Optimal Control of Hybrid Systems with Regional Dynamics

Recently, hybrid control has become increasingly
relevant thanks to modern application domains
involving complex systems, sub-system
interconnections, mode-transitions, and heterogeneous
computational devices. Hybrid models, in which
continuous and discrete dynamics interact, have
proved useful for capturing these types of phenomena.
In this book, we consider hybrid systems with
regional dynamics where transitions between different
regimes occur as the state of the system crosses
given switching surfaces. In particular, we focus on
the associated optimal control problem and present a
hybrid Bellman equation that provides a
characterization of global optimality. The main
benefit of the proposed approach lies in the fact
that it presents both a theoretical representation of
the solution''s structure, and, from a more
application-driven point of view, a practical
algorithm that yields globally optimal solutions in a
regional dynamics framework. The recursive algorithm
is explored through numerous examples including a
heterogeneous multi-agent problem. The results should
be of interest to anyone working in: computer
science, control theory, system dynamics, and
operations research.

Autorentext

is a researcher in the area of system dynamics, learning, andcontrol with emphasis on complex, interconnected systems. SinceApril 2008 she is a PhD candidate at ETH Zürich, Switzerland.She received an M.Sc. from the Georgia Institute of Technology,USA, and a graduate degree in Engineering Cybernetics from theUniversity of Stuttgart, Germany.

Klappentext

Recently, hybrid control has become increasinglyrelevant thanks to modern application domainsinvolving complex systems, sub-systeminterconnections, mode-transitions, and heterogeneouscomputational devices. Hybrid models, in whichcontinuous and discrete dynamics interact, haveproved useful for capturing these types of phenomena.In this book, we consider hybrid systems withregional dynamics where transitions between differentregimes occur as the state of the system crossesgiven switching surfaces. In particular, we focus onthe associated optimal control problem and present ahybrid Bellman equation that provides acharacterization of global optimality. The mainbenefit of the proposed approach lies in the factthat it presents both a theoretical representation ofthe solution's structure, and, from a moreapplication-driven point of view, a practicalalgorithm that yields globally optimal solutions in aregional dynamics framework. The recursive algorithmis explored through numerous examples including aheterogeneous multi-agent problem. The results shouldbe of interest to anyone working in: computerscience, control theory, system dynamics, andoperations research.