Homotopy for rational riccati equations arising in stochastic optimal control

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)B103-B125
JournalSIAM Journal on Scientific Computing
Issue number1
Publication statusPublished - 2015


  • Generalized Stein equation
  • Generalized lyapunov equation
  • Rational algebraic Riccati equation
  • Stochastic algebraic Riccati equation
  • Stochastic optional control

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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