Title:Some Explorations on Linear-Quadratic Stochastic Optimal Control and Zero-Sum Stochastic Differential Game
Time and Venue: May 15, 09:30, N602
Abstract: Firstly, we introduce a new approach called ``equivalent cost functional method” to study the indefinite linear-quadratic (LQ) stochastic optimal control problems. The analysis is featured by the introduction of some equivalent cost functionals which enable us to establish a bridge between the indefinite and positive-definite stochastic LQ problems. With such a bridge, some known resultsof the positive-definite LQ control problem are ``moved” to the indefinite case.
Secondly, we study a two-person zero-sum LQ stochastic differential game problem. From a new viewpoint, we construct a saddle point for the game in feedback control-strategy pair form based on the solution of a Riccati equation. A global solvability to this Riccati equation is obtained. Moreover, we demonstrate an indefinite phenomenon arising from the LQ game.