Numerical solution to generalized Lyapunov/Stein and rational Riccati equations in stochastic control

Hung Yuan Fan, Peter Chang Yi Weng, Eric King Wah Chu

研究成果: 雜誌貢獻期刊論文同行評審

12 引文 斯高帕斯(Scopus)

摘要

We consider the numerical solution of the generalized Lyapunov and Stein equations in ℝn$\mathbb {R}^{n}$, arising respectively from stochastic optimal control in continuous- and discrete-time. Generalizing the Smith method, our algorithms converge quadratically and have an O(n3) computational complexity per iteration and an O(n2) memory requirement. For large-scale problems, when the relevant matrix operators are “sparse”, our algorithm for generalized Stein (or Lyapunov) equations may achieve the complexity and memory requirement of O(n) (or similar to that of the solution of the linear systems associated with the sparse matrix operators). These efficient algorithms can be applied to Newton’s method for the solution of the rational Riccati equations. This contrasts favourably with the naive Newton algorithms of O(n6) complexity or the slower modified Newton’s methods of O(n3) complexity. The convergence and error analysis will be considered and numerical examples provided.

原文英語
頁(從 - 到)245-272
頁數28
期刊Numerical Algorithms
71
發行號2
DOIs
出版狀態已發佈 - 2016 二月 1

ASJC Scopus subject areas

  • Applied Mathematics

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