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- Forsman, Krister, et al.
(författare)
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Constructive Algebra and Control Theory
- 1993
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Ingår i: Proceedings of the 1993 International Symposium on The Mathematical Theory of Networks and Systems. - Linköping : Linköping University. - 9783055016615 ; , s. 149-152
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Rapport (övrigt vetenskapligt/konstnärligt)
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| 2. |
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| 3. |
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| 4. |
- Forsman, Krister, et al.
(författare)
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Fuzzycat : A Fuzzy Control Analysis Tool for Maple
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This report is an abbreviated translation of a M.Sc thesis work about fuzzy control that was carried out by the second author (A.S.) under the supervision of the first author (K.F.) during the fall of 1992. The complete report (in Swedish) is [14]. Fuzzy Control is a design method for nonlinear controllers, which is becoming more and more common in industrial applications. However, a major disadvantage of fuzzy control, is that the controllers obtained are often difficult to analyze mathematically. Instead, much of the analysis so far has been made through simulation. In the thesis work a Maple software tool was developed, with which you could easily design and analyze fuzzy controllers. The tool makes it possible determine the closed expression for fuzzy control laws. It is then possible to analyze the closed loop system by standard methods from non-linear control theory (for example the circle criterion). It also has functions for translating the controller description to a MATLAB function (m-file), for example to be used in the MATLAB simulation environment, Simulink.FuzzyCAT is available by anonymous ftp at the address 130.236.24.1 (or equivalently joakim.isy.liu.se), contained in the file /pup/src/maple/FuzzyCAT/fuzzycat
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| 5. |
- Forsman, Krister, et al.
(författare)
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FuzzyCAT - Towards a Mathematical Analysis of Fuzzy Controllers
- 1993
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Ingår i: Proceedings of the 32nd Conference on Decision and Control. - Linköping : Linköping University Electronic Press. - 0780312988 ; , s. 1284-1285 vol.2
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Konferensbidrag (refereegranskat)abstract
- The aim of this paper is to show that, contrary to what is commonly believed, it is possible to get rather simple analytic expressions for a class of fuzzy controllers. The authors describe a Maple package called FuzzyCAT that supports analysis and simulation of fuzzy controllers. The restrictions made in the program concern the shape of the membership functions, the defuzzification methods available and the number of input and output variables.
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| 6. |
- Forsman, Krister
(författare)
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Implicitization, Graph Ideals and Control Systems
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We discuss how the external behavior of a polynomial automatic control system can be determined, i.e. how to find the differential equation relating the input and the output of the system given a state space description, focussing on algorithmic aspects. This problem is equivalent to what is known as implicitization in computational algebraic geometry and one way of doing this is to perform elimination in so called graph ideals. We compare different methods for implicitization with regard to computational complexity. Moreover, a bound for the degree of the input-output equation in terms of the degrees of the state equations is derived.
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| 7. |
- Forsman, Krister
(författare)
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Localization and Base Change Techniques in Computational Algebra
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This report collects some useful results from commutative algebra and describes how they can be used to decrease the complexity in Gröbner base computations. As a byproduct we see how Gröbner bases relate to characteristic sets. The algorithms presented are well known but have, as far as the author knows not been collected in one place earlier.
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| 8. |
- Forsman, Krister
(författare)
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Optimization, Stability and Cylindrical Decomposition
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Some connections between constructive real algebraic geometry and constrained optimization are exploited. We show how the problem of determining the projection of a real-algebraic variety on a certain axis is equivalent to a problem in nonlinear programming. As an application, Grobner bases are used to deal with an optimization problem arising in the theory of local Lyapunov functions. The problems addressed are: determining critical levels of local Lyapunov functions and investigating robustness using Lyapunov functions. Since the tools used come from commutative algebra and algebraic geometry the differential equations considered are of polynomial type and the Lyapunov functions used are polynomial.
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| 9. |
- Forsman, Krister
(författare)
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POLYCON : Computer Algebra Software for Polynomial Control Systems
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- 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.
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