Graph topology enhancement for text classification

Applied Intelligence - Graph neural networks (GNNs) can deal with complex network structures and model complex syntax structures in natural languages, which makes GNN outstanding in text...     

Extended topology and systems

In this paper is indicated the possible utility of isotonic spaces as a background language for discussing systems. In isotonic spaces the basic duality between neighborhood and convergent first achieves a proper background permitting applications beyond the scope of topological spaces. A generalization of continuity of mappings based on ancestral relations is presented and this definition is applied to establish a necessary and sufficient condition that mappings preserve connectedness. Fortunately for systems theory, it is not necessary to have infinite sets or infinitary operators to apply definitions of neighborhood, convergents, continuity and connectedness.This work was supported in part by a grant from the National Science Foundation.     

Windup prevention for unstable systems

Presented is a windup prevention method for linear, time-invariant, exponentially unstable systems with saturating input nonlinearity such that, given a linear nominal controller and disturbances of known maximum amplitudes, arbitrary reference input sequences do not cause closed loop instability.     

A topology for secure MVS systems

Ultimate protection of computers against programming users appears unachievable. True security seems within reach only within systems without programming users. However, programming has to be done within each computing centre. To meet these conflicting ends, this paper proposes a means of isolating any enterprise's vital data from abuse by fully mutually isolating systems at three security levels from one another.The approach proposed is already partly implemented in major computing centres, though with an effectiveness far from that required. Specifically, it is shown that shared DASD degrades the overall security level to that of the least secure system connected. A higher degree of security, as this paper suggests, is reachable in current systems by defining and implementing a three-level (minimal) topology as part of an overall security strategy.     

Dynamical systems and topology optimization

This paper uses a dynamical systems approach for studying the material distribution (density or SIMP) formulation of topology optimization of structures. Such an approach means that an ordinary differential equation, such that the objective function is decreasing along a solution trajectory of this equation, is constructed. For stiffness optimization two differential equations with this property are considered. By simple explicit Euler approximations of these equations, together with projection techniques to satisfy box constraints, we obtain different iteration formulas. One of these formulas turns out to be the classical optimality criteria algorithm, which, thus, is receiving a new interpretation and framework. Based on this finding we suggest extensions of the optimality criteria algorithm. A second important feature of the dynamical systems approach, besides the purely algorithmic one, is that it points at a connection between optimization problems and natural evolution problems such as bone remodeling and damage evolution. This connection has been hinted at previously but, in the opinion of the authors, not been clearly stated since the dynamical systems concept was missing. To give an explicit example of an evolution problem that is in this way connected to an optimization problem, we study a model of bone remodeling. Numerical examples, related to both the algorithmic issue and the issue of natural evolution represented as bone remodeling, are presented.     

Necessary and sufficient conditions for balancing unstable systems

Necessary and sufficient conditions are given for the existence of balancing transformations for minimal state-space realizations(A, B, C)whereAmay be unstable. These conditions are expressed in terms of the real diagonalizability of the product of the reachability Gramian and the observability Gramian. For symmetric realizations these conditions can be reformulated in terms of the real diagonalizability of the cross Gramian, and we show that minimal symmetric systems can be internally balanced if the associated Hankel matrix is positive semidefinite. Examples are given of minimal systems, including symmetric systems, which cannot be balanced.     

Fault detection and isolation for unstable linear systems

In the design of a residual generator for an unstable plant, the unstable modes are made unobservable from the residual vector. We point out that this cannot be achieved in practice due to the discrepancy between the estimated model and the “true” plant model. Hence, we deduce that it is not possible to design a residual generator for an unstable plant, unless it is stabilized by an adequate controller. As a by-product, we provide expressions which can be used to quantify the effect of modeling uncertainties on the performance of a residual generator. The factorization approach to control theory is used for the developments     

多智能体系统一致性问题的控制器与拓扑协同优化设计

本文考虑多智能体系统一致性问题的控制与拓扑协同优化设计.首先在给定的二次性能指标下,对多智能体系统的分布式一致性控制协议寻优,得到依赖于网络拓扑图拉普拉斯矩阵的最优控制器.其次,为进一步最大限度地减少拓扑之间的连边,又不降低多智能体系统的收敛速度,通过权衡系统的通信能量和控制能量,寻求网络拓扑的优化设计,给出了拓扑优化算法和多智能体系统特征值的优化方法.最后,仿真研究验证了在控制器优化的基础上进一步寻求拓扑优化,可大大提升系统的一致性性能.     

