Title:
Optimal Control of Hybrid Systems with Regional Dynamics

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dc.contributor.advisor Egerstedt, Magnus B.
dc.contributor.author Schöllig, Angela en_US
dc.contributor.committeeMember Anthony Joseph Yezzi
dc.contributor.committeeMember Laurence J. Jacobs
dc.contributor.department Civil and Environmental Engineering en_US
dc.date.accessioned 2008-02-07T18:50:35Z
dc.date.available 2008-02-07T18:50:35Z
dc.date.issued 2007-08-23 en_US
dc.description.abstract In this work, hybrid systems with regional dynamics are considered. These are systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, the attention is focused on the optimal control problem associated with such systems. More precisely, given a specific cost function, the goal is to determine the optimal path of going from a given starting point to a fixed final state during an a priori specified time horizon. The key characteristic of the approach presented in this thesis is a hierarchical decomposition of the hybrid optimal control problem, yielding to a framework which allows a solution on different levels of control. On the highest level of abstraction, the regional structure of the state space is taken into account and a discrete representation of the connections between the different regions provides global accessibility relations between regions. These are used on a lower level of control to formulate the main theorem of this work, namely, the Hybrid Bellman Equation for multimodal systems, which, in fact, provides a characterization of global optimality, given an upper bound on the number of transitions along a hybrid trajectory. Not surprisingly, the optimal solution is hybrid in nature, in that it depends on not only the continuous control signals, but also on discrete decisions as to what domains the system's continuous state should go through in the first place. The main benefit with the proposed approach lies in the fact that a hierarchical Dynamic Programming algorithm can be used to representing both a theoretical characterization of the hybrid solution's structural composition and, from a more application-driven point of view, a numerically implementable calculation rule yielding to globally optimal solutions in a regional dynamics framework. The operation of the recursive algorithm is highlighted by the consideration of numerous examples, among them, a heterogeneous multi-agent problem. en_US
dc.description.degree M.S. en_US
dc.identifier.uri http://hdl.handle.net/1853/19874
dc.publisher Georgia Institute of Technology en_US
dc.subject Hierarchic structure en_US
dc.subject Finite automaton en_US
dc.subject Bellman equation en_US
dc.subject Dynamic programming en_US
dc.subject Optimal control en_US
dc.subject Hybrid systems en_US
dc.subject Multi-agent system en_US
dc.subject.lcsh Control theory
dc.subject.lcsh Mathematical optimization
dc.subject.lcsh Dynamic programming
dc.title Optimal Control of Hybrid Systems with Regional Dynamics en_US
dc.type Text
dc.type.genre Thesis
dspace.entity.type Publication
local.contributor.advisor Egerstedt, Magnus B.
local.contributor.author Egerstedt, Magnus B.
local.contributor.corporatename School of Civil and Environmental Engineering
local.contributor.corporatename College of Engineering
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