Time-optimal Control Problems in the Space of Measures

Relatore:  Giulia Cavagnari - Università di Trento
  giovedì 24 novembre 2016 alle ore 13.30
The thesis deals with the study of a natural extension of classical finite-dimensional time-optimal control problem to the space of positive Borel measures. This approach has two main motivations: to model real-life situations in which the knowledge of the initial state is only probabilistic, and to model the statistical distribution of a huge number of agents for applications in multi-agent systems.
We deal with a deterministic dynamics and treat the problem first in a mass-preserving setting: we give a definition of generalized target, its properties, admissible trajectories and generalized minimum time function, we prove a Dynamic Programming Principle, attainability results, regularity results and a Hamilton-Jacobi-Bellman equation solved in a suitable viscosity sense by the generalized minimum time function, and finally we study the definition of an object intended to reflect the classical Lie bracket but in a measure-theoretic setting.
We also treat a case with mass loss thought for modelling the situation in which we are interested in the study of an averaged cost functional and a strongly invariant target set.
Also more general cost functionals are analysed which take into account microscopical and macroscopical effects, and we prove sufficient conditions ensuring their lower semicontinuity and a Dynamic Programming Principle in a general formulation.

The seminar will be given during the first of the hour slot of Optimization, from 13,30 to 14,30 in room F.

Referente
Antonio Marigonda

Data pubblicazione
23 novembre 2016

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