A survey of numerical methods for solving matrix Riccati differential equations

Abstract

A review of previously developed numerical methods for solving matrix Riccati differential equations (RDEs) arising in optimal control, filtering, and estimation is presented. The following algorithms for solving RDEs are described: the direct integration method; the Davison-Maki method; a negative exponential method; the automatic synthesis program (ASP) matrix iteration procedure; the Schor method for Riccati differential equations; the Chandrasekhar method; a method using an algebraic Riccati solution; Leipnik's method; a square-root algorithm; an almost analytic approximation; and a matrix-valued approach. Their advantages and disadvantages are discussed. The matrix-valued approach is the most useful for stiff RDEs, regardless of whether the equations are time varying or time invariant, symmetric or nonsymmetric, rectangular or square.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>