Ebook: Algebraic Computing in Control: Proceedings of the First European Conference Paris, March 13–15, 1991

Some algebraic, combinatorial and algebraic-differential me- thods have beenused in recent years in order to solve many problems in control theory, by effective algorithms. Imple- mentation of these algorithms generally involves algebraic computation systems and tools. Software realizations are al- ready developed in an increasing number of research centres. The goal of the "First European Conference on Algebraic Com- puting in Control" has been to present the main actual me- thods for analysis and control of systems which naturally lead to the use of algebraic computing. The maintopics and themes are as follows: mathematic tools in control theory that lead to effective algorithms, algebraic computing tools, that are available in the field of control theory, software realizations in control involving algebraic computing.

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Some algebraic, combinatorial and algebraic-differential me- thods have beenused in recent years in order to solve many problems in control theory, by effective algorithms. Imple- mentation of these algorithms generally involves algebraic computation systems and tools. Software realizations are al- ready developed in an increasing number of research centres. The goal of the "First European Conference on Algebraic Com- puting in Control" has been to present the main actual me- thods for analysis and control of systems which naturally lead to the use of algebraic computing. The maintopics and themes are as follows: mathematic tools in control theory that lead to effective algorithms, algebraic computing tools, that are available in the field of control theory, software realizations in control involving algebraic computing.
Content:
Front Matter....Pages -
The symbolic computation of vector field expressions....Pages 1-10
An implementation of tools for graded Lie-algebras in reduce....Pages 11-22
Computer algebra approaches to enzyme kinetics....Pages 23-30
Calcul formel pour la “poursuite singuliere” de trajectories....Pages 31-39
Using symbolic calculus for singularly perturbed nonlinear systems....Pages 40-49
Calcul d'approximations de la solution d'un systeme non lineaire utilisant le logiciel Scratchpad....Pages 50-59
Scratchpad implementation of the local minimal realization of dynamic systems....Pages 60-75
Poincar?'s linearization method applied to the design of nonlinear compensators....Pages 76-114
Program for symbolic and rule-based analysis and design of nonlinear systems....Pages 115-128
Algebraic computations for design of nonlinear control systems....Pages 129-155
Joint use of maple and Basile: Using computer algebra in a CACSD environment....Pages 156-164
Computer algebra for nonlinear output feedback stabilization....Pages 165-177
D?couplage des syst?mes dynamiques non lin?aires....Pages 178-190
Utilisation du calcul formel pour l'etude et la commande des systemes lineaires : approche transfert....Pages 191-199
Fast algorithms for structured matrices and interpolation problems....Pages 200-211
Polynomial dynamical systems over finite fields....Pages 212-222
Computing with P.B.W. in enveloping algebras....Pages 223-240
Rational computation in dioid algebra and its application to performance evaluation of Discrete Event Systems....Pages 241-252
Intrinsic differential algebra....Pages 253-263
Truncated bilinear approximants: Carleman, finite volterra, Pad?-type, geometric and structural automata....Pages 264-278
Generating series for analytic systems....Pages 279-287
Poincare normal form and carleman linearization....Pages 288-306
Control algorithms for chaotic systems....Pages 307-325
Analytical method of solving the differential equations, describing a developing macroeconomical system that is under the influence of scientific and technical progress....Pages 326-333
Practical computation of accessibility, controllability and nilpotent approximations....Pages 334-345
Algebraic computing and linear system control....Pages 346-353
Asymptotic behaviour of nash strategy in linear-quadratic games a computer algebra approach....Pages 354-363
Optimal pole placement by weight selection....Pages 364-374
Algebraic computations for multi-delay systems analysis....Pages 375-385

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Some algebraic, combinatorial and algebraic-differential me- thods have beenused in recent years in order to solve many problems in control theory, by effective algorithms. Imple- mentation of these algorithms generally involves algebraic computation systems and tools. Software realizations are al- ready developed in an increasing number of research centres. The goal of the "First European Conference on Algebraic Com- puting in Control" has been to present the main actual me- thods for analysis and control of systems which naturally lead to the use of algebraic computing. The maintopics and themes are as follows: mathematic tools in control theory that lead to effective algorithms, algebraic computing tools, that are available in the field of control theory, software realizations in control involving algebraic computing.
Content:
Front Matter....Pages -
The symbolic computation of vector field expressions....Pages 1-10
An implementation of tools for graded Lie-algebras in reduce....Pages 11-22
Computer algebra approaches to enzyme kinetics....Pages 23-30
Calcul formel pour la “poursuite singuliere” de trajectories....Pages 31-39
Using symbolic calculus for singularly perturbed nonlinear systems....Pages 40-49
Calcul d'approximations de la solution d'un systeme non lineaire utilisant le logiciel Scratchpad....Pages 50-59
Scratchpad implementation of the local minimal realization of dynamic systems....Pages 60-75
Poincar?'s linearization method applied to the design of nonlinear compensators....Pages 76-114
Program for symbolic and rule-based analysis and design of nonlinear systems....Pages 115-128
Algebraic computations for design of nonlinear control systems....Pages 129-155
Joint use of maple and Basile: Using computer algebra in a CACSD environment....Pages 156-164
Computer algebra for nonlinear output feedback stabilization....Pages 165-177
D?couplage des syst?mes dynamiques non lin?aires....Pages 178-190
Utilisation du calcul formel pour l'etude et la commande des systemes lineaires : approche transfert....Pages 191-199
Fast algorithms for structured matrices and interpolation problems....Pages 200-211
Polynomial dynamical systems over finite fields....Pages 212-222
Computing with P.B.W. in enveloping algebras....Pages 223-240
Rational computation in dioid algebra and its application to performance evaluation of Discrete Event Systems....Pages 241-252
Intrinsic differential algebra....Pages 253-263
Truncated bilinear approximants: Carleman, finite volterra, Pad?-type, geometric and structural automata....Pages 264-278
Generating series for analytic systems....Pages 279-287
Poincare normal form and carleman linearization....Pages 288-306
Control algorithms for chaotic systems....Pages 307-325
Analytical method of solving the differential equations, describing a developing macroeconomical system that is under the influence of scientific and technical progress....Pages 326-333
Practical computation of accessibility, controllability and nilpotent approximations....Pages 334-345
Algebraic computing and linear system control....Pages 346-353
Asymptotic behaviour of nash strategy in linear-quadratic games a computer algebra approach....Pages 354-363
Optimal pole placement by weight selection....Pages 364-374
Algebraic computations for multi-delay systems analysis....Pages 375-385
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