Linear-quadratic differential games: from finite to infinite dimension

Michel C. Delfour. "Linear-quadratic differential games: from finite to infinite dimension." Applicationes Mathematicae 35.4 (2008): 431-446. <http://eudml.org/doc/279928>.

@article{MichelC2008,
abstract = {The object of this paper is the generalization of the pioneering work of P. Bernhard [J. Optim. Theory Appl. 27 (1979)] on two-person zero-sum games with a quadratic utility function and linear dynamics. It relaxes the semidefinite positivity assumption on the matrices in front of the state in the utility function and introduces affine feedback strategies that are not necessarily L²-integrable in time. It provides a broad conceptual review of recent results in the finite-dimensional case for which a fairly complete theory is now available under most general assumptions. At the same time, we single out finite-dimensional concepts that do not carry over to evolution equations in infinite-dimensional spaces. We give equivalent notions and concepts. One of them is the invariant embedding for almost all initial times. Another one is the structural closed loop saddle point. We give complete classifications in terms of open loop values of the game and compare results.},
author = {Michel C. Delfour},
journal = {Applicationes Mathematicae},
keywords = {differential game; two-person; zero-sum; saddle point; value of a game; Riccati differential equation; open loop and closed loop strategies; integrable singularities},
language = {eng},
number = {4},
pages = {431-446},
title = {Linear-quadratic differential games: from finite to infinite dimension},
url = {http://eudml.org/doc/279928},
volume = {35},
year = {2008},
}

TY - JOUR
AU - Michel C. Delfour
TI - Linear-quadratic differential games: from finite to infinite dimension
JO - Applicationes Mathematicae
PY - 2008
VL - 35
IS - 4
SP - 431
EP - 446
AB - The object of this paper is the generalization of the pioneering work of P. Bernhard [J. Optim. Theory Appl. 27 (1979)] on two-person zero-sum games with a quadratic utility function and linear dynamics. It relaxes the semidefinite positivity assumption on the matrices in front of the state in the utility function and introduces affine feedback strategies that are not necessarily L²-integrable in time. It provides a broad conceptual review of recent results in the finite-dimensional case for which a fairly complete theory is now available under most general assumptions. At the same time, we single out finite-dimensional concepts that do not carry over to evolution equations in infinite-dimensional spaces. We give equivalent notions and concepts. One of them is the invariant embedding for almost all initial times. Another one is the structural closed loop saddle point. We give complete classifications in terms of open loop values of the game and compare results.
LA - eng
KW - differential game; two-person; zero-sum; saddle point; value of a game; Riccati differential equation; open loop and closed loop strategies; integrable singularities
UR - http://eudml.org/doc/279928
ER -