One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control
One shot methods for optimal control of distributed parameter systems 1: Finite dimensional control
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分布式参数系统最优控制的一次性方法 1：有限维控制
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
S. Taasan
中科院分区：
文献类型：
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作者：
S. Taasan
摘要：讨论了控制为有限维的椭圆型偏微分方程和椭圆型偏微分方程组的最优控制问题的有效数值处理方法。讨论了分布式控制和边界控制的情况。新方法的主要特点是直接解决完整的优化问题，而不是通过有效的多网格求解器来加速下降法。该方法利用伴随状态实现高效平滑和鲁棒粗化策略。主要思想是在适当的尺度上处理控制变量，即，根据这些函数的平滑度在粗网格上求解对应于光滑函数的控制变量。控制问题的求解是通过求解约束方程两到三次（通过多网格求解器）来实现的。数值算例验证了该方法在分布式控制、点向控制和边界控制问题中的有效性。
Abstract : This paper discusses the efficient numerical treatment of optimal control problems governed by elliptic partial differential equations and systems of elliptic partial differential equations, where the control is finite dimensional. Distributed control as well as boundary control cases are discussed. The main characteristic of the new methods is that they are designed to solve the full optimization problem directly, rather than accelerating a descent method by an efficient multigrid solver for the equations involved. The methods use the adjoint state in order to achieve efficient smoother and a robust coarsening strategy. The main idea is the treatment of the control variables on appropriate scales, i.e., control variables that correspond to smooth functions are solved for on coarse grids depending on the smoothness of these functions. Solution of the control problems is achieved with the cost of solving the constraint equations about two to three times (by a multigrid solver). Numerical examples demonstrate the effectiveness of the method proposed in distributed control case, pointwise control and boundary control problem.