时间:9:00-10:00,Sep 13
地点:N213
摘要: In this talk we study open-loop and closed-loop solvabilities for stochastic linear quadratic (LQ) optimal control problems. A simple example shows that these two solvabilities are different. It is proved that convexity of the cost functional is necessary for the open-loop solvability of the problem, whereas uniform convexity of the cost functional is sufficient.By considering a family of uniformly convex cost functionals, a minimizing sequence, whose convergence is equivalent to the open-loop solvability, is constructed.Then, we establish the key result that the uniform convexity of the cost functional is equivalent to the strongly regular solvability of the corresponding Riccati equation.Further, closed-loop solvability is established by means of regular solvability of the Riccati equation, and finiteness of the LQ problem is characterized by the convergence of the solutions to a family of Riccati equations.