State observers for a class of multi-output nonlinear dynamic systems

This note considers the problem of observer design for a class of multi-output nonlinear systems. A new state observer design methodology for linear time-varying multi-output systems is presented. Furthermore, we show that the same methodology can be extended to a class of multi-output nonlinear systems. Some sufficient conditions for the existence of the proposed observer are obtained, which guarantee that the error of state estimation converges asymptotically to zero. An example is given to demonstrate the effectiveness of the proposed methodology.     

一类具有零动态不确定非线性系统的有限时间镇定问题

研究了一类带有零动态不确定非线性系统的有限时间镇定问题.基于有限时间稳定的Lyapunov理论和反推技术给出了一个状态反馈控制器的设计步骤,解决了这类不确定非线性系统的有限时间镇定问题.     

The Block Criterion for Multiscale Inference About a Density,With Applications to Other Multiscale Problems

The use of multiscale statistics, that is, the simultaneous inference about various stretches of data via multiple localized statistics, is a natural and popular method for inference about, for example, local qualitative characteristics of a regression function, a density, or its hazard rate. We focus on the problem of providing simultaneous confidence statements for the existence of local increases and decreases of a density and address several statistical and computational issues concerning such multiscale statistics. We first review the benefits of employing scale-dependent critical values for multiscale statistics and then derive an approximation scheme that results in a fast algorithm while preserving statistical optimality properties. The main contribution is a methodology for calibrating multiscale statistics that does not require a case-by-case derivation of its specific form. We show that in the above density context the methodology possesses statistical optimality properties and allows for a fast algorithm. We illustrate the methodology with two further examples: a multiscale statistic introduced by Gijbels and Heckman for inference about a hazard rate and local rank tests introduced by Dümbgen for inference in nonparametric regression.

Code for the density application is available as the R package modehunt on CRAN. Additional code to compute critical values, reproduce the hazard rate and local rank example and the plots in the paper as well as datasets containing simulation results and an appendix with all the proofs of the theorems are available online as supplemental material.     

Lyapunov redesign for a class of uncertain systems with delays

We address the robust stabilization problem of a general class of uncertain linear systems with multiple delays from a Lyapunov redesign (LR) methodology that relies on Sliding Mode Control (SMC) theory. The proposed approach, which is based on a well-known (yet not used for LR) class of Lyapunov–Krasovskii functionals, allows us to enlarge the type of uncertain systems with delays that can be stabilized. The uncertainties of the system are compensated within a delay-free sliding manifold that is taken from the time-derivative of the considered functional.     

泛系关系族的泛对称与不动泛系定理

本文在泛系方法论的框架下,将泛对称与不动泛系定理的一些结果推广到了二元关系族的情形.具体地讨论了对于有限论域上的一族二元关系何时存在公共的不动子集的问题,得到了几个确定二元关系族是否存在公共的不动子集的简括的判别定理.其结果推广了传统的不动点理论中有关映射族是否存在公共的不动点的主要判别定理——Markov-Kakutani定理.     

A Proper Generalized Decomposition for the solution of elliptic problems in abstract form by using a functional Eckart-Young approach

The Proper Generalized Decomposition (PGD) is a methodology initially proposed for the solution of partial differential equations (PDE) defined in tensor product spaces. It consists in constructing a separated representation of the solution of a given PDE. In this paper we consider the mathematical analysis of this framework for a larger class of problems in an abstract setting. In particular, we introduce a generalization of Eckart and Young theorem which allows to prove the convergence of the so-called progressive PGD for a large class of linear problems defined in tensor product Hilbert spaces.     

A qualitative mathematical analysis of a class of nonlinear differential equations: Applications in biochemistry

In this paper, we develop a mathematical approach which can be used to display, in a systematic, rigorous and efficient way, various qualitative properties of a large class of dynamical and quasi-steady biochemical models. The applicability of the methodology has been examined for various biochemical reactions, enzyme kinetics and multi enzyme systems.     

Asymptotic analysis of a volterra integral equation

A uniformly valid aymptotic solution is obtained for a class of perturbed Volterra integral equations, in which a naive expansion breaks down as t → ∞. The procedure used is an adaption of the formal methodology presented in [1] for the construction of a uniform asymptotic solution to Volterra equations which possess a boundary layer near t = 0.     

