Abstract
Solving optimal control problems usually consists in modelizing type problem, proving the existence of a solution, choosing a method leadint to a numerical solution and writing a program (generally in FORTRAN). These steps can be automatized using formal calculus and inference techniques. An expert system in stochastic control is presented. It is embedded in the MACSYMA system. After the description of the problem by the user in semi-natural language, the system generates the equations which modelize the problem. Then by using PROLOG (for encoding the used theorems) and symbolic manipulations on the equations, the system can prove the existence of a solution. Finally the system chooses a numerical method to solve it using symbolic differentiations and mtrix inversions and it generates the associated FORTRAN program.
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References
MACSYMA Reference Manual. Version 10. The Mathlab Group, MIT, Laboratory for Computer Science. MIT. December 1983.
Gloess P., Logis User’s Manual. Second Edition. UTC/GI, BP 233, 60206 Compiègne Cedex, France. June 1984.
Davis J. and Moon D., Multics Maclisp Reference Manual, Revision 1, MIT, Laboratory for Computer Science, 1980.
Pitman K.M., The revised MACLISP manual, MIT, Laboratory for Computer Science, 1983.
Queinnec C., LISP: Langage d’un autre type, Edition Eyrolles, 1983.
Adams R.A., Sobolev spaces. Academic Press. 1975.
Lions J.L. and Magenes E., Problèmes aux limites non homogènes et applications, Tome I, Dunod, Paris, 1968.
Lions J.L., Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Gauthier-Villars, Paris, 1969.
Charniak E., MacDermott D. and Riesbeck C., Artificial Intelligence Programming. Lawrence Erlbaum Associates, Hillsdale, New Jersey. 1979.
Bensoussan A. et al., Commande optimale de systèmes stochastiques. RAIRO, Systems Analysis and Control, Vol. 18, n°2. 1984.
Blankenship G.L. et al., An expert system for control and signal processing with automatic FORTRAN code generation. CDC 1984, Las Vegas, to appear.
Gomez C., Quadrat J.P. and Sulem A., Towards an expert system in stochastic control: the Hamilton-Jacobi equation part. Nice, Juin 1984. Springer Verlag, Lecture Notes in Control and Information Sciences, 62.
Gomez C., Quadrat J.P. and Sulem A., Towards an expert system in stochastic control: optimization in the class of local feedbacks. Rome, 1984. To appear.
Gloess P., Understanding Expert systems. Alfred Handy Guide. 1984. To appear.
Feigenbaum E.A. and Barr A., The Handbook of Artificial Intelligence, Heuristics Press, Stanford, California, W. Kaufmann Inc., Los Altos, California. 1982.
Gloess P. and Nguyen D., OBLOGIS, an object oriented implementation of PROLOG in a LISP environment. Colloque International d’Intelligence Artificielle, Marseille, France, October 1984.
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© 1985 Kluwer Academic Publishers
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Gomez, C., Quadrat, J.P., Sulem, A. (1985). Computer Algebra as a Tool for Solving Optimal Control Problems. In: Pavelle, R. (eds) Applications of Computer Algebra. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-6888-5_11
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DOI: https://doi.org/10.1007/978-1-4684-6888-5_11
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-6890-8
Online ISBN: 978-1-4684-6888-5
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