Homotopy for rational riccati equations arising in stochastic optimal control

Liping Zhang, Hung Yuan Fan, Eric King Wah Chu, Yimin Wei

研究成果: 雜誌貢獻文章

3 引文 斯高帕斯(Scopus)

摘要

We consider the numerical solution of the rational algebraic Riccati equations in ℝn, arising from stochastic optimal control in continuous and discrete time. Applying the homotopy method, we continue from the stabilizing solutions of the deterministic algebraic Riccati equations, which are readily available. The associated differential equations require the solutions of some generalized Lyapunov or Stein equations, which can be solved by the generalized Smith methods, of O(n3) computational complexity and O(n2) memory requirement. For large-scale problems, the sparsity and structures in the relevant matrices further improve the efficiency of our algorithms. In comparison, the alternative (modified) Newton's methods require a difficult initial stabilization step. Some illustrative numerical examples are provided.

原文英語
頁(從 - 到)B103-B125
期刊SIAM Journal on Scientific Computing
37
發行號1
DOIs
出版狀態已發佈 - 2015 一月 1

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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