Showing papers on "Discrete time and continuous time published in 1998"

Loss Models: From Data to Decisions

Abstract: Preface. Acknowledgments. PART I: INTRODUCTION. 1. Modeling. PART II: ACTUARIAL MODELS. 2. Random Variables. 3. Basic Distributional Quantities. 4. Classifying and Creating Distributions. 5. Frequency and Severity with Coverage Modifications. 6. Aggregate Loss Models. 7. Discrete Time Ruin Models. 8. Continuous Time Ruin Models. PART III: CONSTRUCTION OF EMPIRICAL MODELS. 9. Review of Mathematical Statistics. 10. Estimation for Complete Data. 11. Estimation for Modified Data. PART IV: PARAMETRIC STATISTICAL METHODS. 12. Parameter Estimation. 13. Model Selection. 14. Five Examples. PART V: ADJUSTED ESTIMATES AND SIMULATION. 15. Interpolation and Smoothing. 16. Credibility. 17. Simulation. Appendix A: An Inventory of Continuous Distributions. Appendix B: An Inventory of Discrete Distributions. Appendix C: Frequency and Severity Relationships. Appendix D: The Recursive Formula. Appendix E: Discretization of the Serverity Distribution. Appendix F: Numerical Optimization and Solution of Systems. References. Index.

Exact, complete, and universal continuous-time worldline Monte Carlo approach to the statistics of discrete quantum systems

Abstract: We show how the worldline quantum Monte Carlo procedure, which usually relies on an artificial time discretization, can be formulated directly in continuous time, rendering the scheme exact. For an arbitrary system with discrete Hilbert space, none of the configuration update procedures contain small parameters. We find that the most effective update strategy involves the motion of worldline discontinuities (both in space and time), i.e., the evaluation of the Green’s function. Being based on local updates only, our method nevertheless allows one to work with the grand canonical ensemble and nonzero winding numbers, and to calculate any dynamical correlation function as easily as expectation values of, e.g., total energy. The principles found for the update in continuous time generalize to any continuous variables in the space of discrete virtual transitions, and in principle also make it possible to simulate continuous systems exactly.

Model-free control of nonlinear stochastic systems with discrete-time measurements

Abstract: Consider the problem of developing a controller for general (nonlinear and stochastic) systems where the equations governing the system are unknown. Using discrete-time measurement, this paper presents an approach for estimating a controller without building or assuming a model for the system. Such an approach has potential advantages in accommodating complex systems with possibly time-varying dynamics. The controller is constructed through use of a function approximator, such as a neural network or polynomial. This paper considers the use of the simultaneous perturbation stochastic approximation algorithm which requires only system measurements. A convergence result for stochastic approximation algorithms with time-varying objective functions and feedback is established. It is shown that this algorithm can greatly enhance the efficiency over more standard stochastic approximation algorithms based on finite-difference gradient approximations.

Finite Markov chain results in evolutionary computation: a tour d'horizon

Abstract: The theory of evolutionary computation has been enhanced rapidly during the last decade. This survey is the attempt to summarize the results regarding the limit and finite time behavior of evolutionary algorithms with finite search spaces and discrete time scale. Results on evolutionary algorithms beyond finite space and discrete time are also presented but with reduced elaboration.

On sliding mode observers via equivalent control approach

Abstract: In this paper, sliding mode observer design principles based on the equivalent control approach are discussed for a linear time invariant system both in continuous and discrete time. For the continuous case, the observer is designed using a recursive procedure; however, the observer is eventually expressed as a replica of the original system with an additional auxiliary input with a certain nested structure. A direct discrete time counterpart of the sliding mode realization of a reduced order asymptotic observer using the discrete time equivalent control is also developed. Simulation of a linearized truck-trailer during a manoeuvre illustrates the approach. Results show the effectiveness and the finite time convergence characteristics of the proposed discrete and continuous time sliding mode observers.

