Stabilization of an uncertain multiple-oscillator system

For a multiple-oscillator system that is subject to the uncertain gains ranging within compact sets, this paper presents a constructive stabilization design. Motivated by nested-saturation control methods, a nested controller that contains multiplicative coefficients is directly designed, and these coefficients are then determined in the stability analysis. By skillfully making transformations, elaborately constructing Lyapunov functions, and using an M-matrix principle, the stability analysis leads to the explicit inequality condition that is expressed by directly using the system parameters.     

Robust graph coloring based on the matrix semi-tensor product with application to examination timetabling

This paper investigates the robust graph coloring problem with application to a kind of examination timetabling by using the matrix semi-tensor product, and presents a number of new results and algorithms. First, using the matrix semi-tensor product, the robust graph coloring is expressed into a kind of optimization problem taking in an algebraic form of matrices, based on which an algorithm is designed to find all the most robust coloring schemes for any simple graph. Second, an equivalent problem of robust graph coloring is studied, and a necessary and sufficient condition is proposed, from which a new algorithm to find all the most robust coloring schemes is established. Third, a kind of examination timetabling is discussed by using the obtained results, and a method to design a practicable timetabling scheme is presented. Finally, the effectiveness of the results/algorithms presented in this paper is shown by two illustrative examples.     

A new neural network algorithm for planarization problems

To deal with the planarization problem widely used in many applications including routing very-large-scale integration （VLSI） circuits, this paper points out that only when its vertices are arranged in some specific order in a line can a planar graph be embedded on a line without any cross connections or cross edges. Energy function is proposed to meet the need of embedding a graph on a single line and route it correctly. A Hopfield network is designed according to the proposed energy function for such embedding and routing. The advantage of the proposed method is that it not only can detect if a graph is a planar one or not, but also can embed a planar graph or the maximal planar subgraph of a non-planar graph on a single line. In addition, simulated annealing is employed for helping the network to escape from local minima during the running of the Hopfield network. Experiments of the proposed method and its comparison with some existent conventional methods were performed and the results indicate that the proposed method is of great feasibility and effectiveness especially for the planarization problem of large graphs.     

Graph-Theoretic Approach to Network Analysis

Networks are a class of general systems represented by becomes a weighted graph visualizing the constraints imposed their UC-structure. Suppressing the nature of elements the network by interconnections rather than the elements themselves. These constraints follow generalized Kirchhoff＇s laws derived from physical constraints. Once we have a graph; then the working environment becomes the graph-theory. An algorithm derived from graph theory is developed within the paper in order to analyze general networks. The algorithm is based on computing all the spanning trees in the graph G with an associated weight. This weight is the product ofadmittance＇s of the edges forming the spanning tree. In the first phase this algorithm computes a depth first spanning tree together with its cotree. Both are used as parents for controlled generation of off-springs. The control is represented in selecting the off-springs that were not generated previously. While the generation of off-springs, is based on replacement of one or more tree edges by cycle edges corresponding to cotree edges. The algorithm can generate a frequency domain analysis of the network.     

Graph-based image segmentation using directional nearest neighbor graph

Graph-based image segmentation techniques generally represent the problem in terms of a graph. In this work, we present a novel graph, called the directional nearest neighbor graph. The construction principle of this graph is that each node corresponding to a pixel in the image is connected to a fixed number of nearest neighbors measured by color value and the connected neighbors are distributed in four directions. Compared with the classical grid graph and the nearest neighbor graph, our method can capture low-level texture information using a less-connected edge topology. To test the performance of the proposed method, a comparison with other graph-based methods is carried out on synthetic and real-world images. Results show an improved segmentation for texture objects as well as a lower computational load.     

