Syntheses of differential games and pseudo-Riccati equations
For differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). Then the closed-loop optimal strategi...
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Hindawi Limited
2002-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337502000817 |
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doaj-e0a0f0119d7b4afd8b83623ba4a295b02020-11-24T22:41:23ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092002-01-0172618310.1155/S1085337502000817Syntheses of differential games and pseudo-Riccati equationsYuncheng You0Department of Mathematics, University of South Florida, Tampa 33620-5700, FL, USAFor differential games of fixed duration of linear dynamical systems with nonquadratic payoff functionals, it is proved that the value and the optimal strategies as saddle point exist whenever the associated pseudo-Riccati equation has a regular solution P(t,x). Then the closed-loop optimal strategies are given by u(t)=−R−1B∗P(t,x(t)), v(t)=−S−1C∗P(t,x(t)). For differential game problems of Mayer type, the existence of a regular solution to the pseudo-Riccati equation is proved under certain assumptions and a constructive expression of that solution can be found by solving an algebraic equation with time parameter.http://dx.doi.org/10.1155/S1085337502000817 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yuncheng You |
| spellingShingle |
Yuncheng You Syntheses of differential games and pseudo-Riccati equations Abstract and Applied Analysis |
| author_facet |
Yuncheng You |
| author_sort |
Yuncheng You |
| title |
Syntheses of differential games and pseudo-Riccati equations |
| title_short |
Syntheses of differential games and pseudo-Riccati equations |
| title_full |
Syntheses of differential games and pseudo-Riccati equations |
| title_fullStr |
Syntheses of differential games and pseudo-Riccati equations |
| title_full_unstemmed |
Syntheses of differential games and pseudo-Riccati equations |
| title_sort |
syntheses of differential games and pseudo-riccati equations |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2002-01-01 |
| description |
For differential games of fixed duration of
linear dynamical systems with nonquadratic payoff functionals, it
is proved that the value and the optimal strategies as saddle
point exist whenever the associated pseudo-Riccati equation has a
regular solution P(t,x). Then the closed-loop optimal
strategies are given by u(t)=−R−1B∗P(t,x(t)), v(t)=−S−1C∗P(t,x(t)). For differential game problems of
Mayer type, the existence of a regular solution to the
pseudo-Riccati equation is proved under certain assumptions and a
constructive expression of that solution can be found by solving
an algebraic equation with time parameter. |
| url |
http://dx.doi.org/10.1155/S1085337502000817 |
| work_keys_str_mv |
AT yunchengyou synthesesofdifferentialgamesandpseudoriccatiequations |
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1725702507152277504 |