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 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     

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.     

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 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     

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.     

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.     

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.     

Linear time-lag systems with side constraints

Necessary and sufficient conditions for an optimal control for linear time-lag optimal control systems with side constraints are given. Also the existence of an optimal control is proved.     

Simple mechanical control systems with constraints

We apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints. Certain simple aspects of the theory of affine connections play an important part in our presentation. The necessary background is presented in order to illustrate how the methods may be applied. The bulk of this paper is devoted to a detailed analysis of some examples of nonholonomic mechanical control systems. We look at the Heisenberg system, the upright rolling disk, the roller racer, and the snakeboard     

Some algorithms solving the unilateral dirichlet problem with two constraints

We consider the Dirichlet problem with two obstacles in the theory of variational inequalities and a finite-dimensional discretization related with a matrix belonging to the class (P)∩(Z). We construct some algorithms which produce monotone sequences. These sequences converge to the solution of the discrete problem starting from lower or upper obstacle.

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Sommario Consideriamo il problema di Dirichlet dei due ostacoli, ben conosciuto nella teoria delle disequazioni variazionali ed una sua discretizzazione relative ad una matrice della classe (P)∩(Z). In questo conteto costruiamo alcuni algoritmi atti a produrre successioni approssimanti, monotone non decrescenti e non crescenti, convergenti alla soluzione del problema discreto a partire rispettivamente dall’ostacolo inferiore e superiore.

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This paper has been partially supported by GNAFA-CNR.     

Asymptotic stability of systems with saturation constraints

In the present paper the authors establish new sufficient conditions for the global asymptotic stability of linear systems operating on the unit hypercube in Rⁿ and of linear systems with partial state saturation constraints. They also determine a set of necessary and sufficient conditions for the global asymptotic stability of second order linear systems with saturation constraints on both states using the above results. Systems of the type considered herein are widely used in several areas of applications, including control systems, signal processing, and artificial neural networks     

Smooth representation of systems with differentiated inputs

Conditions are derived under which the nonlinear input-output systemdot{y}=f(y,u,dot{u})can be represented in the formdot{z} =g(z,u);y= h(z,u). Various implications of the results to stochastic differential equations are considered.     

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.     

A new fusion formula and its application to continuous-time linear systems with multisensor environment

The problem of fusion of local estimates is considered. An optimal mean-square linear combination (fusion formula) of an arbitrary number of local vector estimates is derived. The derived result holds for all dynamic systems with measurements. In particular, for scalar uncorrelated local estimates, the fusion formula represents the well-known result in statistics. The fusion formula is applied to fusion of local Kalman estimates in multisensor filtering problem. Examples demonstrate high accuracy of the proposed fusion formula.     

Optimization of control systems with discontinuities and terminal constraints

The "successive sweep method," a Newton-Raphson algorithm in function space, based upon [1]-[3], is applied to the computation of optimal solutions to control problems which are characterized by terminal constraints and discontinuities in the control functions. The computational technique of using piecewise constant gains is introduced for the successive sweep method in order to reduce computer storage. Two examples are considered. The first example concerns the three-dimensional attitude control of an orbiting vehicle. The second example is the two-dimensional transfer of a low thrust vehicle in a gravitational field.     

Integer least squares with quadratic equality constraints and its application to GNSS attitude determination systems

In this paper we introduce the quadratically constrained integer least-squares problem and show how the LAMBDA method can be used to solve it for the purpose of GNSS attitude determination. The integer least-squares principle with quadratic equality constraints (ILSQE) is used to formulate our cost function. The solution of the ILSQE problem is derived and it is shown how the solution can be computed efficiently and rigorously with a novel LAMBDA based method. Experimental results with various single frequency GPS receivers are given to show the effectiveness of the proposed method. The method is also compared with some current methods of GNSS attitude determination. Apart from its efficiency, the proposed method is shown to dramatically improve the success rates of integer ambiguity GNSS attitude resolution. Recommended by Editor Hyun Seok Yang. This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology (No. R11-2008-014-02001-0). The research of the second author was done in the framework of his ARC International Linkage Professorial Fellowship, at Curtin University of Technology, Perth, Australia, with Professor Will Featherstone as his host. These supports are greatly acknowledged. Chansik Park received the B.S., M.S., and Ph.D. degrees in Electrical Engineering from Seoul National University in 1984, 1986, and 1997 respectively. He is currently with the School of Electrical and Computer Engineering, Chungbuk National University, Cheongju, Korea. His research interests include GNSS, SDR, AJ, ITS and WSN. Peter J. G. Teunissen has 20 years of research experience in GNSS Positioning and Navigation. He is the inventor of the LAMBDA method for GNSS carrier phase ambiguity resolution. He is the Head of the Department of Earth Observation and Space Systems of the Delft University of Technology and a member of the Royal Netherlands Academy of Sciences.     

A new generic scheme for functional logic programming with constraints

In this paper we propose a new generic scheme CFLP풟, intended as a logical and semantic framework for lazy Constraint Functional Logic Programming over a parametrically given constraint domain 풟. As in the case of the well known CLP풟 scheme for Constraint Logic Programming, 풟 is assumed to provide domain specific data values and constraints. CFLP풟 programs are presented as sets of constrained rewrite rules that define the behavior of possibly higher order and/or non-deterministic lazy functions over 풟. As a main novelty w.r.t. previous related work, we present a Constraint Rewriting Logic CRWL풟 which provides a declarative semantics for CFLP풟 programs. This logic relies on a new formalization of constraint domains and program interpretations, which allows a flexible combination of domain specific data values and user defined data constructors, as well as a functional view of constraints. This research has been partially supported by the Spanish National Projects MELODIAS (TIC2002-01167), MERIT-FORMS (TIN2005-09207-C03-03) and PROMESAS-CAM (S-0505/TIC/0407).