On-board torquemanagement approach to the E-COSM benchmark problem with a prediction-based engine assignment

This paper proposes an energy management strategy for the benchmark problem of E-COSM 2021 to improve the energy efficiency of hybrid electric vehicles (HEVs) on a road with a slope. We assume that HEVs are in a connected environment with real-time vehicle-to-everything information, including geographic information, vehicle-to-infrastructure information and vehicle-to-vehicle information. The benchmark problem to be solved is based on HEV powertrain control using traffic information to achieve fuel economy improvements while satisfying the constraints of driving safety and travel time. The proposed strategy includes multiple rules and model predictive control (MPC). The rules of this strategy are designed based on external environment information to maintain safe driving and to determine the driving mode. To improve fuel economy, the optimal energy management strategy is primarily considered, and to perform real-time energy management via RHC-based optimization in a connected environment with safety constraints, a key issue is to predict the dynamics of the preceding vehicle during the targeted horizon. Therefore, this paper presents a real-time model-based optimization strategy with learning-based prediction of the vehicle’s future speed. To validate the proposed optimization strategy, a powertrain control simulation platform in a traffic-in-the-loop environment is constructed, and case study results performed on the constructed platform are reported and discussed.     

Balance properties and stabilization of min-max systems

A variety of problems in operations research, performance analysis, manufacturing, and communication networks, etc., can be modelled as discrete event systems with minimum and maximum constraints. When such systems require only maximum constraints (or dually, only minimum constraints), they can be studied using linear methods based on max-plus algebra. Systems with mixed constraints are called min-max systems in which min, max and addition operations appear simultaneously. A significant amount of work on such systems can be seen in literature. In this paper we provide some new results with regard to the balance problem of min-max functions; these are the structure properties of min-max systems. We use these results in the structural stabilization. Our main results are two sufficient conditions for the balance and one sufficient condition for the structural stabilization. The block technique is used to analyse the structure of the systems. The proposed methods, based on directed graph and max-plus algebra are constructive in nature. We provide several examples to demonstrate how the methods work in practice.     

Crosstalk-Aware Routing Resource Assignment

Crosstalk noise is one of the emerging issues in deep sub-micrometer technology which causes many undesired effects on the circuit performance. In this paper, a Crosstalk-Aware Routing Resource Assignment (CARRA) algorithm is proposed, which integrates the routing layers and tracks to address the crosstalk noise issue during the track/layer assignment stage. The CARRA problem is formulated as a weighted bipartite matching problem and solved using the linear assignment algorithm. The crosstalk risks between nets are represented by an undirected graph and the maximum number of the concurrent crosstalk risking nets is computed as the max clique of the graph. Then the nets in each max clique are assigned to disadjacent tracks. Thus the crosstalk noise can be avoided based on the clique concept. The algorithm is tested on IBM benchmarks and the experimental results show that it can improve the final routing layout a lot with little loss of the completion rate.     

Strong observability as a sufficient condition for non-singularity and lossless convexification in optimal control with mixed constraints

This paper analyzes optimal control problems with linear time-varying dynamics defined on a smooth manifold in addition to mixed constraints and pure control constraints. The main contribution is the identification of sufficient conditions for the optimal controls to be non-singular, which enables exact (or lossless) convex relaxations of the control constraints. The problem is analyzed in a geometric framework using a recent maximum principle on manifolds, and it is shown that strong observability of the dual system on the cotangent space is the key condition. Two minimum time problems are analyzed and solved. A minimum fuel planetary descent problem is then analyzed and relaxed to a convex form. Convexity enables its efficient solution in less than one second without any initial guess.     

Distributed robust MPC for nonholonomic robots with obstacle and collision avoidance

Considering that the inevitable disturbances and coupled constraints pose an ongoing challenge to distributed control algorithms, this paper proposes a distributed robust model predictive control (MPC) algorithm for a multi-agent system with additive external disturbances and obstacle and collision avoidance constraints. In particular, all the agents are allowed to solve optimization problems simultaneously at each time step to obtain their control inputs, and the obstacle and collision avoidance are accomplished in the context of full-dimensional controlled objects and obstacles. To achieve the collision avoidance between agents in the distributed framework, an assumed state trajectory is introduced for each agent which is transmitted to its neighbors to construct the polyhedral over-approximations of it. Then the polyhedral over-approximations of the agent and the obstacles are used to smoothly reformulate the original nonconvex obstacle and collision avoidance constraints. And a compatibility constraint is designed to restrict the deviation between the predicted and assumed trajectories. Moreover, recursive feasibility of each local MPC optimization problem with all these constraints derived and input-to-state stability of the closed-loop system can be ensured through a sufficient condition on controller parameters. Finally, simulations with four agents and two obstacles demonstrate the efficiency of the proposed algorithm.     

