On exponential stability for linear discrete-time systems in Banach spaces

In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical results due to Barbashin [6] and Datko [5]. An illustrative example clarifies the relations between these concepts.     

The utility of rapid application development in large-scale, complex projects

This paper describes an investigation into the utility of an agile development approach known as rapid application development (RAD) within a large-scale development project conducted within the public sector in the UK. Features of RAD as an 'agile' information systems development method (ISDM) are discussed and previous research identifying properties of development environments most conducive to its application are described. A case study is then presented based upon a long-term qualitative investigation of the 'unbundling' of a commercial RAD-like ISDM. The evidence from this case leads us to question established wisdom in relation to appropriate adoption and application of agile development within large-scale and complex development environments.     

Second-order duality for a non-differentiable minimax programming in complex spaces

In this paper, a second-order dual problem for a non-differentiable minimax complex programming problem is formulated. The weak, strong, and strict converse duality theorems are constructed under generalized Θ-bonvexity assumptions. This means that there are no duality gaps between primary problem and its dual problem.     

Covering arrays for efficient fault characterization in complex configuration spaces

Many modern software systems are designed to be highly configurable so they can run on and be optimized for a wide variety of platforms and usage scenarios. Testing such systems is difficult because, in effect, you are testing a multitude of systems, not just one. Moreover, bugs can and do appear in some configurations, but not in others. Our research focuses on a subset of these bugs that are "option-related"-those that manifest with high probability only when specific configuration options take on specific settings. Our goal is not only to detect these bugs, but also to automatically characterize the configuration subspaces (i.e., the options and their settings) in which they manifest. To improve efficiency, our process tests only a sample of the configuration space, which we obtain from mathematical objects called covering arrays. This paper compares two different kinds of covering arrays for this purpose and assesses the effect of sampling strategy on fault characterization accuracy. Our results strongly suggest that sampling via covering arrays allows us to characterize option-related failures nearly as well as if we had tested exhaustively, but at a much lower cost. We also provide guidelines for using our approach in practice.     

The particle swarm - explosion, stability, and convergence in amultidimensional complex space

The particle swarm is an algorithm for finding optimal regions of complex search spaces through the interaction of individuals in a population of particles. This paper analyzes a particle's trajectory as it moves in discrete time (the algebraic view), then progresses to the view of it in continuous time (the analytical view). A five-dimensional depiction is developed, which describes the system completely. These analyses lead to a generalized model of the algorithm, containing a set of coefficients to control the system's convergence tendencies. Some results of the particle swarm optimizer, implementing modifications derived from the analysis, suggest methods for altering the original algorithm in ways that eliminate problems and increase the ability of the particle swarm to find optima of some well-studied test functions     

Simplex sliding mode control for autonomous six‐DOF vehicles with mono‐directional actuators: Robustness,stability, and implementation issues

The position and attitude control of a six‐degree‐of‐freedom vehicle is dealt with in this paper. The actuation system is assumed to consist of a set of mono‐directional devices suitably located and directed. The model of the system is characterized by a large amount of uncertainties, disturbances and measurement errors. The state is assumed fully available and the navigation problems generating smooth references for the state trajectories are supposed already solved. A new attitude guidance algorithm has been developed to enhance robustness with respect to a class of nonsmooth measurement errors. The use of the simplex‐based sliding mode methodology reveals to be simultaneously suitable for the design of the actuation system (position and orientation of the actuators) and the implementation of the control strategy. The chattering phenomenon is strongly attenuated by the introduction of integrators in the input channel and, consequently to this choice, a suitable mechanism to avoid the unbounded growth of the individual thrust of the actuators is designed, while at the same time, achieving a direct control of power losses. The performances of the proposed control scheme are demonstrated by simulation by using mathematical models available in the literature.     

Two necessary conditions for a complex polynomial to be strictlyHurwitz and their applications in robust stability analysis

The necessary conditions for a complex polynomial to be strictly Hurwitz are reviewed and rigorously proved. Both necessary conditions have been extended to cover nonmonic polynomials instead of monic polynomials. Also, based on these two results, some necessary conditions for an interval polynomial to be stable in terms of being strictly Hurwitz are obtained. They can be used to quickly determine the instability of a complex interval polynomial family. Finally, their application to the study of robust stability, in the case where coefficient perturbation intervals are functions of a single parameter, is briefly discussed     

Consistency issues for numerical methods for variance control, withapplications to optimization in finance

