A survey of numerical methods for solving matrix Riccati differential equations

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.<
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