TY - JOUR
T1 - Homotopy for rational riccati equations arising in stochastic optimal control
AU - Zhang, Liping
AU - Fan, Hung Yuan
AU - Chu, Eric King Wah
AU - Wei, Yimin
N1 - Publisher Copyright:
© 2015 Society for Industrial and Applied Mathematics.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Generalized Stein equation
KW - Generalized lyapunov equation
KW - Rational algebraic Riccati equation
KW - Stochastic algebraic Riccati equation
KW - Stochastic optional control
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U2 - 10.1137/140953204
DO - 10.1137/140953204
M3 - Article
AN - SCOPUS:84923912581
SN - 1064-8275
VL - 37
SP - B103-B125
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
IS - 1
ER -