| 1. |
- Forsman, Krister
(författare)
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An Algorithm for Finding Periodic Solutions to Systems of Nonlinear Difference Equations
- 1991
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Ingår i: Proceedings of the 30th IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780304500 ; , s. 2889-2990 vol.3
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Konferensbidrag (refereegranskat)abstract
- An algorithm for finding all N-periodic solutions to systems of nonlinear difference equations is given. The algorithm is based on elimination theory, and in special Gröbner bases. It is applicable to polynomial systems and can handle indeterminate parameters in the system equations. The system is not required to be in state space form; implicit equations are allowed.
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| 2. |
- Forsman, Krister
(författare)
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Construction of Lyapunov Functions Using Gröbner Bases
- 1991
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Ingår i: Proceedings of the 30th IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780304500 ; , s. 798-799 vol.1
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we show how so called Grobner bases can be used when choosing parameters in Lyapunov functions for nonlinear dynamical systems in an optimal way. The method suggested requires the nonlinearities of the system and the Lyapunov function to be of polynomial type. Some concrete examples of how to apply the method is provided.
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| 3. |
- Forsman, Krister, et al.
(författare)
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Input-Output Equations and Observability for Polynomial Delay Systems
- 1994
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Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780319680 ; , s. 880-882 vol.1
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Konferensbidrag (refereegranskat)abstract
- This paper discusses and strengthens a result by Fliess (1988) about input-output equations for polynomial systems with time delays. The proof given is more detailed and it opens the way for constructive methods for determining the input-output behavior. A method based on Grobner's approach is described in detail. Furthermore, some connections with observability are exploited.
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| 4. |
- Forsman, Krister
(författare)
-
Applications of Gröbner Bases to Nonlinear Systems
- 1991
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Ingår i: Proceedings of the First European Control Conference. - Linköping : Linköping University. - 9782866012809 ; , s. 164-169
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Some problems within nonlinear control theory are stated and solved using so called Groebner bases from commutative algebra. The first problem is the one of stability and performance robustness of nonlinear systems subject to structured uncertainty. It is assumed that a Lyapunov function is given, and the quality of the solution depends on this Lyapunov function. It is also indicated how the robustness problem can be reinterpreted in different ways, e.g. in terms of controller design. The second problem is the one of finding a differential equation connecting the input and the output of a system starting from a state space description of it. In all cases the nonlinearities are required to be of polynomial type. The methods suggested are illustrated with concrete examples.
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| 5. |
- 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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| 6. |
- 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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| 7. |
- Forsman, Krister
(författare)
-
Hybrid Control Systems and Comprehensive Gröbner Bases
- 1994
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Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780319680 ; , s. 4092-4097 vol.4
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A class of hybrid systems that can be modeled by polynomial differential equations is investigated. By a hybrid system we mean a system which mixes continuous and discrete variables. All variables in the system have the same time scale. The polynomial models have the advantage that constructive methods are available for system analysis. One such method that occurs naturally in this context is so called comprehensive Grobner bases
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| 8. |
- Forsman, Krister
(författare)
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On Nonlinear Systems with Linear Dynamics
- 1994
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Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780319680 ; , s. 1778-1783 vol.2
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Konferensbidrag (refereegranskat)abstract
- Some classes of polynomial control systems are investigated and characterized in terms of their input-output behavior. The first class are those that can be realized as a set of linear state equations with a polynomial output map. The second class are those that can be realized as a set of homogeneous (w.r.t. some grading) state equations with homogeneous output map.
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| 9. |
- Forsman, Krister
(författare)
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On Rational State Space Realizations
- 1992
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Ingår i: Proceedings of the 2nd IFAC Symposium on Nonlinear Control Systems Design. - Linköping : Linköping University. - 9780080419015 ; , s. 197-202
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 10. |
- Forsman, Krister, et al.
(författare)
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On the Dead-Zone in System Identification
- 1991
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Ingår i: Proceedings of the 9th IFAC Symposium on System Identification and System Parameter Estimation. - Linköping : Linköping University. ; , s. 1410-1414
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A prediction error method for parameter estimation in a dynamical system is studied.The following problems are treated in this paper:When is the DZ estimate inconsistent, and what is the set of parameters which minimizes the criterion in the case of inconsistency?What happens to the variance of the estimate as the DZ is introduced?Does the deadzone give a better estimate than LS when there are unmodelled deterministic disturbances present?What are the relations between identification with a deadzone criterion and so called set membership identification?
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