An accelerated technique for solving one type of discrete-time algebraic Riccati equations
For control and engineering practitioners solving discrete-time algebraic Riccati equations, this work offers a faster algorithm with guaranteed convergence, though it is an incremental improvement over existing methods.
The paper provides sufficient conditions for the existence of a unique positive definite solution to a discrete-time algebraic Riccati equation and proposes an accelerated algorithm achieving any desired order of convergence, performing well even in almost critical cases.
Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati equations. Our contribution is twofold. First, we present sufficient conditions for the existence of a unique positive definite solution. Second, we propose an accelerated algorithm to obtain the positive definite solution with the rate of convergence of any desired order. Numerical experiments strongly support that our approach performs extremely well even in the almost critical case. As a byproduct, we provide show that this method is capable of computing the unique negative definite solution, once it exists.