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Mixed-Integer Representations in Control Design [electronic resource] : Mathematical Foundations and Applications / by Ionela Prodan, Florin Stoican, Sorin Olaru, Silviu-Iulian Niculescu.

By: Prodan, Ionela [author.].
Contributor(s): Stoican, Florin [author.] | Olaru, Sorin [author.] | Niculescu, Silviu-Iulian [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: SpringerBriefs in Control, Automation and Robotics: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2016Edition: 1st ed. 2016.Description: XII, 107 p. 30 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319269955.Subject(s): 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, AutomationAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 629.8312 | 003 Online resources: Click here to access online
Contents:
Introduction -- Non-Covex Region Characterization by Hyperplane Arrangements -- Mixed-Integer Representations -- Examples of Multi-Agent Control Problems -- Conclusions.
In: Springer Nature eBookSummary: 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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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.

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