A Game-Theoretic Approach For Multi-Loop Control System Design

Richter, Andrea

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URL: https://ub-madoc.bib.uni-mannheim.de/35960
URN: urn:nbn:de:bsz:180-madoc-359609
Document Type: Doctoral dissertation
Year of publication: 2014
Place of publication: Mannheim
University: Universität Mannheim
Evaluator: Badreddin, Essameddin
Date of oral examination: 23 May 2013
Publication language: English
Institution: School of Business Informatics and Mathematics > Automation (Badreddin 1999-2008)
Subject: 620 Engineering
Subject headings (SWD): Spieltheorie , Reglerentwurf
Keywords (English): Multi-loop Control System Design , Game Theory
Abstract: A new approach is developed in the present thesis, to tune PI-Controllers in a Multi-loop Control System, regarding to certain control loop properties, constraints and requirements. Several control loops in a Multi-loop Control System interact to a greater or lesser extend, depending on the control loop structure. This behavior could yield to a degradation of one loop requirement due to an optimization of a second control loop in tuning it’s controllers according to another requirement. This is a conflict situation, which could not be avoided, but improved. A consideration of one or more requirements in a Multi-loop Control System is known as a multi-objective optimization problem. To solve such a kind of Multi-objective problem, a new approach is developed that supports finding a fair trade-off from the point of view of all requirements, criteria and each control loop of a Multi-loop Control System. The developed approach uses tools from game theory, which could be applied meaningfully, to describe and solve conflict situations as described within several control loop requirements and criteria. Assistant steps of the approach are that the conflict situation, respectively the Multi-objective optimization problem is structured and described as a game, first. The belonging requirements as well as constraints are formalized mathematically in the next step. Finally, game theory provides several solution concepts to calculate a fair trade-off, which is the solution to the game. In the wide research field of game theory, the structure of information plays a decisive role. This fact leads to a second application in the control theory of the developed approach. Using different information structures of a game, respectively a Multi-loop Control System, leads to a change of the players’ strategy sets. This has a bearing on the final solution of the game. Through this game-theoretic point of view, multiple Multi-loop Control System structures could be analyzed and compared for one and the same control theoretic problem.

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