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.
