EAN: 9783319269931

SPRINGERBRIEFS IN ELECTRICAL AND COMPUTER ENGIN...

In this book  the authors propose efficient characterizations of the non-convex regions that
appear in many control problems  such as those involving collision obstacle avoidance and  in a
broader sense  in the description of feasible sets for optimization-based control design
involving contradictory objectives. The text deals with a large class of systems that require
the solution of appropriate optimization problems over a feasible region  which is neither
convex nor compact. The proposed approach uses the combinatorial notion of hyperplane
arrangement  partitioning the space by a finite collection of hyperplanes  to describe
non-convex regions efficiently. Mixed-integer programming techniques are then applied to
propose acceptable formulations of the overall problem. Multiple constructions may arise from
the same initial problem  and their complexity under various parameters - space dimension 
number of binary variables  etc. - is also discussed. This book is a useful tool for academic
researchers and graduate students interested in non-convex systems working in control
engineering area  mobile robotics and or optimal planning and decision-making.

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