The set of numerical semigroups of a given genus

In this paper we present a new approach to construct the set of numerical semigroups with a fixed genus. Our methodology is based on the construction of the set of numerical semigroups with fixed Frobenius number and genus. An equivalence relation is given over this set and a tree structure is defined for each equivalence class. We also provide a more efficient algorithm based on the translation of a numerical semigroup to its so-called Kunz-coordinates vector.     

Lax pair, cyclic basis, and a new integrable system

A direct approach to zero-curvature representation, as introduced by Marvan is applied to generate a new class of integrable equations by starting with the generic Lax operator (x-part) for a coupled set of nonlinear equations. The class of equation so obtained is more general than those usually obtained with the help of standard recursion operator. Finally some particular type of equations are identified by the special choice of the arbitrary functions occurring in the final solution of the time part of the Lax equation. The methodology is specially useful when the x-part of the Lax operator does not contain any spectral parameter.     

Systemic decision making in AHP: a Bayesian approach

Systemic decision making is a new approach for dealing with complex multiactor decision making problems in which the actors’ individual preferences on a fixed set of alternatives are incorporated in a holistic view in accordance with the “principle of tolerance”. The new approach integrates all the preferences, even if they are encapsulated in different individual theoretical models or approaches; the only requirement is that they must be expressed as some kind of probability distribution. In this paper, assuming the analytic hierarchy process (AHP) is the multicriteria technique employed to rank alternatives, the authors present a new methodology based on a Bayesian analysis for dealing with AHP systemic decision making in a local context (a single criterion). The approach integrates the individual visions of reality into a collective one by means of a tolerance distribution, which is defined as the weighted geometric mean of the individual preferences expressed as probability distributions. A mathematical justification of this distribution, a study of its statistical properties and a Monte Carlo method for drawing samples are also provided. The paper further presents a number of decisional tools for the evaluation of the acceptance of the tolerance distribution, the construction of tolerance paths that increase representativeness and the extraction of the relevant knowledge of the subjacent multiactor decisional process from a cognitive perspective. Finally, the proposed methodology is applied to the AHP-multiplicative model with lognormal errors and a case study related to a real-life experience in local participatory budgets for the Zaragoza City Council (Spain).     

A novel methodology for uncertain nonlinear tracking control systems: Exponential convergence manifold approach

In this paper, we present a novel methodology, for exponential convergence manifold control (ECMC) methodology, to investigate the tracking control of a class of uncertain systems. An ECMC law will drive the plant’s error trajectory exponentially not only to a specific manifold in the error space, but also to the origin, if the exponential convergence condition is satisfied. A numerical example is also provided to illustrate the methodology.     

Synchronization for a class of complex dynamical networks with time-delay

In this study, the synchronization problem is addressed for a class of complex dynamical networks in which every identical node is a time-delayed Lur’e system. Delay-dependent and delay-independent synchronization criteria are established through a decoupling technique, which reduces a group of high-dimensional linear matrix inequalities (LMIs) to the test of two groups of lower-dimensional LMIs. An extension to the synchronization of discrete-time Lur’e networks with time delay is also studied. The efficiency and applicability of the proposed methodology is demonstrated by a numerical example through simulation.     

Estudio probabilista del daño por choque según la metodología PEER. Aplicación a un paso superior sísmicamente aislado

Bridges with deck supported either on sliding or elastomeric bearings are common in mid-seismicity regions. Pounding between deck and abutments is linked with their main seismic vulnerabilities, which can be assessed by estimating the probability of a given state of damage being reached in a given time period. This paper presents a state of the art methodology used to solve that problem, as well as its application to the assessment of the vulnerability of an overpass placed in Granada area (South-east of Spain), belonging to the previously mentioned typology.The Pacific Earthquake Engineering Research Center methodology will be adapted and applied. Their main steps will be briefly presented, although the identification and characterization of damage likely to occur will be described in more detail. The model of the structure, and specially pounding modeling, will also be detailed.Results are interesting since this bridge can be considered as a representative of a widespread class. The adapted methodology may be applied to similar structures. Also, probability values obtained may serve as benchmarks.     

