Homotopy for rational riccati equations arising in stochastic optimal control

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

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume37
Issue number1
DOIs
Publication statusPublished - 2015 Jan 1

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Stochastic Optimal Control
Algebraic Riccati Equation
Riccati equations
Riccati Equation
Homotopy
Stein Equation
Modified Newton Method
Homotopy Method
Lyapunov Equation
Large-scale Problems
Newton-Raphson method
Sparsity
Generalized Equation
Computational complexity
Computational Complexity
Discrete-time
Stabilization
Differential equations
Continue
Numerical Solution

Keywords

  • 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

Cite this

Homotopy for rational riccati equations arising in stochastic optimal control. / Zhang, Liping; Fan, Hung-Yuan; Chu, Eric King Wah; Wei, Yimin.

In: SIAM Journal on Scientific Computing, Vol. 37, No. 1, 01.01.2015, p. B103-B125.

Research output: Contribution to journalArticle

Zhang, Liping ; Fan, Hung-Yuan ; Chu, Eric King Wah ; Wei, Yimin. / Homotopy for rational riccati equations arising in stochastic optimal control. In: SIAM Journal on Scientific Computing. 2015 ; Vol. 37, No. 1. pp. B103-B125.
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