Errors in reduction methods

A mathematical basis is given for comparing the relative merits of various techniques used to reduce the order of large linear and non-linear dynamics problems during their numerical integration. In such techniques as Guyan-Irons, path derivatives, selected eigenvectors, Ritz vectors, etc., the nth order initial value problem of $\text{[}\text{/.y}\text{=}\text{f(y)}$ for t > 0, y(0) given] is typically reduced to the mth order (m ? n) problem of $\text{z}\text{?}\text{= g(z)}$ for t > 0, z(0) given] by the transformation $\text{y}\text{=}\text{Pz}$ where P changes from technique to technique. This paper gives an explicit approximate expression for the reduction error e_i in terms of P and the Jacobian of f. It is shown that: (a) reduction techniques are more accurate when the time rate of change of the response y is relatively small; (b) the change in response between two successive stations contributes to the errors at future stations after the change in response is transformed by a filtering matrix H, defined in terms of P; (c) the error committed at a station propagates to future stations by a mixing and scaling matrix G, defined in terms of P, Jacobian of f, and time increment h. The paper discusses the conditions under which the reduction errors may be minimized and gives guidelines for selecting the reduction basis vector, i.e. the columns of P.     

Equivalence of rational representations of behaviors

This article deals with the equivalence of representations of behaviors of linear differential systems. In general, the behavior of a given linear differential system has many different representations. In this paper we restrict ourselves to kernel and image representations. Two kernel representations are called equivalent if they represent one and the same behavior. For kernel representations defined by polynomial matrices, necessary and sufficient conditions for equivalence are well known. In this paper, we deal with the equivalence of rational representations, i. e. kernel and image representations that are defined in terms of rational matrices. As the first main result of this paper, we will derive a new condition for the equivalence of rational kernel representations of possibly noncontrollable behaviors. Secondly we will derive conditions for the equivalence of rational representations of a given behavior in terms of the polynomial modules generated by the rows of the rational matrices. We will also establish conditions for the equivalence of rational image representations. Finally, we will derive conditions under which a given rational kernel representation is equivalent to a given rational image representation.     

Directional control of the motion of a rolling disk by using a rotor fixed in the disk's plane

This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, and a circular rotor plate fixed in the disk's plane. The disk's motion is controlled by the above-mentioned rotor, a “tillting moment” and a pedalling moment. It is shown here that by applying a kind of inverse dynamics control, the motion of the disk is stabilized about a given angle, while simultaneously controlling its speed and direction in such a manner that the point of contact between the disk and the horizontal plane will be able, during a given time interval [0, t_f], to move from a given point. r_A to a another given point r_B, both of them fixed in the plane.     

The B<Subscript>4</Subscript>-valued propositional logic with unary logical connectives ~<Subscript>1</Subscript> / ~<Subscript>2</Subscript> /¬

A B ₄-valued propositional logic will be proposed in this paper which there are three unary logical connectives ~₁, ~₂, ¬ and two binary logical connectives ∧, ∨, and a Gentzen-typed deduction system will be given so that the system is sound and complete with B ₄-valued semantics, where B ₄ is a Boolean algebra.     

Analog and Digital Representation

In this paper, I argue for three claims. The first is that the difference between analog and digital representation lies in the format and not the medium of representation. The second is that whether a given system is analog or digital will sometimes depend on facts about the user of that system. The third is that the first two claims are implicit in Haugeland's (1998) account of the distinction.

Theoretical and experimental investigation of bidirectional Hopf bifurcations in cascade DC-DC buck converters

This paper deals with two types of bidirectional Hopf bifurcation phenomena in two-stage cascade DC-DC buck converter, which is a popular design solution for obtaining larger conversion rates in distributed power systems (DPS). By means of “exact” cycle-by-cycle numerical simulations, it is found that two types of bidirectional Hopf bifurcations that never occur in standalone buck converter are observed under the variations of some particular circuit parameters. Based on the derived averaged model, theoretical analysis is performed to identify the two types of bidirectional bifurcations by judging in what way the eigenvalue loci of the Jacobian move, and further to reveal their underlying mechanisms. In addition, some behavior boundaries are given in parameter space, and some rules are proposed to avoid the occurrence of the bidirectional Hopf bifurcations. Finally, experimental results are presented for verification purposes.     

A multimode navigation system for an assistive robotics project

Assistive technology is an emerging area, where robotic devices can help individuals with motor disabilities to achieve independence in daily activities. This paper deals with a system that provides remote control of Sony AIBO, a commercial mobile robot, within the assistive project ASPICE. The robot can be controlled by various input devices, including a Brain-Computer Interface. AIBO has been chosen for its friendly-looking aspect, in order to ease interaction with the patients. The development of the project is described by focusing on the design of the robot navigation system. Single step, semi-autonomous and autonomous navigation modes have been realized to provide different levels of control. Automatic collision avoidance is integrated in all cases. Other features of the system, such as the video feedback from the robotic platform to the user, and the use of AIBO as communication aid, are briefly described. The performance of the navigation system is shown by simulations as well as experiments. The system has been clinically validated, in order to obtain a definitive assessment through patient feedback.

