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On the bounded and stabilizing solution of a generalized Riccati differential equation arising in connection with a zero‐sum linear quadratic stochastic differential game
Author(s) -
Dragan V.,
Aberkane S.,
Morozan T.
Publication year - 2019
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2563
Subject(s) - mathematics , riccati equation , differential game , stochastic differential equation , connection (principal bundle) , differential equation , linear quadratic regulator , bounded function , stochastic partial differential equation , mathematical analysis , algebraic riccati equation , optimal control , mathematical optimization , geometry
Summary We study a class of coupled nonlinear matrix differential equations arising in connection with the solution of a zero‐sum two‐player linear quadratic (LQ) differential game for a dynamical system modeled by an Itô differential equation subject to random switching of its coefficients. The system of differential equations under consideration contains as special cases the game‐theoretic Riccati differential equations arising in the solution of the H ∞ control problem from the deterministic and stochastic cases. A set of sufficient conditions that guarantee the existence of the bounded and stabilizing solution of this kind of Riccati differential equations is provided. We show how such stabilizing solution is involved in the construction of the equilibrium strategy of a zero‐sum LQ stochastic differential game on an infinite‐time horizon and give as a byproduct the solution of such a control problem.