The paper is concerned with numerical algorithms for the optimal control of diffusion-type processes when the noise variance also depends on the control. This problem is of increasing importance in applications, particularly in financial mathematics. We discuss the construction of numerical algorithms guaranteed to converge to the true minimum as the discretization level decreases and with acceptable numerical properties. The algorithms are based on the popular Markov chain approximation method. The basic criterion the algorithms must satisfy is a weak “local consistency” condition, which is essential for convergence to the true optimal cost function. This condition is often hard to satisfy by simple algorithms (with essentially only local transitions) when the variance is also controlled. Numerical “noise” can be introduced by the more convenient approximations. This question of “numerical noise” (also called “numerical viscosity”) is dealt with in detail, and methods for eliminating or greatly reducing it are discussed     

Human-machine dynamics in complex information systems: the 'microworld' paradigm as a heuristic tool for developing theory and exploring design issues

Abstract. The term 'complex informated domain' refers to a work environment characterized by high complexity and onerous cognitive demands, in which the management of a remote process is mediated by an information system (IS). Such work environments are typical of highly technical domains, such as industrial process control, but as computer-based information systems penetrate ever deeper into modern businesses, all organizations are taking on the same 'informated' characteristics. This paper reports an experiment using a rich simulation ('a microworld'), which attempted to throw light on human–machine dynamics in such complex environments. Two issues were investigated: the state of the subject (fatigue induced by sleep loss) and the degree of operator control (empowerment) afforded by the IS interface. Results showed that sleep deprivation led to no degradation in overt performance but, contrary to expectations, lower performance was associated with high control operation. A detailed qualitative analysis showed the high control interface to encourage a more proactive control style, whereas fatigue intensified primitive, reactive strategies. The findings emphasize that cognition is a goal-directed, adaptive system not simply an information-processing mechanism. A model of cognitive dynamics is outlined that distinguishes a hierarchy of control levels: anxiety defences, reactive control and strategic control. In general, the experiment shows the potential value to IS research of the microworld paradigm as a tool for developing theory and exploring key design issues.     

A converse Lyapunov theorem for, non-uniform in time, global exponential robust stability

Lyapunov-like characterizations are established for the concepts of, non-uniform in time, global exponential robust stability and input-to-state stability for time-varying control systems.     

Second-order, exact charge conservation for electromagnetic particle-in-cell simulation in complex geometry

A second-order, exact charge-conserving algorithm for accumulating charge and current on the spatial grid for electromagnetic particle-in-cell (EM-PIC) simulation in bounded geometry is presented. The algorithm supports standard EM-PIC exterior boundary conditions and complex internal conductors on non-uniform grids. Boundary surfaces are handled by smoothly transitioning from second to first-order weighting within half a cell of the boundary. When a particle is exactly on the boundary surface (either about to be killed, or just created), the weighting is fully first-order. This means that particle creation and particle/surface interaction models developed for first-order weighting do not need to be modified. An additional feature is the use of an energy-conserving interpolation scheme from the electric field on the grid to the particles. Results show that high-density, cold plasmas with ωpeΔt∼1, and Δx/λD?1, can be modeled with reasonable accuracy and good energy conservation. This opens up a significant new capability for explicit simulation of high-density plasmas in high-power devices.     

New exact solutions for modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces

With the use of some proper transformations and symbolic computation, we present a general and unified method for investigating the general modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces. The work formally shows how to construct the general solutions and some special exact-solutions for mK(m,n) equations in higher dimensional spatial domains. The general solutions not only contain the solutions by Wazwaz [Math. Comput. Simulation 59 (2002) 519] but also contain many new compact and noncompact solutions.     

Assessing the utility of airborne hyperspectral and LiDAR data for species distribution mapping in the coastal Pacific Northwest, Canada

To effectively manage forested ecosystems an accurate characterization of species distribution is required. In this study we assess the utility of hyperspectral Airborne Imaging Spectrometer for Applications (AISA) imagery and small footprint discrete return Light Detection and Ranging (LiDAR) data for mapping 11 tree species in and around the Gulf Islands National Park Reserve, in coastal South-western Canada. Using hyperspectral imagery yielded producer's and user's accuracies for most species ranging from > 52-95.4 and > 63-87.8%, respectively. For species dominated by definable growth stages, pixel-level fusion of hyperspectral imagery with LiDAR-derived height and volumetric canopy profile data increased both producer's (+ 5.1-11.6%) and user's (+ 8.4-18.8%) accuracies. McNemar's tests confirmed that improvements in overall accuracies associated with the inclusion of LiDAR-derived structural information were statistically significant (p < 0.05). This methodology establishes a specific framework for mapping key species with greater detail and accuracy then is possible using conventional approaches (i.e., aerial photograph interpretation), or either technology on its own. Furthermore, in the study area, acquisition and processing costs were lower than a conventional aerial photograph interpretation campaign, making hyperspectral/LiDAR fusion a viable replacement technology.     

