Dipartimento di Matematica, Universita' di Roma "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Roma
Dipartimento di Matematica F. Enriques, Via Saldini 50, 20133 Milano
Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna
Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133, Milano
Universita' degli studi di Milano, Dipartimento di matematica "F. Enriques'', via Saldini 50, 20133 Milano
A typical class of problems that have been addressed over the years is concerned with the well-posedness of an evolution equation with given initial and boundary conditions (the so-called direct problems). In several applied situations, however, initial conditions are hard to know exactly while measurements of the solution at different stages of its evolution might be available. Different techniques have been developed to recover, from such pieces of information, specific parameters governing the evolution such as forcing terms or diffusion coefficients. The whole body of results in this direction is usually referred to as inverse problems. A third way to approach the subject is to try to influence the evolution of a given system through some kind of external action called control. Control problems may be of very different nature: one may aim at bringing a given system to a desired configuration in finite or infinite time (positional control), or rather try to optimize a performance criterion (optimal control).
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Urszula Ledzewicz, Marek Galewski, Andrzej Nowakowski, Andrzej Swierniak, Agnieszka Kalamajska, Ewa Schmeidel. Preface. Discrete and Continuous Dynamical Systems - B, 2014, 19 (8) : i-ii. doi: 10.3934/dcdsb.2014.19.8i
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