The contact problem in Lagrangian systems with redundant frictional bilateral and unilateral constraints and singular mass matrix. The all-sticking contacts problem

Multibody System Dynamics - In this article we analyze the following problem: given a mechanical system subject to (possibly redundant) bilateral and unilateral constraints with set-valued...     

Corner block list representation and its application with boundary constraints

Floorplanning is a critical phase in physical design of VLSI circuits. The stochastic optimization method is widely used to handle this NP-hard problem. The key to the floorplanning algorithm based on stochastic optimization is to encode the floorplan structure properly. In this paper, corner block list (CBL)-a new efficient topological representation for non-slicing floorplan-is proposed with applications to VLSI floorplan. Given a corner block list, it takes only linear time to construct the floorplan. In floorplanning of typical VLSI design, some blocks are required to satisfy some constraints in the final packing. Boundary constraint is one kind of those constraints to pack some blocks along the pre-specified boundaries of the final chip so that the blocks are easier to be connected to certain I/O pads. We implement the boundary constraint algorithm for general floorplan by extending CBL. Our contribution is to find the necessary and sufficient characterization of the blocks along the boundary repre     

A method for the numerical integration of mechanical systems with unilateral constraints: study of impact in multibody systems

Study of mechanical systems with unilateral constraints is associated with forming two systems of equations, a system of differential equations and a system of algebraical equations. Differential equations are used to describe the motion until the moment of impact, i.e. until activation of unilateral constraints. Algebraic equations are used to describe the impact. During numerical integration, transition from one system to another occurs at the points of impact. Even in simple problems, forming algebraic equations represents a complex task.This paper presents a method, the so-called Reduction Method, which provides for the analysis of these systems without forming the algebraic equations. They are substituted by a new system which is easily derived from equations of motion. Compared to methods based on the classical impact theory, using Reduction Method,velocities after the impact are easily computed regardless of the degrees of freedom.     

A new representation of the parameters of lifted systems

Lifting, i.e., discretization with built-in intersample behavior, is an emerging technique for the analysis and design of sampled-data systems. The applicability of the lifting technique, however, is severely limited owing to difficulties in dealing with the parameters of the lifted systems, which are operators over infinite-dimensional spaces rather than finite-dimensional matrices. In this paper, a new representation for the parameters of the lifted systems is proposed. The technical machinery developed in the paper based on this representation simplifies considerably algebraic manipulation over parameters of the lifted systems, thus extending the scope of applicability of the lifting technique. To illustrate the advantages of the proposed approach, the computational issues in the sampled-data H^∞ problem are considered     

Dual representation and its online scheduling method for event-varying DESs with capacity constraints

This research focuses on event varying discrete event systems with capacity and order constraints, and derives two state-space representations that stand for the earliest and latest times of event occurrences. Moreover, we consider rescheduling methods for these representations that can be applied even when the relevant parameters are changed after the commencement of the job. The two state-space representations derived have forms that are similar to dual systems in modern control theory. In online scheduling, it is often essential to keep track of state changes or the float times of jobs continuously. For the calculation of the float times, both earliest and latest times must be calculated. Hence, the derived representations are an attractive tool for solving online scheduling problems.     

Inertial couplings between unilateral and bilateral holonomic constraints in frictionless Lagrangian systems

In this paper, the following problem is analyzed: Given a frictionless Lagrangian system subject to complementarity relations (due to a set of unilateral constraints) that define a linear complementarity problem whose matrix is the so-called Delassus’ matrix, study the influence of a set of bilateral constraints added to the dynamics on the Delassus’ matrix. Two main paths are followed: the Lagrange multipliers method and the reduced coordinates method. The link with optimization (the Gauss’ principle of mechanics) and the case of impacts, are also examined. The kinetic angles between the bilateral and the unilateral constraints are used to study the definiteness of the Delassus’ matrix.     

