On the existence of the stabilizing solution of a class of periodic stochastic Riccati equations

Samir Aberkane (1) , Vasile Dragan (2)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 IMAR - Institute of Mathematics of the Romanian Academy [Bucharest]

This paper is devoted to the characterization of existence and uniqueness conditions for the stabilizing solution of a large class of Riccati equations arising in stochastic dynamic games. As an application of the obtained results, we consider in a second step the problem of a zero-sum two players linear quadratic (LQ) difference game for a stochastic discrete-time dynamical system subject to both random switching of its coefficients and multiplicative noise. We show that in the solution of such a control problem, a crucial role is played by the stabilizing solution of the considered class of Riccati difference equations.

Mots clés: stochastic control; stabilizing solution; Stochastic Riccati equations; zero-sum dynamic games

Domaines: Optimisation et contrôle [math.OC]

Samir Aberkane, Vasile Dragan. On the existence of the stabilizing solution of a class of periodic stochastic Riccati equations. IEEE Transactions on Automatic Control, 2020, 65 (3), pp.1288-1294. ⟨10.1109/TAC.2019.2927589⟩. ⟨hal-02265678⟩