Production scheduling in the process industry

The purpose of this paper is to formulate an optimization model for the production scheduling problem at continuous production sites. The production scheduling activity should produce a monthly schedule that accounts for orders and forecasts of all products. The plan should be updated every day, with feedback on the actual production the previous day. The actual daily production may be lower than the planned production due to disturbances, e.g. disruptions in the supply of a utility. The work is performed in collaboration with Perstorp, a world-leading company within several sectors of the specialty chemicals market. Together with Perstorp, a list of specifications for the production scheduling has been formulated. These are formulated mathematically in a mixed-integer linear program that is solved in receding horizon fashion. The formulation of the model aims to be general, such that it may be used for any process industrial site

On Rational State Space Realizations

. It is investigated when a polynomial inputoutput differential equation can be realized in rational, explicit state space form, i.e. so that all components of the right hand side are rational functions of the states. In the case where there are no inputs the problem is showed to be equivalent to a famous problem in algebraic geometry, which is solved only in various special cases. For systems with inputs the problem is more complicated, as is the discrete time case. An interpretation of the Luroth problem in terms of observability is made. Keywords: Realization theory, polynomial systems, algebraic observability, algebraic geometry, rational varieties 1 Introduction The problem of state space realization of nonlinear systems is a classical one, extensively discussed in the literature. Depending on what kinds of realizations we allow, the problem becomes more or less difficult. The most conservative generalization of the Kalmanian state space theory for linear systems to nonlinear sys..

Don't Panic - The Hitch Hiker's Guide to Gröbner Bases: commutative algebra for amateurs

This report is about Gröbner bases. It is an attempt to explain a little what Gröbner bases are about without introducing commutative algebra, and to show how to use them for solving equation systems. However, being very compact, the report is far from complete. There are lots of examples and Maple computations in the report. Also, it has the words DON'T PANIC inscribed in large friendly letters on its cover

The Hitch Hiker's Guide to Gröbner Bases : Commutative Algebra for Amateurs

This report is about Gröbner bases. It is an attempt to explain a little what Gröbner bases are about without introducing commutative algebra, and to show how to use them for solving equation systems. However, being very compact, the report is far from complete. There are lots of examples and Maple computations in the report

On Rational State Space Realizations (Conference Version)

It is investigated when a polynomial inputoutput differential equation can be realized in rational, explicit state space form, i.e. so that all components of the right hand side are rational functions of the states. In the case where there are no inputs the problem is showed to be equivalent to a famous problem in algebraic geometry, which is solved only in various special cases. For systems with inputs the problem is more complicated, as is the discrete time case. An interpretation of the Luroth problem in terms of observability is made

Some Generic Results on Algebraic Observability and Connections with Realization Theory

We analyze Glad/Fliess algebraic observability for polynomial control systems from a commutative algebraic/algebro-geometric point of view. Furthermore we show some relations between algebraic observability and realization theory for polynomial differential equations. Most issues are treated in a constructive framework, and we use Gröbner bases for performing elimination

POLYCON : Computer Algebra Software for Polynomial Control Systems

This paper describes the features and implementation of the Maple package Polycon which is intended to assist the control theorist in the analysis of nonlinear dynamical systems, in continuous and discrete time. Polycon handles systems where all nonlinearities are polynomial or rational functions. It implements functions that are not available at a "usable" level in other programs, to the author's knowledge. It is supposed to be accessible to non-experts and those that are not familiar with computer algebra, commutative algebra or differential algebra. Polycon is included in the Maple Share Library and thus available by anonymous ftp

Two Themes in Commutative Algebra: Algebraic Dependence and Kähler Differentials

. I reproduce an elementary proof for the jacobian criterion for algebraic dependence and give an introduction to the basics of Kahler differentials. All results presented are known, but some of them are not easily accessible, either because the references are hard to get hold of or because they are difficult to read for non-algebraists. 1 Introduction The aim of this report is twofold: ffl to provide an elementary proof for the jacobian criterion for algebraic dependence ffl to make the concept of Kahler differentials more accessible to non-experts My motivation is mainly applications to control theory; see e.g. [2, 3, 4, 5]. These applications will not be explicitly discussed here, however. Some acquaintance with basic concepts and notation of commutative algebra is required; concepts that will be used without further notice are: algebraic dependence, transcendence degree, ideal, module, k-algebra. However it is not vital that the reader understands all these concepts in detail. C..