Mixed-Integer Representations in Control Design Mathematical Foundations and Applications / [electronic resource] :
by Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu.
- XII, 107 p. 30 illus. in color. online resource.
- SpringerBriefs in Electrical and Computer Engineering, 2191-8112 .
- SpringerBriefs in Electrical and Computer Engineering, .
Introduction -- Non-Covex Region Characterization by Hyperplane Arrangements -- Mixed-Integer Representations -- Examples of Multi-Agent Control Problems -- Conclusions.
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.
9783319269955
10.1007/978-3-319-26995-5 doi
Engineering. System theory. Calculus of variations. Control engineering. Robotics. Automation. Engineering. Control. Systems Theory, Control. Calculus of Variations and Optimal Control; Optimization. Robotics and Automation.