Eigenvector approach for reduced-order optimal control problems of weakly coupled systems

摘要

In this paper we show how to decompose the weakly coupled algebraic Riccati equation and the corresponding linear-quadratic optimal control problem at steady state in terms of reduced-order subproblems by using the eigenvector approach. The eigenvector approach should be used for decomposition of weakly coupled control systems in the cases when the weak coupling parameter is not sufficiently small. In such cases the decomposition methods based on series expansions, fixed point iterations and Newton iterations, either fail to produce solutions of the corresponding algebraic equations or display very slow convergence. In addition, the eigenvector approach provides new tools and novel insight into the nature of the decomposition problem and finds all required solutions without solving the corresponding subsystem Riccati equations.