講座主題：Recent results on Infinite horizon LQ problems for singular Volterra integral equations
專家姓名：周華成
工作單位：中南大學
講座時間：2024年11月15日16:00-17:00
講座地點：數學院大會議室341
主辦單位：煙臺大學數學與信息科學學院
內容摘要：
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.
主講人介紹：
周華成，中南大學教授，博導，國家高層次青年人才。主要從事偏微分方程控制理論研究。曾獲中國科學院院長特別獎。在IEEE Tans. Automat. Control, Automatica, SIAM. J. Conttol Optim, ESAIM Conttol Optim. Calc. Vat, J.Differential Equations, SCIENCECHINA Infotmation Scencs等享有較高國際學術聲譽的數學和控制領域主流刊物發表多篇論文。
