Large-Scale Computing in Control

在这个建议中，我们讨论的算法解决 高阶数值问题，出现在 设计控制律的系统建模与 大量的变量（参数，输入， 输出、状态等）。 特别关注的是 在状态中产生的某些关键矩阵方程上- 太空控制工程 最 常见的此类方程是李雅普诺夫方程和黎卡提方程 方程，其有效的数值解是 详细描述，虽然我们的技术也 更普遍地应用。 相当多的讨论是 专注于大规模矩阵问题，包括 其中矩阵是稀疏的，或者 结构化。 除了继续研究 关于向量实现的算法 超级计算机，如克雷Y-MP， 也可以利用粗粒度并行， 我们现在提议将我们的努力扩展到 计算机，如连接机， 巨大的并行性。 我们提出的许多建议 研究的目的是为 下一代计算机辅助控制系统 设计和分析软件。

In this proposal we discuss algorithms for solving high-order numerical problems that arise in the design of control laws for systems modeled with large numbers of variables (parameters, inputs, outputs, states, etc.). Particular attention is focused on certain key matrix equations arising in state- space-based control engineering. The most common such equations are Lyapunov and Riccati equations, and their effective numerical solution is described in detail, although our techniques also apply more generally. Considerable discussion is focused on large-scale matrix problems, including those in which the matrices are sparse or structured. In addition to continuing our research on algorithms for implementation on vector supercomputers such as the Cray Y-MP for which coarse-grained parallelism can also be exploited, we proposing now to extend our efforts to computers such as the Connection Machine with massive parallelism. Much of our proposed research is intended to lay the groundwork for the next generation of computer-aided control system design and analysis software.