Geodesic
On analytical solutions of matrix Riccati equations
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 231-246.

Voir la notice de l'article provenant de la source Math-Net.Ru

Matrix Riccati equations appear in numerous applications, especially in control engineering. In this paper we derive analytical formulas for exact solutions of algebraic and differential matrix Riccati equations. These solutions are expressed in terms of matrix transfer functions of appropriate linear dynamical systems. 
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Yuri S. Ledyaev. On analytical solutions of matrix Riccati equations. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 231-246. http://geodesic.mathdoc.fr/item/TM_2011_273_a9/

[1] Anderson B.D.O., Moore J.B., Linear optimal control, Prentice-Hall, Englewood Cliffs, NJ, 1971 | MR | Zbl

[2] Brockett R.W., Finite dimensional linear systems, J. Wiley Sons, New York, 1970 | Zbl

[3] Clarke F.H., Optimization and nonsmooth analysis, J. Wiley Sons, New York, 1983 | MR | Zbl

[4] Clarke F.H., Methods of dynamic and nonsmooth optimization, CBMS–NSF Reg. Conf. Ser. Appl. Math., 57, SIAM, Philadelphia, PA, 1989 | MR | Zbl

[5] Clarke F.H., Ledyaev Yu.S., Stern R.J., Wolenski P.R., Nonsmooth analysis and control theory, Springer, New York, 1998 | MR

[6] Clarke F.H., Vinter R.B., “The relationship between the maximum principle and dynamic programming”, SIAM J. Control and Optim., 25:5 (1987), 1291–1311 | DOI | MR | Zbl

[7] Gamkrelidze R.V., Principles of optimal control theory, Plenum Press, New York, 1978 | MR | Zbl

[8] Kalman R.E., “Contributions to the theory of optimal control”, Bol. Soc. Mat. Mex. Ser. 2, 5 (1960), 102–119 | MR | Zbl

[9] Lancaster P., Rodman L., Algebraic Riccati equations, Clarendon Press, Oxford, 1995 | MR | Zbl

[10] Ledyaev Yu.S., “On generic existence and uniqueness in nonconvex optimal control problems”, Set-Valued Anal., 12:1–2 (2004), 147–162 | DOI | MR | Zbl

[11] Leonov G.A., Shumafov M.M., Metody stabilizatsii lineinykh upravlyaemykh sistem, Izd-vo S.-Peterb. un-ta, SPb., 2005

[12] Letov A.M., “Analiticheskoe konstruirovanie regulyatorov. IV”, Avtomatika i telemekhanika, 22:4 (1961), 425–435 | MR | Zbl

[13] Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mischenko E.F., Matematicheskaya teoriya optimalnykh protsessov, Fizmatgiz, M., 1961

[14] Reid W.T., Riccati differential equations, Acad. Press, New York, 1972 | MR

[15] Widder D.V., The Laplace transform, Princeton Univ. Press, Princeton, NJ, 1941 | MR

[16] Willis B.H., Brockett R.W., “The frequency domain solution of regulator problems”, IEEE Trans. Autom. Control, AC-10 (1965), 262–267 | DOI | MR