Exact Decompositions of Algebraic Riccati Equations

Abstract

In this chapter, the algebraic Riccati equations of both singularly perturbed and weakly coupled control systems are completely and exactly decomposed into two reduced-order algebraic Riccati equations. The decomposed algebraic Riccati equations are nonsymmetric ones. It is shown that ~e Newton method is very efficient for solving the obtained nonsymmetric algebraic Riccati equations. Due to complete and exact decomposition of the Riccati equations, we have obtained the parallel algorithms· for solving these equations. The presented procedure might produce a new insight in the singularly perturbed and weakly coupled optimal filtering and control problems since the corresponding reduced order optimal filters and controllers are completely decoupled. The decompositions of the algebraic Lyapunov equations for both singularly perturbed and weakly coupled systems are presented in Section 3.5 in the context of the complete decomposition of the differential Lyapunov equations.