An accelerated technique for solving one type of discrete-time algebraic Riccati equations

作者：Lin Matthew M; Chiang Chun Yueh

来源：Journal of Computational and Applied Mathematics, 2018, 338: 91-110.

DOI：10.1016/j.cam.2018.02.004

• Algebraic Riccati equations
• Sherman morrison woodbury formula
• Positive definite solution
• Semigroup property
• Doubling algorithm
• r-superlinear with order r

Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and H-infinity 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 show that this method is capable of computing the unique negative definite solution, once it exists.

• 出版日期2018-8-15