Knowledge shifts in a probability classroom: a case study coordinating two methodologies

Knowledge shifts are essential in the learning process in the mathematics classroom. Our goal in this study is to better understand the mechanisms of such knowledge shifts, and the roles of the individuals (students and teacher) in realizing them. To achieve this goal, we combined two approaches/methodologies that are usually carried out separately: the Abstraction in Context approach with the RBC+C model commonly used for the analysis of processes of constructing knowledge by individuals and small groups of students; and the Documenting Collective Activity approach with its methodology commonly used for establishing normative ways of reasoning in classrooms. This combination revealed that some students functioned as “knowledge agents,” meaning that they were active in shifts of knowledge among individuals in a small group, or from one group to another, or from their group to the whole class or within the whole class. The analysis also showed that the teacher adopted the role of an orchestrator of the learning process and assumed responsibility for providing a learning environment that affords argumentation and interaction. This enables normative ways of reasoning to be established and enables students to be active and become knowledge agents.     

Operations research methodology life cycle trend phases as recorded in journal articles

This paper applies life cycle concepts to forecast and explore trends in the publication rates of operations research (OR) methodology journal articles. The confirmatory part of this study seeks to show the accuracy of life cycles to forecast a trend for a single OR methodology. The exploratory part of this study extends the use of life cycle forecasting to a broader collection of OR methodologies. This part of the study entails a collection of keywords for OR methodologies from over 8000 journal articles. The results show a life cycle can be used to forecast a trend in OR journal article methodology productivity based on keyword listings. This paper also reveals trends in methodology usage for leading OR journals in Europe and the US. The existence and use of life cycle trends in the OR methodology research have ramifications on new directions for research, research funding, and OR textbook content.     

Automated generation of LFT-based parametric uncertainty descriptions from generic aircraft models

A computer assisted modelling methodology is developed for the generation of linearized models with parametric uncertainties described by Linear Fractional Transformations (LFTs). The starting point of the uncertainty modelling is a class of generic nonlinear aircraft models with explicit parametric dependence used for simulation purposes. The proposed methodology integrates specialized software tools for object-oriented modelling, for simulation, and for numerical as well as symbolic computations. The methodology has many generic features being applicable to similar nonlinear model classes.     

The existence of minimal large positive solutions for a class of nonlinear cooperative systems

In this paper we establish the existence of the minimal large positive solution for a general class of nonlinear cooperative systems including the simplest prototype of García-Melián et al. (2016). Precisely, based on the existence of a large positive supersolution, we can infer the existence of the minimal large positive solution. Moreover, we also give some sufficient easily computable conditions for the existence of a large positive supersolution. Our results generalize, very substantially, some of the findings of García-Melián et al. (2016) adopting a rather novel methodology.     

Toward unified analysis and controller synthesis for a class of hybrid systems

This work defines a new class of hybrid systems called state-based switched (SBS) systems that have numerous important engineering applications. The characterizing feature of these systems is that the discrete-event dynamics are associated with the continuous-time state making a specific function be equal to zero. The choice of this function is application specific and for the closed-loop SBS systems defined in this paper it is related to the execution of a desired set of tasks from a pre-specified mission plan. For this broad class of SBS systems, the paper presents a unified analysis and controller synthesis methodology based on Lyapunov theory. Depending on the details of the mission plan, the closed-loop hybrid system will be divided into two subclasses: sequential and non-sequential. The controller design procedure for both subclasses consists of the same two steps: finding a control law and finding a stabilizing switching rule. For static state and output feedback of sequential hybrid systems, the paper proposes a new hybrid sequential sliding-mode controller. It is proven that the control mission can be accomplished for sequential hybrid systems under static state and output feedback using this new controller. A similar framework is investigated for the more complex class of nonsequential hybrid systems and a systematic procedure for designing the switching rule is presented for some specific instances of these systems.     

Composite indicator development using utility function and fuzzy theory

Construction companies use composite indicators (CIs) to evaluate their overall project performance. However, the conventional methodology of CIs development causes indiscrimination, relative calibration, and redundancy. To address these problems, we propose a novel methodology that uses fuzzy theories. The proposed methodology includes a utility function for normalizing, a fuzzy measure for weighting, and a fuzzy integral for aggregating. We conducted a case study to assess the quality of the proposed methodology versus the alternative methodologies on 25 real projects of a construction company. The result showed that the measurement reliability of the proposed normalization method (1.96) is greater than that of the two different normalization methods (10.44 and 2.8, respectively). In addition, the measurement accuracy of the proposed aggregation method is greater than those of the four different aggregation methods. Therefore, our proposed methodology can more consistently and accurately help evaluate the overall project performance or success.