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Some properties of extremal solutions of zero-sum differential games

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1 Author(s)
T. Johnson ; Massachusetts Institute of Technology, Cambridge, MA, USA

Necessary conditions for infinite-time linear-quadratic two-player differential games with perfect state information are examined in the light of Willems' work on the algebraic Riccati equation [1]. Necessary conditions for the nonzero-sum game do not always reduce precisely to those of the zero-sum game, when the weighting parameters of the cost index are taken as those of a zero-sum game. Formulation of zero-sum game problems in extended L2-spaces reveals the existence of nonstabilizing but infimal controls, and explicit frequency-domain conditions for existence of solutions and stabilizing solutions are established through the algebraic Riccati equation (ARE).

Published in:

IEEE Transactions on Automatic Control  (Volume:20 ,  Issue: 4 )