Solving Differential Matrix Riccati Equations by a piecewise-linearized method based on the conmutant equation

Abstract

Differential Matrix Riccati Equations play a fundamental role in control theory, for example, in optimal control, filtering and estimation, decoupling and order reduction, etc. In this paper a piecewise-linearized method based on the conmutant equation to solve Differential Matrix Riccati Equations (DMREs) is described. This method is applied to develop two algorithms which solve these equations: one for time-varying DMREs and another for time-invariant DMREs, also MATLAB implementations of the above algorithms are developed. Since MATLAB does not have functions which solve DMREs, two algorithms based on a BDF method are also developed. All implemented algorithms have been compared, under equal conditions, at both precision and computational costs. Experimental results show the advantages of solving non-stiff DMREs and in particular stiff DMREs by the proposed algorithms.