A finite deformation continuum\discrete model for the description of fragmentation and damage in brittle materials

Abstract: A dynamic finite element analysis of large displacements, high strain rate deformation behavior of brittle materials is presented in total Lagrangian coordinates. A continuum\discrete damage model capable of capturing fragmentation at two size scales is derived by combining a continuum damage model and a discrete damage model for brittle failure. It is assumed that size and distribution of potential fragments are known a priori, through either experimental findings or materials properties, and that macrocracks can nucleate and propagate along the boundaries of these potential fragments. The finite deformation continuum multiple-plane microcracking damage model accounts for microcracks within fragments. Interface elements, with cohesive strength and reversible unloading before debonding, between potential fragments describe the initiation of macrocracks, their propagation, and coalescence leading to the formation of discrete fragments. A surface-defined multibody contact algorithm with velocity dependent friction is used to describe the interaction between fragments and large relative sliding between them. The finite element equations of motion are integrated explicitly using a variable time step. Outputs are taken at discrete time intervals to study material failure in detail. The continuum\discrete damage model and the discrete fragmentation model, employing interface elements alone, are used to simulate a ceramic rod on rod impact. Stress wave attenuation, fragmentation pattern, and overall failure behavior, obtained from the analyses using the two models, are compared with the experimental results and photographs of the failing rod. The results show that the continuum\discrete model captures the stress attenuation and rod pulverization in agreement with the experimental observations while the pure discrete model underpredicts stress attenuation when the same potential fragment size is utilized. Further analyses are carried out to study the effect of potential fragment size and friction between sliding fragments. It is found that compared with the continuum\discrete damage model, the discrete fragmentation model is more sensitive to the multi-body discretization.

Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem

Abstract: Due to its obvious practical relevance, the Time-Cost Tradeoff Problem has attracted the attention of many researchers over the last forty years. While the Linear Time-Cost Tradeoff Problem can be solved in polynomial time, its discrete variant is known to be NP-hard. We present the first approximation algorithms for the Discrete Time-Cost Tradeoff Problem. Specifically, given a fixed budget we consider the problem of finding a shortest schedule for a project. We give an approximation algorithm with performance ratio 3/2 for the class of projects where all feasible durations of activities are either 0, 1, or 2. We extend our result by giving approximation algorithms with performance guarantee Olog l, where l is the ratio of the maximum duration of any activity to the minimum nonzero duration of any activity. Finally, we discuss bicriteria approximation algorithms which compute schedules for a given deadline or budget such that both project duration and cost are within a constant factor of the duration and cost of an optimum schedule for the given deadline or budget.

Discrete-Time Models of Bond Pricing

Abstract: We explore a variety of models and approaches to bond pricing, including those associated with Vasicek, Cox-Ingersoll-Ross, Ho and Lee, and Heath-Jarrow-Morton, as well as models with jumps, multiple factors, and stochastic volatility. We describe each model in a common theoretical framework and explain the reasoning underlying the choice of parameter values. Our framework has continuous state variables but discrete time, which we regard as a convenient middle ground between the stochastic calculus of high theory and the binomial models of classroom fame. In this setting, most of the models we examine are easily implemented on a spreadsheet.

Some stationary processes in discrete and continuous time

Abstract: A number of stationary stochastic processes are presented with properties pertinent to modelling time series from turbulence and finance. Specifically, the one-dimensional marginal distributions have log-linear tails and the autocorrelation may have two or more time scales. Discrete time models with a given marginal distribution are constructed as sums of independent autoregressions. A similar construction is made in continuous time by considering sums of Ornstein-Uhlenbeck-type processes. To prepare for this, a new property of self-decomposable distributions is presented. Also another, rather different, construction of stationary processes with generalized logistic marginal distributions as an infinite sum of Gaussian processes is proposed. In this way processes with continuous sample paths can be constructed. Multivariate versions of the various constructions are also given.

New computational results on the discrete time/cost trade-off problem in project networks

Abstract: We describe a new exact procedure for the discrete time/cost trade-off problem in deterministic activity-on-the-arc networks of the CPM type, where the duration of each activity is a discrete, nonincreasing function of the amount of a single resource (money) committed to it. The objective is to construct the complete and efficient time/cost profile over the set of feasible project durations. The procedure uses a horizon-varying approach based on the iterative optimal solution of the problem of minimising the sum of the resource use over all activities subject to the activity precedence constraints and a project deadline. This optimal solution is derived using a branch-and-bound procedure which computes lower bounds by making convex piecewise linear underestimations of the discrete time/cost trade-off curves of the activities to be used as input for an adapted version of the Fulkerson labelling algorithm for the linear time/cost trade-off problem. Branching involves the selection of an activity in order to partition its set of execution modes into two subsets which are used to derive improved convex piecewise linear underestimations. The procedure has been programmed in Visual C ++ under Windows NT and has been validated using a factorial experiment on a large set of randomly generated problem instances.

