Multicriterion Aerodynamic Shape Design Optimization and Inverse Problems Using Control Theory and Nash Games |
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Authors: | Z Tang J-A Désidéri J Périaux |
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Institution: | (1) College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, China;(2) Opale Project Team, INRIA, Sophia–Antipolis, France;(3) CIMNE, UPC, Barcelona, Spain |
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Abstract: | Multicriterion design is gaining importance in aeronautics in order to cope with new needs of society. In the literature,
contributions to single discipline and/or single-point design optimization abound. The goal of this paper is to introduce
a new approach combining the adjoint method with a formulation derived from game theory for multipoint aerodynamic design
problems. Transonic flows around lifting airfoils are analyzed via Euler computations. Airfoil shapes are optimized according
to various aerodynamic criteria. The notion of player is introduced. In a competitive Nash game, each player attempts to optimize
its own criterion through a symmetric exchange of information with others. A Nash equilibrium is reached when each player,
constrained by the strategy of the others, cannot improve further its own criterion. Specific real and virtual symmetric Nash
games are implemented to set up an optimization strategy for design under conflict.
This work has benefited partially from the support of the National Science Foundation of China Grant NSFC-10372040 and Scientific
Research Foundation (SRF) for Returned Overseas Chinese Scholars (ROCS) Grant 2003-091. The first author acknowledges the
support of INRIA (Institut National de Recherche en Information et en Automatique), France. |
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Keywords: | Aerodynamics Multicriterion optimization Nash games Control theory Adjoint method Inverse problems |
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