کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4609414 | 1338510 | 2016 | 27 صفحه PDF | دانلود رایگان |
In this paper, we study optimal actuator location of the minimum norm controls for a multi-dimensional heat equation with control defined in the space L2(Ω×(0,T))L2(Ω×(0,T)). The actuator domain is time-varying in the sense that it is only required to have a prescribed Lebesgue measure for any moment. We select an optimal actuator location so that the optimal control takes its minimal norm over all possible actuator domains. We build a framework of finding the Nash equilibrium so that we can develop a sufficient and necessary condition to characterize the optimal relaxed solutions for both actuator location and corresponding optimal control of the open-loop system. The existence and uniqueness of the optimal classical solutions are therefore concluded. As a result, we synthesize both optimal actuator location and corresponding optimal control into a time-varying feedbacks.
Journal: Journal of Differential Equations - Volume 261, Issue 6, 15 September 2016, Pages 3588–3614