Optimal guaranteed cost control of discrete‐time uncertain linear systems

Abstract: This paper considers the problem of constructing a controller which quadratically stabilizes an uncertain system and minimizes a guaranteed cost bound on a quadratic cost function. The solution is obtained via a parameter-dependent linear matrix inequality problem. © 1998 John Wiley & Sons, Ltd.

Hybrid systems and optimal control

Abstract: The aim of this paper is to treat some optimal control problems for a class of hybrid systems. We start providing a definition of hybrid system inspired by the concept introduced by Artstein (1995), who defines hybrid control in relation to stabilization problems for a classical control system. The same definition proved to be successful to tackle other stabilization problems. In this paper, we consider a class of systems with hybrid features and optimization problems for this class of systems. The word hybrid is motivated by the fact that these systems are characterized by the presence of both a continuous time evolution and a discrete time evolution. A trajectory for these systems evolves following some dynamical constraint and at some fixed or variable times (called location switching times) it jumps following the rules of a discrete time evolution. The definition of hybrid system we give is quite general and covers many interesting applications.

Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision

Abstract: This paper studies the relation between multi-period discrete-time and continuous-time principal-agent models. We explicitly derive the continuous-time model as a limit of discrete-time models with ever shorter periods and show that the optimal incentive scheme in the continuous model, which is linear in accounts, can be approximated by a sequence of optimal incentive schemes in the discrete models. For a variant of the discrete-time model in which the principal observes only total profits at the end of the last period and where the agent can destroy profits unnoticed we show, that if the length of each period is sufficiently small, then an incentive scheme that is linear in total profits is approximately optimal.

Circles and spirals: population persistence in a spatially explicit predator-prey model

Abstract: The primary aim of the work reported in this paper is to elucidate the relationship between discrete and continuous deterministic representations of spatial population processes. Our experimental vehicle is a spatially explicit version of the Rosenzweig-McArthur model with immobile prey and a diffusively dispersing predator. We find that careful formulation of the discrete representation leads to essentially complete behavioral concordance between the two representations. We examine the invasions that follow localized introduction of predators into such a system and show that the biological realism of the model predictions can be greatly enhanced by preventing in situ regrowth of predator populations from densities that should be interpreted as representing local extinction. We exploit the close concordance of behavior between continuous and discrete representations by using the discrete version to perform a wide range of numerical experiments on one-dimensional and two-dimensional systems, while turning to the continous version to provide approximate analytic results for the natural time and space scales of the predicted population patterns. We conclude by discussing the implications of our findings for the experimental and theoretical study of spatial population dynamics.

Support Vector Machines for System Identification

Abstract: Support vector machines (SVM) are used for system identification of both linear and nonlinear dynamic systems. Discrete time linear models are used to illustrate parameter estimation and nonlinear models demonstrate model structure identification. The VC-dimension of a trained SVM indicates the model accuracy without using separate validation data. We conclude that SVM have potential in the field of dynamic system identification, but that there are a number of significant issues to be addressed.

Discrete-time and continuous-time approaches to dynamic microsimulation reconsidered

Abstract: In this paper the continuous-time competing-risk approach to dynamic microsimulation modelling and approaches based on a discrete-time framework are compared in a systematic way. Besides the basic modelling approaches the possibilities to extend the models to include quantitative and qualitative dependent variables, to use macroeconomic explanatory variables, and to account for dependencies between microunits are discussed. However, most attention is paid to the problems of causality, of simultaneity and of stochastic dependencies between the partial processes in multivariate models. The main conclusion is that a discrete-time framework with comparatively short time periods appears to be best suited for causal modelling in dynamic microsimulation models.

Input Force Reconstruction Using a Time Domain Technique

Abstract: A time domain method is presented for estimating the discrete input forces acting on a structure based upon its measured response. The structure is essentially transformed into its own loads transducer. A set of inverse system Markov parameters, in which the roles of input and output are reversed, is estimated from forward system Markov parameters using a linear predictive scheme. Inputs and acceleration outputs are assumed to be collocated to maintain minimum phase. Subsequently, any set of measured operational sensor data of any time duration can be convolved with the inverse Markov parameters to produce estimates of the input forces. This problem is ill-posed, so a regularization technique is employed to stabilize computations. A stability analysis is performed to illustrate the effects of the regularization. Predicted pseudo-forces qualitatively approximate the actual input forces and, when applied back to the structure, produce accelerations which accurately match the measured operational sensor data.

