Mixed-Integer Representations in Control Design Mathematical Foundations and Applications - Prodan, Ionela; Stoican, Florin; Olaru, Sorin; Niculescu, Silviu-Iulian.; SpringerLink (Online service) (Cham : Springer International Publishing : Imprint: Springer, 2016)
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 auseful 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.
Introduction -- Non-Covex Region Characterization by Hyperplane Arrangements -- Mixed-Integer Representations -- Examples of Multi-Agent Control Problems -- Conclusions.
Keywords: Control engineering; System theory; Control theory; Mathematical optimization; Calculus of variations; Robotics; Automation; Control and Systems Theory; Systems Theory, Control; Calculus of Variations and Optimization; Control, Robotics, Automation