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| HAL: hal-00408588, version 1 |
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| IFAC Workshop on Control Applications of Optimisation, CAO'09, Jyväskylä : Finland (2009) |
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| Open-Loop Stackelberg Strategy for Linear-Quadratic games via Matrix Pencil Approach |
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Marc Jungers 1Hisham Abou-Kandil 2 |
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| (2009-05-06) |
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| This paper deals with solving non-symmetric algebraic Riccati systems (NARS) and non-symmetric algebraic Riccati equations (NARE), from Stackelberg strategy with an open-loop information structure applied on linear-quadratic games. A matrix pencil method is chosen for its theoretical and numerical eciency. The main result provides a one-to-one correspondance between disconjugate proper deflating subspaces of a characteristic matrix pencil and the solutions of NARS and NARE. It is shown that this approach is more relevant than ones in the literature, because classical assumptions of some matrix invertibility could be avoided. |
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| 1: | Centre de recherche en automatique de Nancy (CRAN) |
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CNRS : UMR7039 – Université Henri Poincaré - Nancy I – Institut National Polytechnique de Lorraine (INPL) |
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| 2: | Systèmes et Applications des Technologies de l'Information et de l'Energie (SATIE) |
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CNRS : UMR8029 – École normale supérieure de Cachan - ENS Cachan |
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| 3: | Faculty of Automatic Control and Computers |
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University Polytehnica Bucharest |
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| Subject | : | Engineering Sciences/Automatic |
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| Game Theory – Open-Loop Stackelberg Strategy – Matrix Pencils |
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| hal-00408588, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00408588 | |
| oai:hal.archives-ouvertes.fr:hal-00408588 | |
| From: Marc Jungers | |
| Submitted on: Friday, 31 July 2009 11:01:42 | |
| Updated on: Friday, 31 July 2009 11:01:42 | |