Variable structure control of discretized continuous-time systems

Abstract: A discrete-time variable structure control technique is presented for uncertain continuous-time systems. The design algorithm makes use of the concept of time-delay control in order to estimate the effects of the system perturbations inside the switching region. The controller performances have been evaluated by simulation using a benchmark problem proposed in literature. A satisfactory behavior is obtained also in the presence of remarkable uncertainties, showing noticeable robustness with respect to parameter variations and external disturbances. Moreover, the time-response characteristics can be shaped by the designer, properly tuning the control algorithm parameters.

On the queueing system

Abstract: This paper considers an infinite server queue in discrete time in which arrivals are in batches of variable size X and service is provided in batches of fixed size R. We obtain analytical results for the number of busy servers and waiting customers at pre-arrival and arbitrary epochs. For the number of busy servers we obtain a recursive relation for the partial binomial moments and explicit expressions for the marginal binomial moments both in transient and steady states. Special cases are also considered

A recurrent neural network for modelling dynamical systems.

Abstract: We introduce a recurrent network architecture for modelling a general class of dynamical systems. The network is intended for modelling real-world processes in which empirical measurements of the external and state variables are obtained at discrete time points. The model can learn from multiple temporal patterns, which may evolve on different timescales and be sampled at non-uniform time intervals. We demonstrate the application of the model to a synthetic problem in which target data are only provided at the final time step. Despite the sparseness of the training data, the network is able not only to make good predictions at the final time step for temporal processes unseen in training, but also to reproduce the sequence of the state variables at earlier times. Moreover, we show how the network can infer the existence and role of state variables for which no target information is provided. The ability of the model to cope with sparse data is likely to be useful in a number of applications, including, in particular, the modelling of metal forging.

H ∞ State Feedback Control for Generalized Continuous/Discrete Time Delay System

Abstract: In this paper, we consider the problem of designing H^∞ state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases, respectively. The generalized time delay system problems are solved on the basis of LMI(linear matrix inequality) technique considering time delays. The sufficient condition for the existence of controller and H^∞ state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be rewritten as a LMI form in terms of transformed variables. The proposed controller design method can be extended into the problem of robust H^∞ state feedback controller design method easily.

A simplified approach to time-domain modeling of avalanche photodiodes

Abstract: A simplified algorithm for calculating time response of avalanche photodiodes (APDs) is presented. The algorithm considers the time course of avalanche processes for the general case of position-dependent double-carrier multiplications including the dead space effect. The algorithm is based on a discrete time setting ideally suited for computer modeling and can be applied to any APD structure. It gives a fast and accurate estimation of the time and frequency response of APDs. As an example, the present method is applied to InP-InGaAs separate absorption, grading, charge, and multiplication (SAGCM) APDs. The variation of multiplication pain with bias voltage and 3-dB electrical bandwidth at different multiplication gain obtained using the new algorithm show good agreement with experimental results. The algorithm can be used to study temperature dependence of APD characteristics and can be easily extended to calculate the excess noise factor.

Local search methods for the discrete time/resource trade‐off problem in project networks

Abstract: In this paper we consider the discrete time/resource trade-off problem in project networks. Given a project network consisting of nodes (activities) and arcs (technological precedence relations), in which the duration of the activities is a discrete, nonincreasing function of the amount of a single renewable resource committed to it, the discrete time/resource trade-off problem minimizes the project makespan subject to precedence constraints and a single renewable resource constraint. For each activity, a work content is specified such that all execution modes (duration/resource requirement pairs) for performing the activity are allowed as long as the product of the duration and the resource requirement is at least as large as the specified work content. We present a tabu search procedure which is based on a decomposition of the problem into a mode assignment phase and a resource-constrained project scheduling phase with fixed mode assignments. Extensive computational experience, including a comparison with other local search methods, is reported. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 553–578, 1998

A /spl gamma/-attenuation problem for discrete-time time-varying stochastic systems with multiplicative noise

Abstract: The aim of this paper is to develop an H/sub /spl infin//-type theory for discrete time time-varying systems with multiplicative noise. Based on a version of the bounded real lemma corresponding to this class of systems, necessary and sufficient conditions for the existence of a stabilizing deterministic controller ensuring an imposed level of attenuation are derived in terms of the solutions of two linear matrix inequalities (LMI) satisfying a complementary rank condition. Moreover, explicit formulae for such controller are obtained in the case when some additional conditions are assumed. As a particular case, we consider the same problem for discrete-time time-varying periodic systems with multiplicative noise, for which it is shown that a periodic /spl gamma/-attenuating controller may be computed as function of a certain extended LMI system.