3 Search Results for "T�rnquist, Johanna"

A railway timetable is typically planned one year in advance, but may be revised several times prior to the time of operation in order to accommodate on-demand slot requests for inserting additional trains and network maintenance. Revising timetables is a computationally demanding task, given the many dependencies and details to consider. In this paper, we focus on the potential of using optimization-based scheduling approach for revising train timetables during short term planning, from one week to few hours before the actual operation. The approach relies on a MILP (Mixed Integer Linear Program) model which is solved by using the commercial solver Gurobi. In a previous experimental study, the MILP approach was used to revise a significant part of the annual timetable for a sub-network in Southern Sweden to insert additional trains and allocate time slots for urgent maintenance. The results showed that the proposed MILP approach in many cases generates feasible, good solutions rather fast. However, proving optimality was in several cases time-consuming, especially for larger problems. Thus, there is a need to investigate and develop strategies to improve the computational performance. In this paper, we present results from a study, where a number of valid inequalities has been selected and applied to the MILP model with the aim to reduce the computation time. The experimental evaluation of the selected valid inequalities showed that although they can provide a slight improvement with respect to computation time, they are also weakening the LP relaxation of the model.

Modern techniques for the design and analysis of control strategies for nonlinear dynamical systems are often based on the simulation of the open-loop as well as the closed-loop dynamical behavior of suitable mathematical models. In control engineering, continuous-time and discrete-time state-space representations are widely used which are given by sets of ordinary differential equations and difference equations, respectively. In addition to these representations, sets of differential algebraic equations are commonly used. Since we will focus on computational techniques which are applied for the design and mathematical verification of controllers for lumped parameter systems, i.e., systems which do not contain elements with distributed parameters, partial differential equations will not be considered in this talk. The prerequisite for the design and robustness analysis of each control system is the identification of mathematical models which describe the dynamics of the plant to be controlled as well as the available measurement devices with a sufficient accuracy. The model identification task comprises the derivation of physically motivated state equations, their parameterization based on measured data, as well as simplifications to apply specific approaches for controller design. In the design stage, both open-loop and closed-loop control strategies can be considered. Since dynamical system models are subject to uncertain parameters and uncertain initial conditions in most practical applications, detailed mathematical formulations of the desired dynamics of the controlled system are necessary. These specifications involve the definition of robustness with respect to the above-mentioned uncertainties. For linear system representations, robustness is commonly specified in terms of regions in the complex domain containing all admissible poles of the closed-loop transfer functions ($Gamma$-stability) or in terms of specifications of worst-case bounds for the frequency response ($mathcal{B}$-stability) [1]. However, these specifications do not allow for inclusion of bounds for the state variables which are often available in the time domain if controllers are designed for safety critical applications. Especially for nonlinear dynamical systems, pole assignment based on the linearization of nonlinear mathematical models generally leads to the necessity for the analysis of asymptotic stability of the resulting closed-loop dynamics. In this presentation, we will give an overview of the potential use of validated techniques for the analysis and design of controllers for nonlinear dynamical systems with uncertainties, where the systems under consideration will be subject to constraints for both state and control variables. As an application scenario the design of robust control strategies for a biological wastewater treatment process will be discussed. In the design and the verification process, constraints for both state and control variables which are given by guaranteed interval bounds in the time domain are taken into account. Suitable computational techniques are, for example, based on an extension of the validated initial value problem solver {sc ValEncIA-IVP} [2,6]. For that purpose, differential sensitivities of the trajectories of all state variables with respect to variations of the parameters of the mathematical system model as well as the adaptation of controller parameters are computed. This information can then be used for online identification and adaptation of parameters during the operation of a closed-loop controller as well as in offline design, verification, and optimization. Here, the interval arithmetic routines for sensitivity analysis allow to compute guaranteed differential sensitivity measures for system models with both nominal parameters and interval uncertainties. The presented interval arithmetic techniques are the basis for a general purpose tool for the analysis and the design of robust and optimal control strategies for uncertain dynamical systems. The presentation is concluded with an outlook on the formulation of control problems using sets of differential algebraic equations. Possibilities for the extension of {sc ValEncIA-IVP} to this type of system representation will be summarized. Relations between the presented interval arithmetic approach and methods for stabilizing control of nonlinear dynamical systems which make use of structural system properties such as differential flatness [3] and exact feedback linearization are highlighted [4,5]. In the latter case, input-output linearization as well as (in special cases) input-to-state linearization are of practical importance. References: [1] J. Ackermann, P. Blue, T. B"unte, L. G"uvenc, D. Kaesbauer, M. Kordt, M. Muhler, and D. Odenthal, {it{Robust Control: The Parameter Space Approach}}, Springer--Verlag, London, 2nd edition, 2002. [2] E. Auer, A. Rauh, E. P. Hofer, and W. Luther, {it{Validated Modeling of Mechanical Systems with {sc SmartMOBILE}: Improvement of Performance by {sc ValEncIA-IVP}}}, In Proceedings of Dagstuhl Seminar 06021: Reliable Implementation of Real Number Algorithms: Theory and Practice, Lecture Notes in Computer Science, Dagstuhl, Germany, 2006. In print. [3] M. Fliess, J. Lévine, P. Martin, and P. Rouchon, {it{Flatness and Defect of Nonlinear Systems: Introductory Theory and Examples}}, International Journal of Control, vol. 61, pp. 1327--1361, 1995. [4] H. K. Khalil, {it{Nonlinear Systems}}, Prentice-Hall, Upper Saddle River, New Jersey, 3rd edition, 2002. [5] H. J. Marquez, {it{Nonlinear Control Systems}}, John Wiley & Sons, Inc., New Jersey, 2003. [6] A. Rauh and E. Auer, {{www.valencia-ivp.com}}.

This paper provides an overview of the research in railway scheduling and dispatching. A distinction is made between tactical scheduling, operational scheduling and re-scheduling. Tactical scheduling refers to master scheduling, whereas operational scheduling concerns scheduling at a later stage. Re-scheduling focuses on the re-planning of an existing timetable when deviations from it have occurred. 48 approaches published between 1973 and 2005 have been reviewed according to a framework that classifies them with respect to problem type, solution mechanism, and type of evaluation. 26 of the approaches support the representation of a railway network rather than a railway line, but the majority has been experimentally evaluated for traffic on a line. 94 % of the approaches have been subject to some kind of experimental evaluation, while approximately 4 % have been implemented. The solutions proposed vary from myopic, priority-based algorithms, to traditional operations research techniques and the application of agent technology.This paper provides an overview of the research in railway scheduling and dispatching. A distinction is made between tactical scheduling, operational scheduling and re-scheduling. Tactical scheduling refers to master scheduling, whereas operational scheduling concerns scheduling at a later stage. Re-scheduling focuses on the re-planning of an existing timetable when deviations from it have occurred. 48 approaches published between 1973 and 2005 have been reviewed according to a framework that classifies them with respect to problem type, solution mechanism, and type of evaluation. 26 of the approaches support the representation of a railway network rather than a railway line, but the majority has been experimentally evaluated for traffic on a line. 94 % of the approaches have been subject to some kind of experimental evaluation, while approximately 4 % have been implemented. The solutions proposed vary from myopic, priority-based algorithms, to traditional operations research techniques and the application of agent technology.