Riccati differential equations arise in many different areas and are particularly important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff Riccati differential equations. We show how to apply exponential Rosenbrock-type integrators to get approximate solutions. Two typical exponential integration schemes are considered. The implementation issues are addressed and some low-rank approximations are exploited based on high quality numerical algebra codes. Numerical comparisons demonstrate that the exponential integrators can obtain high accuracy and efficiency for solving large-scale systems of stiff Riccati differential equations.

Riccati微分方程出现在许多不同的领域，在控制理论领域特别重要。在本文中，我们考虑了刚性Riccati微分方程大规模系统的数值积分。我们展示了如何应用指数型Rosenbrock型积分器来获得近似解。考虑了两种典型的指数积分方案。解决了实现问题，并基于高质量的数字代数代码开发了一些低秩近似。数值比较表明，指数积分器可以求解较大的刚性Riccati微分方程组，具有较高的精度和效率。