A new probabilistic relaxation scheme and its application to edgedetection

This paper presents a new scheme for probabilistic relaxation labeling that consists of an update function and a dictionary construction method. The nonlinear update function is derived from Markov random field theory and Bayes' formula. The method combines evidence from neighboring label assignments and eliminates label ambiguity efficiently. This result is important for a variety of image processing tasks, such as image restoration, edge enhancement, edge detection, pixel classification, and image segmentation. The authors successfully applied this method to edge detection. The relaxation step of the proposed edge-detection algorithm greatly reduces noise effects, gets better edge localization such as line ends and corners, and plays a crucial role in refining edge outputs. The experiments show that our algorithm converges quickly and is robust in noisy environments     

Solution to indeterminate multipoint impact with frictional contact using constraints

This work presents a method for determining the post-impact behavior of a rigid body undergoing multiple, simultaneous impact with friction. A discrete algebraic model is used with an event-driven function which finds impact events. In this work, the indeterminate nature of the equations of motion encountered at impact is examined. Velocity constraints are developed based on the rigid body assumption to address the equations and an impact law is used to determine the impulsive forces. The slip-state of each impact point is then determined and appropriate methods are used to resolve the post-impact velocities. These techniques are applied to a 3-D model of a ball which is forced to impact a corner between the ground and two wall planes. Additionally, a rocking block example is considered. Simulations are presented for 2-D and 3-D cases of the ball example, and a 2-D model of the rocking block problem to demonstrate the effectiveness of the proposed approach.     

A new approach for estimating controllable and recoverable regions for systems with state and control constraints

In this paper the problem of estimating controllable and recoverable regions for classes of nonlinear systems in the presence of uncertainties, state and control constraints is considered. A new computational technique is proposed based upon a ray‐gridding idea in contrast to the usual gridding techniques. The new technique is also based on the positive invariance principle and the use of piecewise linear (PL) Lyapunov functions to generate polytopic approximations to the controllable/recoverable region with arbitrary accuracy. Various types of stabilizing controllers achieving certain trade‐offs between robustness, performance and safety, while respecting state and control constraints, can be easily generated. The technique allows the approximation of nonlinear systems via piecewise linear uncertain models which reduces the conservatism associated with linear uncertain models. Copyright © 2002 John Wiley & Sons, Ltd.     

Solving problems with unilateral constraints by DAE methods

We study trajectories of mechanical systems with unilateral constraints under the additional assumption that always a given number of constraints is active. A reformulation as a problem with bilateral conditions yields a drastic reduction in the number of constraints, but in general, we are faced with regularity problems. We illustrate our approach in the special case of a dynamical rigid body contact problem. In particular, we present a regularization technique which leads to the definition of generalized solutions and a quite effective numerical method on the basis of algorithms for differential–algebraic systems. The results are applied to a wheel–rail contact problem of actual interest to railway engineers.     

具有双面约束单点摩擦多体系统的数值计算方法

研究了一类具有双面约束单点摩擦的单自由度多体系统动力学方程的算法问题.首先给出了系统的动力学方程,该方程具有很强的非光滑性,不能应用已有的一些光滑系统的数值方法研究系统的动力学特性.因此,本文利用方程的特点和所求变量的物理含义,给出了一种简便的数值计算方法.该方法的计算效率和精度与迭代法相比均较高.     

Semidefinite relaxation for linear programs with equilibrium constraints

In this paper, we present a semidefinite programming (SDP) relaxation for linear programs with equilibrium constraints (LPECs) to be used in a branch‐and‐bound (B&B) algorithm. The procedure utilizes the global optimal solution of LPECs and was motivated by the B&B algorithm proposed by Bard and Moore for linear/quadratic bilevel programs, where complementarities are recursively enforced. We propose the use of the SDP relaxation to generate bounds at the nodes of the B&B tree. Computational results compare the quality of the bounds given by the SDP relaxation with the ones given by conventional linear programming relaxations.     

A differential representation for multivariable linear systems with disturbances

It is shown how to compute a differential representation for a multivariable linear system with disturbancesdot{x}(t)=Ax(t)+Bu(t)+ W_{x}w(t)y(t)=Cx(t)+ Eu(t)+ W_{y}w(t). Explicit formulas forM_{y}(D)andM_{z}(D)in a differential equivalent representationP(D)z(t)=u(t)+M_{z}(D)w(t)y(t)=R(D)z(t)+M_{y}(D)w(t)are presented in this paper.     

