A new iterative algorithm to solve periodic riccati differential equations with sign indefinite quadratic terms

Yantao Feng; Andras Varga; Brian D.O. Anderson; Marco Lovera

doi:10.1109/TAC.2010.2101710

A new iterative algorithm to solve periodic riccati differential equations with sign indefinite quadratic terms

Yantao Feng^*, Andras Varga, Brian D.O. Anderson, Marco Lovera

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

An iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed. In our algorithm, we replace the problem of solving a PRDE with an indefinite quadratic term by the problem of solving a sequence of PRDEs with a negative semidefinite quadratic term which can be solved by existing methods. The global convergence and the local quadratic rate of convergence are both established. A numerical example is given to illustrate our algorithm.

Original language	English
Article number	5672768
Pages (from-to)	929-934
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	56
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2010.2101710
Publication status	Published - Apr 2011

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10.1109/TAC.2010.2101710

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abstract = "An iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed. In our algorithm, we replace the problem of solving a PRDE with an indefinite quadratic term by the problem of solving a sequence of PRDEs with a negative semidefinite quadratic term which can be solved by existing methods. The global convergence and the local quadratic rate of convergence are both established. A numerical example is given to illustrate our algorithm.",

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AU - Anderson, Brian D.O.

AU - Lovera, Marco

PY - 2011/4

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N2 - An iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed. In our algorithm, we replace the problem of solving a PRDE with an indefinite quadratic term by the problem of solving a sequence of PRDEs with a negative semidefinite quadratic term which can be solved by existing methods. The global convergence and the local quadratic rate of convergence are both established. A numerical example is given to illustrate our algorithm.

AB - An iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed. In our algorithm, we replace the problem of solving a PRDE with an indefinite quadratic term by the problem of solving a sequence of PRDEs with a negative semidefinite quadratic term which can be solved by existing methods. The global convergence and the local quadratic rate of convergence are both established. A numerical example is given to illustrate our algorithm.

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A new iterative algorithm to solve periodic riccati differential equations with sign indefinite quadratic terms

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