Cavagnari, Giulia (2016) Time-optimal control problems in the space of measures. PhD thesis, University of Trento.
|PDF - Doctoral Thesis|
|PDF - Doctoral Thesis |
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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 an 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 takes into account microscopical and macroscopical effects, and we prove sufficient conditions ensuring their lower semicontinuity and a dynamic programming principle in a general formulation.
|Item Type:||Doctoral Thesis (PhD)|
|Subjects:||Area 01 - Scienze matematiche e informatiche > MAT/05 ANALISI MATEMATICA|
|Uncontrolled Keywords:||time-optimal control, optimal transport, differential inclusions, set-valued analysis, controllability, dynamic programming, multi-agent system, Lie bracket|
|Repository Staff approval on:||30 Nov 2016 10:16|
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