An optimization model of the portfolio adjusting problem with fuzzy return and a SMO algorithm

Based on possibilistic mean and variance theory, this paper deals with the portfolio adjusting problem for an existing portfolio under the assumption that the returns of risky assets are fuzzy numbers and there exist transaction costs in portfolio adjusting precess. We propose a portfolio optimization model with V-shaped transaction cost which is associated with a shift from the current portfolio to an adjusted one. A sequential minimal optimization (SMO) algorithm is developed for calculating the optimal portfolio adjusting strategy. The algorithm is based on deriving the shortened optimality conditions for the formulation and solving 2-asset sub-problems. Numerical experiments are given to illustrate the application of the proposed model and the efficiency of algorithm. The results also show clearly the influence of the transaction costs in portfolio selection.     

Stabilization and control of the motion of a rolling disk by using two overhead rotors

This work deals with the stabilization and control of a system which is composed of a disk rolling on a plane, a controlled slender rod that is pivoted through its center of mass about the disk's center and two overhead rotors with their axes fixed in the upper part of the rod (see Figures 1 and 2). The rod is controlled in such a manner that it is always aligned along the line passing through the points O and C, where O denotes the center of the disk and C denotes the point of contact between the disk and the plane. The upper rotor rotates in a plane that passes through the disk's axis and the rod, whereas the lower rotor rotates in a plane that is perpendicular to the rod (see Figures 1 and 2). By using a kind of inverse dynamics control a control strategy is proposed under which the disk's inclination is stabilized about its vertical position and the disk's motion is able asymptotically to track any given smooth ground trajectory.     

Remarks on folding behavior and plant Jacobian of neural network direct controller for its stability

Simulation results of our previous papers show a neural network direct controller which performs well by the use of folding behavior. This paper presents an analytical approach for the questions related to the folding behavior. The intermediate value theorem answers these questions. There is the suitable plant input for any plant output, although the plant is nonlinear. The same sign of the plant Jacobian can be selected for any plant output. We can use the same sign of the neural network parameter η, although the plant is nonlinear. This paper also presents how we tune the neural network parameter η based on the above analytical approach. The approach of this paper deals with the static continuous nonlinear plant. However, I believe that it is helpful to understand the neural network performance for the dynamical plant. This paper also presents future works based on this analytical approach.     

Generalizing Inverse Compositional and ESM Image Alignment

Inverse compositional (IC) image alignment (Baker and Matthews in Int. J. Comput. Vis. 56(3):221–255, 2004) uses the symmetry between the roles of the fixed and moving images for faster processing. However, it requires implementation of compositional optimizer update steps. The IC approach can be viewed as an efficient way of computing the similarity measure derivative relative to the fixed image warp parameters. Since the mapping between the fixed and moving warp parameters is continuous and differentiable, this derivative can be converted into the moving warp space using the chain rule. This avoids the need for compositional update steps. Our generalization also allows the efficient second order method (ESM) (Malis in Proceedings of the 2004 IEEE International Conference on Robotics and Automation (ICRA04), pp. 1843–1848, 2004; Benhimane and Malis in IEEE/RSJ International Conference on Intelligent Robots and Systems, 2004; Malis and Benhimane in Robot. Auton. Syst. 52(1):39–52, 2005) to be applied to general parameterizations of the transformation. Experiments using multiple similarity measures and optimizers show that our generalized IC method equals or exceeds the performance of the original IC approach. The generalized ESM approach is more reliable than the classic approach as it increases the capture radius of the optimization.     

Question-guided stubborn set methods for state properties

This paper presents two stubborn set methods for alleviating the state explosion problem when reasoning about state properties. The first method makes it possible to determine whether a state of the system is reachable in which a given state predicate holds. The second method makes it possible to determine if from all reachable states it is possible to reach a state where a given state predicate holds. The novelty of the two methods is that they rely on so-called up sets and down sets rather than the notion of visible transitions which causes earlier methods to give only limited reduction of the state space, especially when considering state predicates referring to many of the state variables of the system. The suggested stubborn set methods have been implemented in the LoLA tool, and we report on some experimental results obtained with this computer tool together with some general guidance for applying the two question-guided stubborn set methods and their different implementations in verification. The two methods are presented in the context of Petri Nets, but are applicable also to other state and action oriented modelling formalisms for which the basic stubborn set theory is applicable.