模型转换中特性保持的描述与验证

模型转换主要用于模型的演化、求精以及重构.模型转换需要遵循一定的约束规则以保持模型的某些特性.模型演化通常要求保持已有的接口;模型重构则必须保证重构前后的软件具有相同的外部行为特性.为了严格证明某个模型转换规则是否满足这些约束,特性保持约束必须形式化地加以描述.为了实现证明过程的自动化,需要总结通用的证明过程并给出实现算法.提出了一种基于图转换的特性保持约束描述机制,将模型演化与重构中的转换规则以及特性保持约束都描述为图转换规则.借助图转换的冲突检测机制,给出了严格证明转换规则是否满足特性保持约束的算法.     

Formal foundation of consistent EMF model transformations by algebraic graph transformation

Model transformation is one of the key activities in model-driven software development. An increasingly popular technology to define modeling languages is provided by the Eclipse Modeling Framework (EMF). Several EMF model transformation approaches have been developed, focusing on different transformation aspects. To validate model transformations with respect to functional behavior and correctness, a formal foundation is needed. In this paper, we define consistent EMF model transformations as a restricted class of typed graph transformations using node type inheritance. Containment constraints of EMF model transformations are translated to a special kind of graph transformation rules such that their application leads to consistent transformation results only. Thus, consistent EMF model transformations behave like algebraic graph transformations and the rich theory of algebraic graph transformation can be applied to these EMF model transformations to show functional behavior and correctness. Furthermore, we propose parallel graph transformation as a suitable framework for modeling EMF model transformations with multi-object structures. Rules extended by multi-object structures can specify a flexible number of recurring structures. The actual number of recurring structures is dependent on the application context of such a rule. We illustrate our approach by selected refactorings of simplified statechart models. Finally, we discuss the implementation of our concepts in a tool environment for EMF model transformations.     

Change-driven model transformations

In this paper, we investigate change-driven model transformations, a novel class of transformations, which are directly triggered by complex model changes carried out by arbitrary transactions on the model (e.g. editing operation, transformation, etc). After a classification of relevant change scenarios, we identify challenges for change-driven transformations. As the main technical contribution of the current paper, we define an expressive, high-level language for specifying change-driven transformations as an extension of graph patterns and graph transformation rules. This language generalizes previous results on live model transformations by offering trigger events for arbitrarily complex model changes, and dedicated reactions for specific kinds of changes, making this way the concept of change to be a first-class citizen of the transformation language. We discuss how the underlying transformation engine needs to be adapted in order to use the same language uniformly for different change scenarios. The technicalities of our approach will be discussed on a (1) model synchronization case study with non-materialized target models and (2) a case study on detecting the violation of evolutionary (temporal) constraints in the security requirements engineering domain.     

Propagation of constraints along model transformations using triple graph grammars and borrowed context

Fundamental properties of model transformations based on triple graph grammars (TGGs) have been studied extensively including syntactical correctness, completeness, termination and functional behavior. But up to now, it is an open problem how domain specific properties that are valid for a source model can be preserved along model transformations such that the transformed properties are valid for the derived target model. This question shows up in enterprise modeling. Here, modeling activities related to different domains are handled by different parties, and their models need to be consistent and integrated into one holistic enterprise model later on. So, support for decentralized modeling processes is needed. One technical aspect of the needed support in this case is the (bidirectional) propagation of constraints because that enables one party to understand and check the constraints of another party. Therefore, we analyze in the framework of TGGs how to propagate constraints from a source model to an integrated model and, afterwards, to a target model, such that, whenever the source model satisfies the source constraint, also the integrated and target model satisfy the corresponding integrated and target constraint. In our main new results we show under which conditions this is possible.     

Bridging the gap between formal semantics and implementation of triple graph grammars

The correctness of model transformations is a crucial element for model-driven engineering of high-quality software. A prerequisite to verify model transformations at the level of the model transformation specification is that an unambiguous formal semantics exists and that the implementation of the model transformation language adheres to this semantics. However, for existing relational model transformation approaches, it is usually not really clear under which constraints particular implementations really conform to the formal semantics. In this paper, we will bridge this gap for the formal semantics of triple graph grammars (TGG) and an existing efficient implementation. While the formal semantics assumes backtracking and ignores non-determinism, practical implementations do not support backtracking, require rule sets that ensure determinism, and include further optimizations. Therefore, we capture how the considered TGG implementation realizes the transformation by means of operational rules, define required criteria, and show conformance to the formal semantics if these criteria are fulfilled. We further outline how static and runtime checks can be employed to guarantee these criteria.     

