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Synthesis of linear quadratic control laws on basis of linear matrix inequalities. (English. Russian original) Zbl 1118.49028

Autom. Remote Control 68, No. 3, 371-385 (2007); translation from Avtom. Telemekh. 68, No. 3, 3-18 (2007).
Summary: Classic problems of control law construction for a linear dynamic object that is optimal by the quadratic criterion in the determinate and stochastic cases are reduced, as is known, to solving nonlinear matrix Riccati equations. It is shown that the notion of \(H_{2}\)-norm of a system transfer matrix makes it possible to formulate and solve the stated problems in terms of linear matrix inequalities.

MSC:

49N10 Linear-quadratic optimal control problems
93C05 Linear systems in control theory
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[1] Kalman, R., Falb, P., and Arbib, M., Topics in Mathematical System Theory, New York: McGraw-Hill, 1969. Translated under the title Ocherki po matematicheskoi teorii sistem, Moscow: Mir, 1971. · Zbl 0231.49001
[2] Kwakernaak, H. and Sivan, R., Linear Optimal Control Systems, New York: Wiley, 1972. Translated under the title Lineinye optimal’nye sistemy upravleniya, Moscow: Mir, 1977.
[3] Andreev, Yu.N., Upravlenie konechnomernymi lineinymi ob”ektami (Control of Finite-dimensional Linear Objects), Moscow: Nauka, 1976. · Zbl 0353.93003
[4] Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM, 1994. · Zbl 0816.93004
[5] Gahinet, P., Nemirovski, A., Laub, A.J., and Chilali, M., The LMI Control Toolbox. For Use with Matlab. User’s Guide, Natick: MathWorks, 1995.
[6] Balandin, D.V. and Kogan, M.M., Sintez zakonov upravleniya na osnove lineinykh matrichnykh neravenstv (Synthesis of Control Laws on the Basis of Linear Matrix Inequalities), Moscow: Fizmatlit, 2006. · Zbl 1124.93001
[7] Colaneri, P., Geromel, J.C., and Locatelli, A., Control Theory and Design, San Diego: Academic, 1997.
[8] Iwasaki, T., Skelton, R.E., and Geromel, J.C., Linear Quadratic Suboptimal Control with Static Output Feedback, Syst. Control Lett., 1994, vol. 23, no. 6, pp. 421–430. · Zbl 0873.49021 · doi:10.1016/0167-6911(94)90096-5
[9] El Ghaoui, L., Oustry, F., and Rami, M.A., A Cone Complementarity Linearization Algorithm for Static Output-Feedback and Related Problems, IEEE Trans. Automat. Control, 1997, vol. 42, no. 8, pp. 1171–1176. · Zbl 0887.93017 · doi:10.1109/9.618250
[10] Iwasaki, T., The Dual Iteration for Fixed Order Control, IEEE Trans. Automat. Control, 1999, vol. 44, no. 4, pp. 783–788. · Zbl 0957.93029 · doi:10.1109/9.754818
[11] Balandin, D.V. and Kogan, M.M., An Optimization Algorithm for Checking Feasibility of Robust H -control Problem for Linear Time-varying Uncertain Systems, Int. J. Control, 2004, vol. 77, no. 5, pp. 498–503. · Zbl 1061.93034 · doi:10.1080/00207170410001674028
[12] Balandin, D.V. and Kogan, M.M., Synthesis of Controllers on the Basis of a Solution to Linear Matrix Inequalities and a Search Algorithm for Reciprocal Matrices, Avtom. Telemekh., 2005, no. 1, pp. 82–99. · Zbl 1130.93346
[13] Horn, R.A. and Johnson, C.R., Matrix Analysis, Cambridge: Cambridge Univ. Press, 1985. Translated under the title Matrichnyi analiz, Moscow: Mir, 1989. · Zbl 0576.15001
[14] Gahinet, P. and Apkarian, P., A Linear Matrix Inequality Approach to H Control, Int. J. Robust Nonlinear Control, 1994, vol. 4, pp. 421–448. · Zbl 0808.93024 · doi:10.1002/rnc.4590040403
[15] Balandin, D.V. and Kogan, M.M., Optimal Perturbation Damping in Linear Control Systems, Diff. Urav., 2005, vol. 41, no. 11, pp. 1550–1557. · Zbl 1127.93049
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