A numerical investigation of the P-equations relating the matrix Riccati equation to a linear state equation



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A general interest in the matrix Riccati-type non-linear differential equation has developed in recent years due to its appearance in engineering problems including optimum control and filtering theory. Denman and his associates have done a great deal of work studying the Riccati equation and have developed a set or relations, the P-system of equations, which relate the Riccati equation to an ordinary linear state equation. A numerical method has been developed which allows a recursive solution of the Riccati equation. Other relations have been developed including an error term, and initial condition expression and a "kickhack" relation. A thorough numerical investigation of P-system relations has not been performed to date. This research will perform that numerical investigation in order to establish the validity of the P-system equations and determine their accuracy in solving the Riccati-equation. The thesis summarizes the P-system equations and their development. It describes the digital program used to perform the numerical investigation. The test systems used in the study are described and the numerical results generated during the research are presented.