对流冷却的双线性控制：从开环到闭环
Bilinear Control of Convection-Cooling: From Open-Loop to Closed-Loop
摘要：
本文研究了一种通过不可压缩速度场来强化对流冷却的双线性控制问题。讨论了最优开环控制和闭环反馈控制设计。讨论了表征最优解的一阶和二阶最优性条件。特别地，瞬时控制的方法被应用于建立反馈规律。此外，还研究了直接利用最优性系统和适当的数值离散格式来构造反馈律的问题。在计算上，实现闭环反馈控制比实现最优开环控制容易得多，因为后者需要在时间上向前求解状态方程，以及在时间上向后求解伴随方程以及非线性最优性条件。严格的分析和数值实验来证明我们的想法和验证的控制设计的有效性。
英文摘要：
This paper is concerned with a bilinear control problem for enhancing convection-cooling via an incompressible velocity field. Both optimal open-loop control and closed-loop feedback control designs are addressed. First and second order optimality conditions for characterizing the optimal solution are discussed. In particular, the method of instantaneous control is applied to establish the feedback laws. Moreover, the construction of feedback laws is also investigated by directly utilizing the optimality system with appropriate numerical discretization schemes. Computationally, it is much easier to implement the closed-loop feedback control than the optimal open-loop control, as the latter requires to solve the state equations forward in time, coupled with the adjoint equations backward in time together with a nonlinear optimality condition. Rigorous analysis and numerical experiments are presented to demonstrate our ideas and validate the efficacy of the control designs.
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