This proposal describes an interdisciplinary research project whose principal objective is to extend the computational frontiers of control and system theory. A hierarchy of computational considerations is outlined, ranging from small-order problems to large-order problems. Recent analytic techniques which demonstrate numerical limitations of standard algorithms for the former will be improved and extended. However, the principal research thrust will be towards high-order problems for which rather few dependable numerical techniques presently exist, particularly for problems arising from models in so-called second-order matrix form. Such models arise naturally throughout most branches of engineering and the sciences. It is proposed to extend various control and system theory algorithms to exploit the special matrix structures available in the ubiquitous second-order equations. Parallel algorithms and specialized computing architectures offer promising opportunities to meet the challenge of advanced control strategies for both on-line and off-line computations. By examining problems of fundamental and generic interest (especially those generated by second-order models), this project will contribute parallel algorithms and software to support computations arising in problems ranging from active control for high performance aircraft engines to vibration control for large space structures to control of interconnected power systems. Such applications will require at least an order of magnitude improvement in speed and the size of problems solvable. Close attention will be paid to basic numerical issues such as conditioning and stability; and implementation of algorithms into reliable and robust software will facilitate effective technology transfer to industry, government, and academia.
