讲座摘要

An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead to the asymptotic limit of the state non-zero. Under the stabilizability condition, for any (admissible) closed-loop strategy, an invariant measure is proved to exist, which makes the ergodic cost functional well-defined and the EC problem well-formulated. Sufficient conditions, including those allowing the weighting matrices of cost functional to be indefinite, are introduced for finiteness and solvability for the EC problem. Some comparisons are made between the solvability of EC problem and the closed-loop solvability of stochastic linear quadratic optimal control problem in the infinite horizon. Regularized EC problem is introduced to be used to obtain the optimal value of the EC problem.

报告人简介

魏庆萌，东北师范大学副教授，吉林省第五批创新拔尖人才，获得国家自然科学面上项目资助、国家自然科学青年基金资助、吉林省优秀青年人才基金资助。2013年博士毕业于山东大学，博士毕业论文被评为山东省优秀博士学位论文，山东大学优秀博士论文。