Graph rewriting systems for the entity-relationship approach

Sequential graph rewriting systems are proposed as a meta-level formalism providing the concise and sound definition of different ER diagram languages. These rewriting systems can be used to define ER-based approaches for various DB modelling subtasks like schema design, evolution and integration. In addition, they are a natural choice for syntax directed ER CASE workbenches. In particular, by using specialized ER graph rewriting systems as meta input for CASE tools, the resulting tool behavior can be guided and controlled. Moreover, grammar driven modelling tools can be easily adapted for the needs of a particular enterprise or software factory without superimposing a particular ER dialect on the end users. Additional benefits result from the use of ER graph rewriting systems as a comparison framework for the continuously enlarging set of ER dialects.

The presentation includes material on the ER graph rewriting formalism, i.e., the actual tool, as well as an introduction to some formal graph rewriting prerequisites. An exemplary application, in particular ER graph generation, is used to clarify the underlying formal concepts.     

Balancing transformations for unstable nonminimal linear systems

It is shown that an unstable nonminimal continuous (discrete) realization (A, B, C) can be transformed via a similarity transformation into a balanced one if and only if the product of the controllability, observability Gramians is similar to a real diagonal matrix Λ. If, in addition, the eigenvalues of A , say λ, satisfy the relation λ_i+λ _j≠0(λ_iλ_j≠1) then the matrix Λ will always be positive semidefinite, and a balanced realization with its minimal part in the internally balanced form can always be obtained     

A versatile controller design software for unstable systems

A new software utility for use with linear unstable plants is developed. The software is in the Matlab environment, and it is based on Youla parameterization. The software optimizes the location of all coprime factors. A two-layer optimization approach is used to arrive at the desired controller. At the inner layer, an exact model-matching optimization procedure is utilized, and a stable design is obtained. This optimization process is then placed inside a nonlinear optimization routine to optimize the assumed locations of the poles of the coprime factors. The software is applied to an unstable plant, and the results are compared with two other techniques.     

Path-following for linear systems with unstable zero dynamics

A constructive solution to the path-following problem for MIMO linear systems with unstable zero dynamics is developed. While the original control variable steers the system output along the path, the path parameter θ is used as an additional control to stabilize zero dynamics with a feedback law which is nonlinear due to the path constraint. A sufficient condition for solvability of the path-following problem is given in terms of the geometric properties of the path. When this condition is satisfied, an arbitrary small L₂ norm of path-following error can be achieved, thus avoiding performance limitations of the standard reference tracking problem imposed by unstable zero dynamics.     

Linear feedback systems and the graph topology

It is established for general linear systems that the gap metric induces the coarsest topology with respect to which both closed-loop stability and closed-loop performance are robust properties. In earlier works, similar topological results were obtained by exploiting the existence of particular coprime-factor system representations, not known to exist in general. By contrast, the development here does not rely on any specific system representations. Systems are simply characterized as subspaces of norm bounded input-output pairs, and the analysis hinges on the underlying geometric structure of the feedback stabilization problem. Unlike other work developed within such a framework, fundamental issues concerning the causality of feedback interconnections are discussed explicitly. The key result of this paper concerns the difference between linear feedback interconnections, with identical controllers, in terms of a performance/robustness related closed-loop mapping. Upper and lower bounds on the induced norm of this difference are derived, allowing for possibly infinite-dimensional input-output spaces and time-varying behavior. The bounds are both proportional to the gap metric distance between the plants, which clearly demonstrates the gap to be an appropriate measure of the difference between open-loop systems from the perspective of closed-loop behavior. To conclude, an example is presented to show that bounds of the form derived here for linear systems do not hold in a general nonlinear setting     

