Paolo Mariano, Università di Firenze
Covariance of the second law
Lunedì 03 Febbraio 2014, ore 17:00 precise
Dipartimento di Matematica, Politecnico di Milano, Via Bonardi 9 - Aula Consiglio VII piano | |
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VASUDEVAN SRINIVAS, School of Mathematics, Tata Institute of Fundamental Research, Mumbai
ALGEBRAIC VERSUS TOPOLOGICAL ENTROPY FOR SURFACES OVER FINITE FIELDS
Lunedì 09 Dicembre 2013, ore 17:00
Dipartimento di Matematica, Università di Milano, Via Saldini | |
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NGÔ BẢO CHÂU, The University of Chicago
ARITHMETIC OF SOME INTEGRABLE SYSTEM
Lunedì 28 Ottobre 2013, ore 16:30
Università di Milano, Dipartimento di Matematica, Via Saldini | |
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EDWARD WITTEN, Institute for Advanced Study, Princeton
A NEW LOOK AT THE JONES POLYNOMIAL OF A KNOT
Lunedì 14 Ottobre 2013, ore 16:30
Università di Milano, Dipartimento di Matematica, Via Saldini | |
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STANISLAV SMIRNOV, Université de Genève
2D LATTICE MODELS AND CONFORMAL INVARIANCE
Martedì 17 Settembre 2013, ore 16:30
Università di Milano, Dipartimento di Matematica, Via Saldini | |
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RICHARD VINTER, Imperial College London - Dept. of Electrical and Electronic Engineering
OPTIMAL CONTROL OF SYSTEMS WITH TIME DELAY
Lunedì 24 Giugno 2013, ore 14:00 precise
Politecnico di Milano, Dipartimento di Matematica - Aula Seminari VI piano |
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Abstract
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Optimal control theory provides a unified framework for studying the minimization of a performance index over a class of state trajectories satisfying a dynamic constraint. Minimizing state trajectories may be optimal flight paths in aeronautical engineering, a most profitable resource extraction policy in mathematical economics, a solution to a Hamiltonian system, or have other interpretations. Typically the dynamic constraint takes the form of a controlled differential equation. But in certain applications the differential equation involves time delays in state and control variables, which may arise from transportation delays in chemical processing, finite speed of signals in communications links, or by other mechanisms.
From a theoretical point of view, the optimal control of systems with time delay have many fascinating and unusual features. These systems are infinite dimensional, to the extent that the true state is an entire trajectory segment (an element in an infinite dimensional function space), yet necessary conditions of optimality may be studied by means of variational techniques developed for finite dimensional, delay-free systems. One the other hand, questions of existence of optimal controls and sufficient conditions via Hamilton Jacobi equations are, in some ways, much more complicated for time delay systems and, currently, only partly resolved.
This talk will provide an overview of the theory. It will include recent advances in the derivation of necessary conditions of optimality for time delay systems. Illustrations of their practicality will be provided by applications to problems in ecological control and other areas. |
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