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題名 Numerical Solutions for Stochastic Continuous-Time Algebraic Riccati Equations
作者 郭岳承
Huang, Tsung-Ming;Kuo, Yueh-Cheng;Li, Ren-Cang;Lin, Wen-Wei
貢獻者 應數系
關鍵詞 stochastic state-dependent linear control; matrix Riccati equation; fixed-point iteration; doubling algorithm; Newton’s method
日期 2025-09
上傳時間 30-Jan-2026 11:07:02 (UTC+8)
摘要 We are concerned with efficient numerical methods for stochastic continuous-time algebraic Riccati equations (SCARE). Such equations frequently arise from the state-dependent Riccati equation approach which is perhaps the only systematic way today to study nonlinear control problems. Often, involved Riccati-type equations are of small scale, but have to be solved repeatedly in real time. A new inner-outer iterative method that combines the fixed-point strategy and the structure-preserving doubling algorithm (SDA) is proposed. It is proved that the method is monotonically convergent to the desired stabilizing solution. Previously, Newton’s method has been called to solve SCARE, but it was mostly investigated from its theoretical aspects rather than numerical aspects in terms of robust and efficient numerical implementation. For that reason, we revisit Newton’s method for SCARE, focusing on how to make Newton’s method practical. Finally numerical experiments are conducted to validate the new method and robust implementations of Newton’s method.
關聯 SIAM Journal on Matrix Analysis and Applications, Vol.46, No.3, pp.1675-1700
資料類型 article
DOI https://doi.org/10.1137/24M1635156
dc.contributor 應數系
dc.creator (作者) 郭岳承
dc.creator (作者) Huang, Tsung-Ming;Kuo, Yueh-Cheng;Li, Ren-Cang;Lin, Wen-Wei
dc.date (日期) 2025-09
dc.date.accessioned 30-Jan-2026 11:07:02 (UTC+8)-
dc.date.available 30-Jan-2026 11:07:02 (UTC+8)-
dc.date.issued (上傳時間) 30-Jan-2026 11:07:02 (UTC+8)-
dc.identifier.uri (URI) https://ah.lib.nccu.edu.tw/item?item_id=180867-
dc.description.abstract (摘要) We are concerned with efficient numerical methods for stochastic continuous-time algebraic Riccati equations (SCARE). Such equations frequently arise from the state-dependent Riccati equation approach which is perhaps the only systematic way today to study nonlinear control problems. Often, involved Riccati-type equations are of small scale, but have to be solved repeatedly in real time. A new inner-outer iterative method that combines the fixed-point strategy and the structure-preserving doubling algorithm (SDA) is proposed. It is proved that the method is monotonically convergent to the desired stabilizing solution. Previously, Newton’s method has been called to solve SCARE, but it was mostly investigated from its theoretical aspects rather than numerical aspects in terms of robust and efficient numerical implementation. For that reason, we revisit Newton’s method for SCARE, focusing on how to make Newton’s method practical. Finally numerical experiments are conducted to validate the new method and robust implementations of Newton’s method.
dc.format.extent 98 bytes-
dc.format.mimetype text/html-
dc.relation (關聯) SIAM Journal on Matrix Analysis and Applications, Vol.46, No.3, pp.1675-1700
dc.subject (關鍵詞) stochastic state-dependent linear control; matrix Riccati equation; fixed-point iteration; doubling algorithm; Newton’s method
dc.title (題名) Numerical Solutions for Stochastic Continuous-Time Algebraic Riccati Equations
dc.type (資料類型) article
dc.identifier.doi (DOI) 10.1137/24M1635156
dc.doi.uri (DOI) https://doi.org/10.1137/24M1635156