讲座主题：Recent results on Infinite horizon LQ problems for singular Volterra integral equations

专家姓名：周华成

工作单位：中南大学

讲座时间：2024年11月15日16:00-17:00

讲座地点：数学院大会议室341

主办单位：烟台大学数学与信息科学学院

内容摘要：

In this talk, we presents some recent results on the singular linear Volterra integral control system with quadratic cost functional over the infinite time horizon. The existence of the solution to the mentioned control system with time-varying /constants coefficients is first proved and then the characterization of the existence and uniqueness of the optimal control under proper conditions is explored by maximum principle type necessary conditions. When the coefficients are constant matrices, the singular Volterra integral equation is reduced to the classical Caupto fractional system. In such cases, we show that if $\alpha\in(0,1/2]$, the finiteness of the cost functional implies the initial value must be equal to zero which results in that there is no optimal control whence the initial value is not zero. For the non-zero initial value, the overtaking optimal control is studied, and both the existence and nonexistence of a solution for overtaking optimal control in various cases are established by characterizing the weight function. For $\alpha\in(1/2,1)$, we show that the cost functional must be finite. Moreover, the optimal control for linear quadratic optimal control of the fractional system with $\alpha\in(1/2,1)$ cannot be obtained by linear feedback with a constant gain satisfying an algebraic Riccatic equation is concluded.

主讲人介绍：

周华成，中南大学教授，博导，国家高层次青年人才。主要从事偏微分方程控制理论研究。曾获中国科学院院长特别奖。在IEEE Tans. Automat. Control, Automatica, SIAM. J. Conttol Optim, ESAIM Conttol Optim. Calc. Vat, J.Differential Equations, SCIENCECHINA Infotmation Scencs等享有较高国际学术声誉的数学和控制领域主流刊物发表多篇论文。