含摩擦滑移铰及驱动约束多刚体系统数值算法

研究了具有驱动约束及非光滑滑移铰多体系统动力学方程的建模与数值计算方法．将驱动约束视为非定常约束，非光滑滑移铰视为双边定常约束，滑移铰的摩擦模型采用库仑摩擦模型；应用第一类Lagrange方程建立系统的动力学方程，应用距离函数建立滑移铰的约束方程；将线性互补方法和Baumgarte约束稳定化方法引入，以解决滑移铰法向约束力的计算以及约束方程违约问题．最后应用曲柄摇杆机构作为算例，说明该方法的有效性．     

一种适合于DiffServ网络的多播路由算法

提出一种适合于DiffServ网络的QoS多播路由算法PQMRD,它针对组成员不同类别的QoS请求采取不同的路由策略来选取路径,同时进行分类的接纳控制和资源预留。实验结果表明,PQMRD缓解了现有多播算法中因所有业务选择相同路径而引起的服务类间的不公平性问题。     

A port-Hamiltonian formulation of physical switching systems with varying constraints

This paper extends a generic method to design a port-Hamiltonian formulation modeling all geometric interconnection structures of a physical switching system with varying constraints. A non-minimal kernel representation of this family of structures (named Dirac structures) is presented. It is derived from the parameterized incidence matrices which are a mathematical representation of the primal and dual dynamic network graphs associated with the system. This representation has the advantage of making it possible to model complex physical switching systems with varying constraints and to fall within the framework of passivity-based control.     

A visual representation of cellular automata-like systems

Cellular automata (CA) models and corresponding algorithms have a rich theoretical basis, and have also been used in a great variety of applications. A number of programming languages and systems have been developed to support the implementation of the CA models. However, these languages focus on computational and performance issues, and do not pay enough attention to programming productivity, usability, understandability, and other aspects of software engineering.In this paper, we describe a new special-purpose programming language developed for visual specification, presentation, and explanation of CA systems within a visual programming environment, as well as, for programming them. This language is based on using visual patterns, colors, and animation for representing the CA system structures and operations on these structures, and for performing editing and composing manipulations with corresponding software components. Examples of the CA algorithm representations and some details of the environment implementation are presented.     

A systematic representation of path constraints for implicit path enumeration technique

Accuracy of implicit path enumeration technique (IPET), which statically estimates the worst‐case execution time of a program using integer linear programming, relies on flow information captured as flow facts. Unfortunately, flow facts are inadequate for capturing complex and often subtle path constraints such as causalities. Manual annotation often introduces many disjunctions, and performance of IPET computation suffers significantly. This paper proposes a technique of encoding a subset of path constraints into flow facts. The technique has advantages over conventional approaches: (1) translation process is fully automated and (2) efficient IPET computation is possible because generated flow facts are compact in that they contain at most one disjunction. To demonstrate the effectiveness of our technique, a software tool was implemented to automatically generate flow facts for the subset of path constraints and case study has been conducted using public benchmark suites, GNU openSSH codes, and Korea multi‐purpose satellite (KOMPSAT‐1) software. Copyright © 2009 John Wiley & Sons, Ltd.     

Regulator problem for linear systems with constraints on control and its increment or rate

This paper discusses the problem of constraints on both control and its rate or increment, for linear systems in state space form, in both the continuous and discrete-time domains. Necessary and sufficient conditions are derived for autonomous linear systems with constrained state increment or rate (for the continuous-time case), such that the system evolves respecting incremental or rate constraints. A pole assignment technique is then used to solve the inverse problem, giving stabilizing state feedback controllers that respect non-symmetrical constraints on both control and its increment or rate. An illustrative example shows the application of the method on the double integrator problem.     

A new probabilistic relaxation scheme

Let a vector of probabilities be associated with every node of a graph. These probabilities define a random variable representing the possible labels of the node. Probabilities at neighboring nodes are used iteratively to update the probabilities at a given node based on statistical relations among node labels. The results are compared with previous work on probabilistic relaxation labeling, and examples are given from the image segmentation domain. References are also given to applications of the new scheme in text processing.