Control of Distributed Nonlinear Systems and Semiconductor Manufacturing

该方案讨论了用于控制分布式和非线性系统的偏微分方程方法。特别是，重点是某些关键半导体制造工艺的基准领域，包括蚀刻，沉积和光刻。我们还将讨论一些利用偏态Toeplitz理论对分布参数系统进行鲁棒控制的新方向。这允许人们将H -最优和次最优补偿器的设计简化为有限维线性代数问题，其维度仅取决于权重的麦克米伦度，而不是工厂的（状态空间）维度。因此，即使对于无限维系统，我们也被简化为有限矩阵操作。我们还将考虑这些思想的一些随时间变化的概括。

ECS-9700588 Tannenbaum The proposal deals with partial differential equation methods for the control of distributed and nonlinear systems. In particular, the focus is on the benchmark area of certain key semiconductor manufacturing processes including etching, deposition and lithography. We will also discuss some new directions we are taking on the robust control of distributed parameter systems using skew Toeplitz theory. This allows one to reduce the design of H -optimal and suboptimal compensators to finite dimensional linear algebra problem, the dimension of which only depends on the McMillan degrees of the weights and not the (state-space) dimension of the plant. Thus even for infinite dimensional systems, we are reduced to finite matrix manipulations. We will also consider some time-varying generalizations of these ideas.