The Train Benchmark: cross-technology performance evaluation of continuous model queries

In model-driven development of safety-critical systems (like automotive, avionics or railways), well-formedness of models is repeatedly validated in order to detect design flaws as early as possible. In many industrial tools, validation rules are still often implemented by a large amount of imperative model traversal code which makes those rule implementations complicated and hard to maintain. Additionally, as models are rapidly increasing in size and complexity, efficient execution of validation rules is challenging for the currently available tools. Checking well-formedness constraints can be captured by declarative queries over graph models, while model update operations can be specified as model transformations. This paper presents a benchmark for systematically assessing the scalability of validating and revalidating well-formedness constraints over large graph models. The benchmark defines well-formedness validation scenarios in the railway domain: a metamodel, an instance model generator and a set of well-formedness constraints captured by queries, fault injection and repair operations (imitating the work of systems engineers by model transformations). The benchmark focuses on the performance of query evaluation, i.e. its execution time and memory consumption, with a particular emphasis on reevaluation. We demonstrate that the benchmark can be adopted to various technologies and query engines, including modeling tools; relational, graph and semantic databases. The Train Benchmark is available as an open-source project with continuous builds from https://github.com/FTSRG/trainbenchmark.     

Parametrizing and graphing nonsingular cubic curves

Elliptic functions are used to parametrize and graph nonsingular cubic curves. First, a sequence of transformations is derived that reduces a third degree equation to a standard equation. A parametrization in terms of elliptic functions is given for the graph of the standard equation. The transformations convert this parametrization to a parametrization of the graph of the given equation. The details of using this parametrization for computer graphing are presented.     

基于图切割的图像自动分割方法

针对图切割在图像分割中的研究主要集中于交互式图像分割,提出一种基于图切割,对彩色图像和灰度图像均可进行自动分割的方法。通过对图像进行初始化,建立能量函数的数据项、光滑项,图切割求解及迭代执行等步骤自动实现图像的分割,既无需用户人工交互进行约束,也无需对图像建模及对数据分布进行估计,可以较快速度获得良好的分割结果。通过实验对彩色图像和灰度图像进行自动分割,实验结果验证该方法的有效性。     

Modeling and Verifying Graph Transformations in Proof Assistants

This paper takes first steps towards a formalization of graph transformations in a general setting of interactive theorem provers, which will form the basis for proofs of correctness of graph transformation systems. Whereas graph rewriting is usually performed by mapping a pattern graph into a source graph by means of a graph morphism and then carrying out operations on the image node and edge set, this article generalises the notion of pattern graph to path expressions, which are formulae in a fragment of first-order logic. We examine the correspondence with traditional graph rewriting and show that this interpretation is beneficial when formally reasoning about model transformations with the aid of proof assistants.     

Introducing requirements traceability support in model-driven development of web applications

In this work, we present an approach that introduces requirements traceability capabilities in the context of model-driven development of Web applications. This aspect allows us to define model-to-model transformations that not only provide a software artifact of lower abstraction (as model-to-model transformations usually do) but also to provide feedback about how they are applied. This feedback helps us to validate whether transformations are correctly applied. In particular, we present a model-to-model transformation that allows us to obtain navigational models of the Web engineering method OOWS from a requirements model. This transformation is defined as a set of mappings between these two models that have been implemented by means of graph transformations. The use of graph transformations allows us to develop a tool-supported strategy for applying mappings automatically. In addition, mechanisms for tracing requirements are also included in the definition of graph transformations. These mechanisms allow us to link each conceptual element to the requirements from which it is derived. In particular, we focus on tracing requirements throughout the navigational model, which describe the navigational structure of a Web application. To take advantage of these traceability mechanisms, we have developed a tool that obtains traceability reports after applying transformations. These reports help us to study aspects such as whether requirements are all supported, the impact of changing a requirement, or how requirements are modelled.