The recursive reduced-order numerical solution of the singularly perturbed matrix differential Riccati equation. (English) Zbl 0649.93023

Grodt, T.; Gajic, Z.

IEEE Trans. Autom. Control 33, No. 8, 751-754 (1988).

Under stabilizability-observability conditions imposed on a singularly perturbed system, an efficient numerical method for solving the corresponding matrix differential Riccati equation is obtained in terms of reduced-order problems. The order reduction is achieved via the use of the Chang transformation applied to the Hamiltonian matrix of a singularly perturbed linear-quadratic control problem. In addition, an efficient numerical recursive algorithm with quadratic rate of convergence is developed for solving algebraic equations comprising the Chang transformation.

MSC:

93B40	Computational methods in systems theory (MSC2010)
34E15	Singular perturbations for ordinary differential equations
47A62	Equations involving linear operators, with operator unknowns
93B17	Transformations
93C05	Linear systems in control theory
93C15	Control/observation systems governed by ordinary differential equations

Keywords:

matrix differential Riccati equation; reduced-order problems; Chang transformation; singularly perturbed linear-quadratic control problem; numerical recursive algorithm