报告题目：Stochastic LQand Associated Riccati equation of PDEs Driven by State- and Control-Dependent White Noise
报 告 人：汤善健教授（复旦大学）
The optimalstochastic control problem with a quadratic cost functional for linear partialdifferential equations (PDEs) driven by a state- and control-dependent whitenoise is formulated and studied. Both finite- and infinite-time horizonsare considered. The multiplicative white noise dynamics of the system give rise to a new phenomenon of singularity to the associated Riccatiequation and even to the Lyapunov equation. Well-posedness of both Riccatiequation and Lyapunov equation are obtained for the first time. Thelinear feedback coefficient of the optimal control turns out to besingular and expressed in terms of the solution of the associated Riccatiequation. The null controllability is shown to be equivalent to the existenceof the solution to Riccati equation with the singular terminal value. Finally, the controlled Anderson model is addressed as an illustratingexample.
This is a jointwork with Ying Hu, University of Rennes 1, France.