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- Germundsson, Roger, et al.
(författare)
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A Constructive Approach to Algebraic Observability
- 1991
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Ingår i: Proceedings of the 30th IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780304500 ; , s. 451-452
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Konferensbidrag (refereegranskat)abstract
- The authors address the problem of observability of polynomial discrete-time systems. The ideal theoretic definition is translated to effective computations in terms of Grobner bases. Linear system observability is a special case, and for general polynomial systems n samples are needed to determine observability, where n is the state dimension. The formulation yields a decision criterion as well as an implicit form of an observer.
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| 2. |
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| 3. |
- Germundsson, Roger
(författare)
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A Tetris Controller : An Example of a Discrete Event Dynamic System
- 1991
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we build a controller for a Tetris game. A model inspired by control theory is used and a control law derived. This control law has certain degrees of freedom, i.e. some parameters to tune. Stochastic approximation is used to derive the "optimal" controller within this framework. An implementation of this control law with an existing Tetris game has been done and all code is available inorder for more control schemes to be proposed. This process is also proposed as a test case for discrete event methods.
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| 4. |
- Germundsson, Roger, et al.
(författare)
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A Unified Constructive Study of Linear, Nonlinear and Discrete Event Systems
- 1995
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Starting from the behavioral point of view a system is defined by its set of behaviors. In discrete time this is a relation over D N and hence a very infinite object. A model is a relation over D N for some finite N that can be extended to a behavior. Furthermore properties of a system is defined in terms of its behavior. Starting from a constructive point of view we need to be able to represent and manipulate systems. A natural choice is to use some a constructive model, i.e. one that can be finitely represented and manipulated. We will consider four such classes of models: polynomial and linear relations over finite and infinite fields. There are a number of restrictions on the geometric (or behavioral) operations that are possible for each of these classes and still remain within the class. If we want to interpret our models as systems and analyze system properties, then several properties become impossible to compute. Some examples: The set of reachable states for a polynomial model over an infinite field is in general impossible to compute. It may converge to be fractal. The set of reacable states ik steps or less in a linear model cannot be represented as a linear set in general.
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| 5. |
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| 6. |
- Germundsson, Roger
(författare)
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Analysis of Polynomial Dynamical Systems over Finite Fields
- 1992
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This document formulates and solves a number of problems associated with reachability for polynomial dynamical systems over finite fields. This class of systems is intended as a general model class for Discrete Event Systems.
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| 7. |
- Germundsson, Roger
(författare)
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Basic Results on Ideals and Varieties in Finite Fields
- 1991
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The connection between ideals and varieties for polynomial rings over finite fields is investigated. An extension to Hilbert's NullstellenSatz is given for these ideals. Furthermore projections and embeddings of these is examined. These results basically give ideal theoretic formulations for several algebro-geometric questions. This in turn is translated to Grobner basis and polynomial remainder calculations. Anexample implementation in Mathematica is also given.
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| 8. |
- Germundsson, Roger
(författare)
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Logic Proofs : Through Ideal Inclusions
- 1991
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The two approaches of propositional logic (semantic and proof theoretic) are found to have equivelent formulations in commutative algebra over finite fields. In particular the semantic approach correspond to an algebro geometric formulation and the proof theoretic correspond to an ideal theoretic framework. Based on this correspondence a new completeness proof is given. An implementation of this proof system in Mathematica is also given.
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| 9. |
- Germundsson, Roger
(författare)
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Logic Proofs = Ideal inclusions
- 1991
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The two approaches of propositional logic (semantic and proof theoretic) are found to have equivalent formulations in commutative algebra over finite fields. In particular the semantic approach corresponds to an algebro geometric formulation and the proof theoretic corresponds to an ideal theoretic framework. Based on this correspondence a new completeness proof is given. An implementation of this proof system in Mathematica is also given which basically is based on Grobner basis computations.
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| 10. |
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