Positive Systems: Proceedings of the First Multidisciplinary by David G. Luenberger (auth.), Luca Benvenuti, Alberto De

By David G. Luenberger (auth.), Luca Benvenuti, Alberto De Santis, Lorenzo Farina (eds.)

This ebook includes the court cases of the 1st Multidisciplinary overseas Symposium on optimistic platforms concept and purposes (POSTA 2003) held in Rome, Italy, on August 28-30, 2003. confident structures are structures within which the appropriate variables imagine nonnegative values. those platforms are very common in purposes the place variables symbolize optimistic amounts equivalent to populations, items, funds, time, facts packets flowing in a community, densities of chemical species, chances and so forth. the purpose of the symposium used to be to affix jointly researchers operating within the varied parts concerning optimistic platforms corresponding to telecommunications, economic climate, biomedicine, chemistry and physics so that it will offer a multidisciplinary discussion board the place they've got the chance to replace rules and examine ends up in a unifying framework.

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Additional info for Positive Systems: Proceedings of the First Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2003), Rome, Italy, August 28–30, 2003

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Markov Processes and Related Fields, 3(4), 1997. (565-597). 10. D. Stoyan. Comparison Methods for Queues and Other Stochastic Models. J. Wiley and Sons, 1983. 11. L. Truffet. Some Ideas to Compare Bellman Chains. Kybernetika-Special issue on max-plus algebra, 39(2), April 2003. (To appear). fr Abstract. This paper deals with control of (max,+)-linear systems when a disturbance acts on system state. In a first part we synthesize the greatest control which allows to match the disturbance action. Then, we look for an output feedback which makes the disturbance matching.

Priestley. Introduction to Lattices and Order. Cambridge University Press, 1990. 7. S. Gaubert and R. Katz. Reachability and invariance problems in max-plus algebra. In POSTA’2003, Roma, August 2003. 8. M. Lhommeau. Th`ese, LISA - Universit´e d’Angers, 2003. In preparation. 54 Mehdi Lhommeau, Laurent Hardouin, and Bertrand Cottenceau 9. E. -L. Boimond, L. -L. Ferrier. Just-in-Time Control of Timed Event Graphs Update of Reference Input, Presence of Uncontrollable Input. IEEE Trans. on Automatic Control, 45(11):2155–2158, November 2000.

Proof. F = ε is a solution of (10) (since M (ε) = CA∗ S), hence the greatest solution, if it exists, also achieves equality. From (10), we seek for the greatest feedback verifying (CA∗ BF )∗ CA∗ S CA∗ S. Since RCA∗ S : x → xCA∗ S is residuated (cf. Corollary 1), we have (CA∗ BF )∗ CA∗ S CA∗ S ⇔ (CA∗ BF )∗ CA∗ S /◦ CA∗ S. According to (2), the last expression shows that 5 6 In a manufacturing system, q may represent the supply of raw material which is a priori known. The problem is then very similar to the problem introduced in [9] which establishes an optimal open-loop control in presence of known uncontrollable inputs.

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