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Journal of Automation and Information Sciences
SJR: 0.232 SNIP: 0.464 CiteScore™: 0.27

ISSN 印刷: 1064-2315
ISSN オンライン: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v48.i11.10
pages 1-6

On Solution of the Generalized Riccati Equations

Vladimir B. Larin
S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

要約

The procedures, appearing while the synthesis of the optimal control of linear time-invariant systems, are considered. The algorithms of finding the maximal solutions of the generalized Riccati equations, arising both in the problems with continuous and with discrete time, are presented. These algorithms are based on the procedures of linear matrix inequalities.

参考

  1. Rami M.A., Zhou X.Y., Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic control, IEEE Trans. Automat. Control, 2000, 45, No. 6, 1131–1142.

  2. Ivanov I.G., Accelerated LMI solvers for the maximal solution to a asset of discrete-time algebraic Riccati equations, Appl. Math. E-Notes, 2012, 12, 228–238.

  3. Ivanov I.G., Hasanov V.I., Perturbation estimates for the two kinds of algebraic Riccati equations arising in a arising in stochastic control, J. of Numer. Math. and Stochastics, 2014, 6(1), 1–20.

  4. Prach A., Tekinalp O., Bernstein D.S., Infinite-horizon linear-quadratic control by forward propagation of the differential Riccati equation, IEEE Control Systems Magaz., 2015, 78–93.

  5. Zhang L., Fan H-Y., Chu E K.-W., Wei Y., Homotopy for rational Riccati equations arising in stochastic optimal control, SIAM J. Sci. Comput., 2015, 37, No. 1, B103–B125.

  6. Boyd S., Ghaoui L.E., Feron E., Balakrishnan V., Linear matrix inequalities in system and control theory, SIAM, Philadelphia, 1994.

  7. Gahinet P., Nemirovski A., Laub A.J., Chilali M., LMI control toolbox users guide, The Math Works Inc., 1995.

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