for sensor fault diagnosis.

In this paper, we propose a control Lyapunov function based on a nonlinear controller for a turbocharged diesel engine. A model-based approach is used which predicts the experimentally observed engine performance for a biodiesel. The basic idea is to develop an inverse optimal control and to employ a Lyapunov function in order to achieve good performances. The obtained controller gain guarantees the global convergence of the system and regulates the flows for the variable geometry turbocharger as well as exhaust gas recirculation systems in order to minimize the NO_x emission and the smoke of a biodiesel engine. Simulation of the control performances based on professional software and experimental results show the effectiveness of this approach.

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.

In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage of certain values for feedback and delay parameters allows simulating the heart action when an accessory conducting pathway is present (Wolff-Parkinson-White syndrome).

The paper offers a new approach to handling difficult parametric inverse problems in elasticity and thermo-elasticity, formulated as global optimization ones. The proposed strategy is composed of two phases. In the first, global phase, the stochastic hp-HGS algorithm recognizes the basins of attraction of various objective minima. In the second phase, the local objective minimizers are closer approached by steepest descent processes executed singly in each basin of attraction. The proposed complex strategy is especially dedicated to ill-posed problems with multimodal objective functionals. The strategy offers comparatively low computational and memory costs resulting from a double-adaptive technique in both forward and inverse problem domains. We provide a result on the Lipschitz continuity of the objective functional composed of the elastic energy and the boundary displacement misfits with respect to the unknown constitutive parameters. It allows common scaling of the accuracy of solving forward and inverse problems, which is the core of the introduced double-adaptive technique. The capability of the proposed method of finding multiple solutions is illustrated by a computational example which consists in restoring all feasible Young modulus distributions minimizing an objective functional in a 3D domain of a photo polymer template obtained during step and flash imprint lithography.

In this paper, application of an evolutionary strategy to positioning a GI/M/1/N-type finite-buffer queueing system with exhaustive service and a single vacation policy is presented. The examined object is modeled by a conditional joint transform of the first busy period, the first idle time and the number of packets completely served during the first busy period. A mathematical model is defined recursively by means of input distributions. In the paper, an analytical study and numerical experiments are presented. A cost optimization problem is solved using an evolutionary strategy for a class of queueing systems described by exponential and Erlang distributions.

Backtrack-style exhaustive search algorithms for NP-hard problems tend to have large variance in their runtime. This is because “fortunate” branching decisions can lead to finding a solution quickly, whereas “unfortunate” decisions in another run can lead the algorithm to a region of the search space with no solutions. In the literature, frequent restarting has been suggested as a means to overcome this problem. In this paper, we propose a more sophisticated approach: a best-firstsearch heuristic to quickly move between parts of the search space, always concentrating on the most promising region. We describe how this idea can be efficiently incorporated into a backtrack search algorithm, without sacrificing optimality. Moreover, we demonstrate empirically that, for hard solvable problem instances, the new approach provides significantly higher speed-up than frequent restarting.

We present a primal sub-gradient method for structured SVM optimization defined with the averaged sum of hinge losses inside each example. Compared with the mini-batch version of the Pegasos algorithm for the structured case, which deals with a single structure from each of multiple examples, our algorithm considers multiple structures from a single example in one update. This approach should increase the amount of information learned from the example. We show that the proposed version with the averaged sum loss has at least the same guarantees in terms of the prediction loss as the stochastic version. Experiments are conducted on two sequence labeling problems, shallow parsing and part-of-speech tagging, and also include a comparison with other popular sequential structured learning algorithms.

In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To present our statement, we use Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN, there exists a Փ strictly positive m vector such that A_Փ≤ 0. The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is designed for practical applications, guarantees that anomalies can be detected without domain knowledge, and can be easily implemented into existing commercial systems that do not support the verification of workflows. The validity of the proposed method is successfully demonstrated by application examples.

The work concerns formal verification of workflow-oriented software models using the deductive approach. The formal correctness of a model’s behaviour is considered. Manually building logical specifications, which are regarded as a set of temporal logic formulas, seems to be a significant obstacle for an inexperienced user when applying the deductive approach. A system, along with its architecture, for deduction-based verification of workflow-oriented models is proposed. The process inference is based on the semantic tableaux method, which has some advantages when compared with traditional deduction strategies. The algorithm for automatic generation of logical specifications is proposed. The generation procedure is based on predefined workflow patterns for BPMN, which is a standard and dominant notation for the modeling of business processes. The main idea behind the approach is to consider patterns, defined in terms of temporal logic, as a kind of (logical) primitives which enable the transformation of models to temporal logic formulas constituting a logical specification. Automation of the generation process is crucial for bridging the gap between the intuitiveness of deductive reasoning and the difficulty of its practical application when logical specifications are built manually. This approach has gone some way towards supporting, hopefully enhancing, our understanding of deduction-based formal verification of workflow-oriented models.