Solution errors in finite element analysis

The development of the finite element method so far indicates that it is a discretization technique especially suited for positive definite, self-adjoint, elliptic systems, or systems with such components. The application of the method leads to the discretized equations in the form of $\text{u}\text{?}\text{=}\text{f(u)}$, where u lists the response of the discretized system at n preselected points called nodes. Instead of explicit expressions, vector function f and its Jacobian f,_u are available only numerically for a numerically given u. The solution of $\text{u}\text{?}\text{=}\text{f(u)}$ is usually a digital computer. Due to finiteness of the computer wordlength, the numerical solution $\text{u}{}_{\mathrm{c}}$ is in general different from u. Let $\text{u}\text{(}\text{x}\text{, t)}$ denote the actual response of the system in continuum at points corresponding to those of u. In the literature. $\text{u}\text{(}\text{x}\text{, t)-}\text{u}$ is called the discretization errors, $\text{u}\text{-}\text{u}{}_{\mathrm{c}}$ the round-off errors, and the s is. $\text{u}\text{(}\text{x}\text{, t)-}\text{u}{}_{\mathrm{c}}$ is called the solution errors. In this paper, a state-of-the-art survey is given on the identification, growth, relative magnitudes, estimation, and control of the components of the solution errors.     

Combined Asynchronous/Synchronous Packet Switching Architecture: QoS Guarantees for Integrated Parallel Computing and Real-Time Traffic

This paper focuses on the challenging problem of integrating real-time traffic with data traffic on the same network, while having predictable quality of service (QoS) guarantees. Predictable QoS guarantees mean both deterministic and probabilistic (with a known probability distribution) functions of loss, delay, and jitter. As of today there are only limited solutions to this problem. This work presents, to the best of our knowledge, the first coherent system solution, for combining, on one hand, bursty data traffic with deterministic no loss due to congestion, and on the other hand, periodic real-time traffic with deterministic bandwidth guarantees, constant jitter, and bounded delay. The principles of this architecture facilitate the implementation of a scalable multimedia system that will combine or integrate distributed/parallel computing (e.g., over a network of PC/workstations) with real-time applications (e.g., interactive video teleconferencing).     

Evaluation and monitoring of video quality for UMA enabled video streaming systems

This paper deals with monitoring user perception of multimedia presentations in a Universal Multimedia Access (UMA) enabled system using objective no-reference (NR) metrics. These NR metrics are designed for an UMA-enabled system, in a novel architecture, for a multimedia viewer. The first metric measures block-edge impairments in a video frame at the receiver end, based on the observation that they occur in regions with low spatial activity. The second metric evaluates the quality of the reconstructed video frame in the event of packet loss. Here, the structure of the artifact is itself exploited for the evaluation. Both the metrics involve low computational complexity and are feasible for real-time monitoring of streaming video in a multimedia communication scenario. Further, in rate-adaptive streaming of video, these metrics could serve as feedback parameters to dynamically adapt the bit rates based on network congestion.

Theoretical and methodological issues related to long term creative cognition: the case of musical composition

The theme of large temporal span of cognition is emerging as a key issue in cognitive anthropology and ergonomics. We will consider it through the analysis of a musical composition process, that of Voi(rex) by Philippe Leroux, in which sketches and score writing are articulated through the use of different kinds of computer software. After presenting the data collecting method, we will consider the analysis of the resulting data concerning the writing of two movements of Voi(rex). Such an analysis will allow us: (1) to draw methodological conclusions about the time and mode of inquiry; (2) to specify the notion of situated cognition in situations essentially pre-established by the actor; (3) to set out two families of theoretical results relating to large temporal span cognitive phenomena: the first concerns the notion of an idea and its role in the development of the creative process; the second deals with the notion of the appropriation of tools and the making of situated individual cognition.

Universal realization

A study is made of input-process machines, in the sense of Arbib and Manes, and their behavior. For a given input-process X: K → K the categories Mach(X) of machines and Beh(X) of behaviors are constructed, also a functor E: Mach(X) → Beh(X) which assigns to each machine its behavior. It is shown that E has a left adjoint and that abstract Nerode realization is universal. A consequence is a characterization of minimal realization functors: a result similar to those arrived at by Goguen for machines in closed categories. We then show that by restricting machine and behavior morphisms, realization is universal for the most general type of Nerode realization, i.e., reflexive Nerode realization.     

Point-to-point and collision avoidance control of the motion of an autonomous bicycle

This work deals with the stabilization and collision avoidance control of a riderless bicycle (see Figure 1). It is assumed here that the bicycle is controlled by a pedalling torque, a directional torque, and by a rotor mounted on the crossbar that generates a tilting torque.Given two points r_A, r_B, and a circular obstacle in the horizontal plane. Also, given a time interval [0, t_f], where 0 < t_f < ∞. It is shown here that by applying a kind of inverse dynamics control, the motion of the bicycle is stabilized while simultaneously controlling its speed and direction in such a manner that the point of contact between the bicycle's rear wheel and the horizontal plane will be able, during [0, t_f], to move from r_A to r_B without hitting the obstacle.