On an Iterative Technique for Riccati Equation Computations

Authors

David L. Kleinman

Year

1968

Journal Paper

Algorithm

Kleinman algorithm

Source

IEEE Transactions on Automatic Control

Identifiers

DOI 10.1109/TAC.1968.1098829

Abstract¶

In this correspondence an iterative technique for solving the linear regulator problem with infinite terminal time is presented. The scheme is based on the method of successive substitutions, which has been applied elsewhere to solve linear regulator problems, subject to the assumption of a finite terminal time. The results presented below are based on research reported by this author, in which successive substitution methods were applied to solve the infinite time problem. By using the concept of a cost matrix, it is directly shown that the iterations are monotonically convergent. Recently, Puri and Glover have obtained similar results by applying concepts of the Hamilton-Jacobi theory. This latter technique gives an interesting and different insight to the nature of the iterative scheme.

Summary¶

An efficient algorithm for designing the continuous-time linear quadratic regulator / solving the continuous-time algebraic Riccati equation is proposed and proven to be globally convergent with a quadratic rate. It was later shown that Kleinman's algorithm is an instance of the dynamic programming technique of policy iteration, which itself is an application of Newton's method to the Bellman equation.