ABSTRACT
In this chapter we show how to exactly decompose the algebraic Riccati equations of deterministic and stochastic multimodeling in terms of one pure-slow and two pure-fast algebraic Riccati equations. The algebraic Riccati equations obtained are of reduced-
order and nonsymmetric. However, their O(є) perturbations (where and є1, є2 are small positive singular perturbation parameters) are symmetric. The Newton method is perfectly suited for solving the nonsymmetric reduced-order pure-slow and pure-fast algebraic Riccati equations since excellent initial guesses are available from their O(є) perturbed reduced-order symmetric algebraic Riccati equations that can be solved rather easily. Derivations are done in detail for the regulator type algebraic Riccati equation. We use duality between optimal linear filtering and regulation in order to derive the corresponding decomposition for the filter type algebraic Riccati equation. In addition, we show how to completely decompose the optimal Kalman filter of the multimodeling structures in terms of one pure-slow and two pure-fast well-defined reduced-order, independent Kalman filters. The 9-th order model of a power control system and the 8-th order model of a passenger car are used to demonstrate efficiency of the proposed techniques. The proposed decomposition schemes might facili-tate new approaches to filtering and control multimodeling problems that are conceptually simpler and numerically more efficient than the ones previously used to solve corresponding multimodeling problems.
