Mixed-integer Representations in Control Design ― Mathematical Foundations and Applications

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.

Ionela Prodan received the B.E. degree from the University “Politehnica” of Bucharest, Romania in 2009. She continued her studies with a PhD in Control Engineering (2009-2012) at Supelec, Gif-sur-Yvette, France and a one year and half (2013-2014) postdoctoral fellowship within the Chair on Systems Science and the Energetic Challenge - EDF, Ecole Centrale Paris and Supelec, France. From September 2014 she is an Assistant Professor at INP Grenoble, Laboratory of Conception and Integration of Systems (LCIS EA 3747), Valence, France. Prodan’s PhD thesis “Control of Multi-Agent Systems in the Presence of Constraints” was selected as one of the three finalists of the “European PhD Award on Control for Complex and Heterogeneous Systems”, campaign 2012-2013 (presented at ECC’14, Strasbourg, France, June 26th, 2014). She was awarded with a “Bourse Dorothy LEET/AFFDU” (Association Francaise des Femmes Diplomees des Universites), campaign 2014. She is the author of 5 journal papers, 2 book chapters and of over 20 international conference papers. Her research interests include constrained optimization-based control, set-theoretic methods, mixed-integer programming and their application to energy systems and multi-agent dynamical systems in general.