Exact decomposition of the algebraic Riccati equation of deterministic multimodeling optimal control problems

In this paper we show how to exactly decompose the algebraic Riccati equations of deterministic 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(ε) perturbations (where ε=||_ε2^ε1|| and ε₁, ε₂ 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(ε) perturbed reduced-order symmetric algebraic Riccati equations that can be solved rather easily. The proposed decomposition scheme might facilitates new approaches to multimodeling control problems that are conceptually simpler and numerically more efficient than the ones previously used