A New Computationally Effective Algorithm for Solving the Discrete Riccati Equation

The Riccati Equation(RE) plays an important role in many fields of mathematics, science, and engineering, such as optimal control, estimation, game theory, radiative transfer, communications, and integral equations. Its solution constitutes an integral prerequisite to the solution of important problems in the above fields. In most applications it is essential that the solution to the RE be obtained in the shortest possible time. This is the reason that computationally efficient as well as numerically robust procedures for solving the RE are sought. A computationally effective algorithm that solves the discrete Riccati Equation, which we call the General Chandrasekhar-Type Algorithm (GCTA), is proposed in this paper. Moreover, the GCTA is used in conjunction with the well known Doubling Algorithm (DA), thus resulting in a new family of algorithms for solving the RE. The performance of these algorithms is investigated through several simulation examples. Finally, we establish the computational requirements of these algorithms. The question of how long the initial time interval over which the GCTA should be used to provide initial conditions for the DA is also addressed. It is found that such a unique optimal interval exists. Simulation results show that we have a maximum percent gain of the order of 30-50 % when this interval is used instead of an arbitrarily chosen one.