Reinforcement learning for context awareness and intelligence in wireless networks: Review, new features and open issues

In wireless networks, context awareness and intelligence are capabilities that enable each host to observe, learn, and respond to its complex and dynamic operating environment in an efficient manner. These capabilities contrast with traditional approaches where each host adheres to a predefined set of rules, and responds accordingly. In recent years, context awareness and intelligence have gained tremendous popularity due to the substantial network-wide performance enhancement they have to offer. In this article, we advocate the use of reinforcement learning (RL) to achieve context awareness and intelligence. The RL approach has been applied in a variety of schemes such as routing, resource management and dynamic channel selection in wireless networks. Examples of wireless networks are mobile ad hoc networks, wireless sensor networks, cellular networks and cognitive radio networks. This article presents an overview of classical RL and three extensions, including events, rules and agent interaction and coordination, to wireless networks. We discuss how several wireless network schemes have been approached using RL to provide network performance enhancement, and also open issues associated with this approach. Throughout the paper, discussions are presented in a tutorial manner, and are related to existing work in order to establish a foundation for further research in this field, specifically, for the improvement of the RL approach in the context of wireless networking, for the improvement of the RL approach through the use of the extensions in existing schemes, as well as for the design and implementation of RL in new schemes.     

Managing water in complex systems: An integrated water resources model for Saskatchewan,Canada

Using a system dynamics approach, an integrated water resources system model is developed for scenario analysis of the Saskatchewan portion of the transboundary Saskatchewan River Basin in western Canada. The water resources component is constructed by emulating an existing Water Resources Management Model. Enhancements include an irrigation sub-model to estimate dynamic irrigation demand, including alternative potential evapotranspiration estimates, and an economic sub-model to estimate the value of water use for various sectors of the economy. Results reveal that the water resources system in Saskatchewan becomes increasingly sensitive to the selection of evapotranspiration algorithm as the irrigation area increases, due to competition between hydropower and agriculture. Preliminary results suggest that irrigation expansion would decrease hydropower production, but might increase the total direct economic benefits to Saskatchewan. However, indirect costs include reduction in lake levels and river flows.     

On necessary conditions for scale-freedom in complex networks,with applications to computer communication systems

Many complex networks exhibit a scale-free, power-law distribution of vertex degrees. This common feature is a consequence of two generic mechanisms relating to the formation of real networks: (i) networks tend to expand over time through the addition of new vertices and (ii) new vertices attach preferentially to those that are already well connected. We show that for many natural or man-made complex networks possessing a scale-free power-law distribution with the exponent γ ≥ 2, the number of degree-1 vertices, when nonzero, is of the same order as the network size N and that the average degree is of order at most log N. Our results expose another necessary characteristic of such networks. Furthermore, our method has the benefit of relying only on conditions that are static and easily verified for arbitrary networks. We use the preceding results to derive a closed-form formula approximating the distance distribution in scale-free networks. Such distributions are applied extensively in the fields of computer communication and software architecture, among other domains.     

Finite difference schemes on grids with local refinement in time and space for parabolic problems I. Derivation,stability, and error analysis

Finite difference schemes for parabolic initial value problems on cell-centered grids in space (rectangular for two space dimensions) with regular local refinement in space as in time are derived and their stability and convergence properties are studied. The construction of the finite difference schemes is based on the finite volume approach by approximation of the balance equation. Thus the derived schemes preserve the mass (or the heat). The approximation at the grid points near the fine and coarse grid interface is based on the approach proposed by the authors in a previous paper for selfadjoint elliptic equations. The proposed schemes are implicit of backward Euler type and are shown to be unconditionally stable. Error analysis is also presented.     

Decision aid system founded on nonlinear valuation,dispersion-based weighting and correlative aggregation for wire rope selection in slope stability cable nets

This paper presents a decision aid system to address hierarchically structured decision-making problems based on the determination of the satisfaction provided by a group of alternatives in relation to multiple conflicting subcriteria grouped into criteria. The system combines the action of three new methods related to the following concepts: nonlinear valuation, dispersion-based weighting and correlative aggregation. The first includes five value functions that allow the conversion of the ratings of the alternatives regarding the subcriteria into the satisfaction they produce in a versatile and simple manner through the Beta Cumulative Distribution Function. The use of measures of dispersion to weight the subcriteria by giving more importance to those factors that can make a difference due to their heterogeneity is revised to validate it when the values are not normally distributed. Dependencies between subcriteria are taken into account through the determination of their correlation coefficients, whose incorporation adjusts the results provided by the system to favour those alternatives having a balanced behaviour with respect to conflicting aspects. The overall satisfaction provided by each alternative is determined using a prioritisation operator to avoid compensation between criteria when aggregating the subcriteria. The system was tested through a novel field of application such as the selection of wire rope to form slope stability cable nets.