Multi-physics interpolation for the topology optimization of piezoelectric systems

Unlike single-physics static structural problems, the topology optimization of piezoelectric systems involves three different material coefficient groups, such as the mechanical, electrical, and electromechanical coefficient groups, which correspondingly necessitate three values of penalty exponents. Earlier investigations have shown that stable convergence cannot be ensured if the exponents are selected arbitrarily or based simply on typical rules used for static structural problems. Here, stable convergence implies that the use of more materials can yield better system performance and a distinct void–solid distribution is favored over an intermediate material distribution during the optimization process. However, no rule for choosing the values of penalty exponents has yet been studied for piezoelectric systems and in fact, they have been chosen mainly by trial and error. In this work, two conditions that the three penalty exponents must satisfy for stable convergence are derived for one-dimensional problems and their effectiveness for two-dimensional problems is investigated. The first condition is an intrinsic condition ensuring better energy conversion efficiency between mechanical and electric energy for more piezoelectric material usage and the second one is an objective-dependent condition favoring a distinct void–solid distribution over an intermediate material distribution for the same amount of piezoelectric material used. In this study, we consider the design of piezoelectric actuators, sensors and energy harvesters that can be analyzed by static analysis. Several numerical examples are solved to check the validity of the proposed conditions.     

多智能体系统通信拓扑最优设计

运用控制理论,矩阵论及最小二乘等理论,研究了多智能体系统的分组一致性与系统通信拓扑图的拉普拉斯矩阵属于特征值0的特征向量之间的关系.给出了在线性协议控制下,系统达到一致性和分组一致性,其通信拓扑的设计方法.提出了一阶多智能体系统的总能量概念,并得到了系统在能量最省时通信拓扑的最优设计.仿真实例佐证本文主要结论的正确性.     

Second-order consensus for multi-agent systems with switching topology and communication delay

In this paper, two kinds of consensus problems for second-order agents under directed and arbitrarily switching topologies are investigated, that is, the cases without and with communication delay. For the former, by constructing a new kind of digraph and employing a new graphic method, we can specify the least convergence rate for all the agents to reach consensus. For the latter, in virtue of a matrix inequality method, a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus. This, on the other hand, shows that consensus can be reached if the delay is small enough. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results.     

Structural topology optimization of multibody systems

Flexible multibody dynamics (FMD) has found many applications in control, analysis and design of mechanical systems. FMD together with the theory of structural optimization can be used for designing multibody systems with bodies which are lighter, but stronger. Topology optimization of static structures is an active research topic in structural mechanics. However, the extension to the dynamic case is less investigated as one has to face serious numerical difficulties. One way of extending static structural topology optimization to topology optimization of dynamic flexible multibody system with large rotational and transitional motion is investigated in this paper. The optimization can be performed simultaneously on all flexible bodies. The simulation part of optimization is based on an FEM approach together with modal reduction. The resulting nonlinear differential-algebraic systems are solved with the error controlled integrator IDA (Sundials) wrapped into Python environment by Assimulo (Andersson et al. in Math. Comput. Simul. 116(0):26–43, 2015). A modified formulation of solid isotropic material with penalization (SIMP) method is suggested to avoid numerical instabilities and convergence failures of the optimizer. Sensitivity analysis is central in structural optimization. The sensitivities are approximated to circumvent the expensive calculations. The provided examples show that the method is indeed suitable for optimizing a wide range of multibody systems. Standard SIMP method in structural topology optimization suggests stiffness penalization. To overcome the problem of instabilities and mesh distortion in the dynamic case we consider here additionally element mass penalization.