On the game Riccati equations arising in Hinfini control problems

Abstract : In the state-space approach to H optimal control, feasibility of some closed-loop attenuation g is characterized in terms of a pair of game Riccati equations depending on g. This paper is concerned with the properties of these equations as g varies. The most general problem is considered (D11 0) and a thorough analysis of the variations of the Riccati solutions provides insight into the behavior near the optimum and into the dependence on g of the suboptimality conditions. In addition, concavity is established for a criterion which synthesizes the three conditions X 0, Y 0, and p(XY) < g 2. As a result, a numerically reliable Newton scheme can be devised to compute the optimal g. Most presented results are extensions of earlier contributions. The main concern here is to provide a complete and synthetic overview as well as results and formulas tailored to the development of numerically-sound algorithms.
Type de document :
[Research Report] RR-1643, INRIA. 1992
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Soumis le : mercredi 24 mai 2006 - 16:56:51
Dernière modification le : vendredi 25 mai 2018 - 12:02:05
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  • HAL Id : inria-00074917, version 1



Pascal Gahinet. On the game Riccati equations arising in Hinfini control problems. [Research Report] RR-1643, INRIA. 1992. 〈inria-00074917〉



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