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A Game-Theoretic Approach For Multi-Loop Control System Design
Richter, Andrea
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URL:
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https://ub-madoc.bib.uni-mannheim.de/35960
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URN:
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urn:nbn:de:bsz:180-madoc-359609
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Document Type:
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Doctoral dissertation
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Year of publication:
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2014
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Place of publication:
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Mannheim
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University:
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Universität Mannheim
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Evaluator:
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Badreddin, Essameddin
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Date of oral examination:
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23 May 2013
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Publication language:
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English
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Institution:
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School of Business Informatics and Mathematics > Automation (Badreddin 1999-2008)
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Subject:
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620 Engineering
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Subject headings (SWD):
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Spieltheorie , Reglerentwurf
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Keywords (English):
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Multi-loop Control System Design , Game Theory
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Abstract:
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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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