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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2002-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337502000817 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549478038503424 |
|---|---|
| author | Yuncheng You |
| author_facet | Yuncheng You |
| author_sort | Yuncheng You |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-e0a0f0119d7b4afd8b83623ba4a295b0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-e0a0f0119d7b4afd8b83623ba4a295b02025-02-03T06:11:13ZengWileyAbstract 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 |
| spellingShingle | Yuncheng You Syntheses of differential games and pseudo-Riccati equations Abstract and Applied Analysis |
| title | 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_short | Syntheses of differential games and pseudo-Riccati equations |
| title_sort | syntheses of differential games and pseudo riccati equations |
| url | http://dx.doi.org/10.1155/S1085337502000817 |
| work_keys_str_mv | AT yunchengyou synthesesofdifferentialgamesandpseudoriccatiequations |