ABSTRACT
In this chapter, we show how to exactly decompose the algebraic Riccati equation of continuous-time singularly perturbed control systems into two reduced-order algebraic Riccati equations corresponding to slow and fast time scales. The reduced-order algebraic Riccati equations obtained are nonsymmetric. The Newton algorithm is very efficient for solving these nonsymmetric algebraic Riccati equations since excellent initial guesses are readily available from the reduced-order, symmetric, algebraic Riccati equations that represent O(є) perturbations of the nonsymmetric, reduced-order, pure-slow and purefast, algebraic Riccati equations. Due to complete and exact decomposition of the Riccati equation, and due to order-reduction, we have obtained an efficient parallel algorithm for solving this equation-the most important equation of the linear-quadratic optimal control and filtering theory.
