| 1. |
- 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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| 2. |
- Forsman, Krister
(författare)
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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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| 3. |
- 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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| 4. |
- Forsman, Krister
(författare)
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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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| 5. |
- 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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| 6. |
- Forsman, Krister, et al.
(författare)
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Some Finiteness Issues in Differential Algebraic Systems Theory
- 1994
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Ingår i: Proceedings of the 33rd IEEE Conference on Decision and Control. - Linköping : Linköping University. - 0780319680 ; , s. 1112-1117 vol.2
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The elimination problem in differential algebraic systems theory is discussed. The focus is on finiteness questions, such as conditions for the elimination ideal to be finitely generated.
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| 7. |
- Forsman, Krister
(författare)
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A MATLAB Function for Plotting Phase Planes Interactively
- 1992
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A MATLAB-function serving as a sort of graphical interface to the MATLAB ODE-solver ode45 is presented. The main use of it is to facilitate phase plane analysis of nonlinear 2-D systems via simulation. The numerical integration of the system is mouse-operated via the ginput-function. After each choice of initial value a simulation is made and plotted in the phase plane.
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| 8. |
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| 9. |
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| 10. |
- Forsman, Krister
(författare)
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A Short Maple Primer
- 1992
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Maple is a nice and powerful computer algebra system. There is also a very readable manual for Maple. However, many people do not do symbolic calculations every day and may need to use the program only occasionally. This is a manual for those people. It is totally incomplete, it has examples instead of general syntax description of the commands, it only accounts for a small fraction of the existing functions.The basic idea is: look here for the function you need, and if there is not enough information about it here (there typically won't be) use the on-line documentation or read the real manual. The Maple-version described here is version V. Caveat: since the functions are mostly explained by examples, most of them have more facilities and are more powerful than it appears here.
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