Abstract
This paper briefly considers solutions of primary statements of problem of anisotropic analysis of time-invariant systems and problems of synthesis of suboptimal and γ-optimal anisotropic controllers and filters for the time-invariant systems. Numerical procedures for finding the respective solutions are described. To demonstrate the efficiency of the proposed algorithms, illustrative numerical examples are given.
Similar content being viewed by others
References
Semyonov, A.V., Vladimirov, I.G., and Kurdjukov, A.P., Stochastic Approach to H ∞-Optimization, Proc. 33rd IEEE Conf. Decision Control, Florida, USA, 1994, pp. 2249–2250.
Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., Anisotropy of Signals and Entropy of Linear Stationary Systems, Dokl. Math., 1995, vol. 74, no. 3, pp. 388–390.
Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., On Computing the Anisotropic Norm of Linear Discrete-Time-Invariant Systems, Proc. 13th IFAC World Congr., San-Francisco, California, USA, 1996, pp. 179–184.
Vladimirov, I.G., Kurdyukov, A.P., and Semyonov, A.V., The Stochastic Problem of H ∞ Optimization, Dokl. Math., 1995, vol. 52, pp. 155–157.
Vladimirov, I.G., Kurdjukov, A.P., and Semyonov, A.V., State-Space Solution to Anisotropy-Based Stochastic H ∞-Optimization Problem, Proc. 13th IFAC World Congr., San-Francisco, USA, 1996, pp. 427–432.
Diamond, P., Kurdjukov, A.P., Semyonov, A.V., and Vladimirov, I.G., Homotopy Methods and Anisotropy-based Stochastic H ∞-Optimization of Control Systems, CADSMAP Research Report 97-14, The University of Queensland, Australia, 1997, pp. 1–22.
Vladimirov, I.G., Kurdyukov, A.P., Maximov, E.A., and Timin, V.N., Anizotropiinaya teoriya upravleniya— novyi podkhod k stokhasticheskomu robastnomu upravleniyu (Anisotropic Control Theory as a New Approach to Robust Stochastic Control), Trudy IV konferentsii “Identifikatsiya sistem i zadachi upravleniya” (Proc. IV Conf. “Identification of Systems and Control Problems”), Moscow, Russia, 2005, pp. 9–32.
Vladimirov, I.G., Diamond, F., and Kloeden, P., Anisotropy-Based Robust Performance Analysis of Finite Horizon Linear Discrete Time Varying Systems, Autom. Remote Control, 2006, vol. 67, no. 8, pp. 1265–1282.
Diamond, P., Vladimirov, I.G., Kurdyukov, A.P., and Semyonov, A.V., Anisotropy-Based Performance Analysis of Linear Discrete Time Invariant Control Systems, Int. J. Control, 2001, no. 74, pp. 28–42.
Tchaikovsky, M.M., Kurdyukov, A.P., and Timin, V.N., Strict Anisotropic Norm Bounded Real Lemma in Terms of Inequalities, Prep. 18th IFAC World Congr., Milano, Italy, 2011, pp. 2332–2337.
Tchaikovsky, M.M. and Kurdyukov, A.P., Strict Anisotropic Norm Bounded Real Lemma in Terms of Matrix Inequalities, Dokl. Math., 2011, vol. 84, no. 3, pp. 895–898.
Tchaikovsky, M.M., Static Output Feedback Anisotropic Controller Design by LMI-based Approach: General and Special Cases, Proc. 2012 Am. Control Conf., Montreal, Canada, 2012, pp. 5208–5213.
Tchaikovsky, M.M., Multichannel Synthesis Problems for Anisotropic Control, Autom. Remote Control, 2016, vol. 77, no. 8, pp. 1351–1369.
Vladimirov, I.G., Anisotropy-based Optimal Filtering in Linear Discrete Time Invariant Systems, CADSMAP Research Report 01-03, The University of Queensland, Australia, 2001.
Timin, V.N., Tchaikovsky, M.M., and Kurdyukov, A.P., A Solution to Anisotropic Suboptimal Filtering Problem by Convex Optimization, Dokl. Math., 2012, vol. 85, no. 3, pp. 443–445.
Timin, V.N., Anisotropy-Based Suboptimal Filtering for the Linear Discrete Time Invariant Systems, Autom. Remote Control, 2013, vol. 74, no. 11, pp. 1773–1785.
Polyak, B.T., Introduction to Optimization, New York: Optimization Software, 1987.
Gahinet, P., Explicit Controller Formulas for LMI-based H ∞ Synthesis, Automatica, 1996, vol. 32, pp. 1007–1014.
Tchaikovsky, M.M., Nikiforov, V.M., Gusev, A.A., and Andreev, K.A., Digital Control of a Gyrostabilized Platform under the Influence of Uncertain Disturbances in the Presence of Measurement Noise, Proc. 23 Saint-Petersburg Int. Conf. Integrated Navigat. Syst., Saint-Petersburg, Russia, 2016, pp. 236–241.
Tchaikovsky, M.M., Kurdyukov, A.P., and Nikiforov, V.M., LMI-based Design of Multichannel Anisotropic Suboptimal Controllers with Application to Control of Gyrostabilized Platform, Proc. 2012 IEEE Multiconf. Syst. Control, Dubrovnik, Croatia, 2012, pp. 1455–1460.
Mariton, M. and Bertrand, R., A Homotopy Algorithm for Solving Coupled Riccati Equations, Optim. Control Appl. Meth., 1985, vol. 6, pp. 351–357.
Khargonekar, P.P., Rotea, M.A., and Baeyens, E., Mixed H 2/H ∞ Filtering, Int. J. Robust Nonlin. Control, 1996, vol. 6, pp. 313–330.
Timin, V.N. and Kurdyukov, A.P., Mnogokriterial’naya suboptimal’naya anizotropiinaya fil’tratsiya lineinykh diskretnykh statsionarnykh sistem (Multiobjective Suboptimal Anisotropic Filtering of Linear Discrete Time-Invariant Systems), XII Vseross. soveshchanie po problemam upravleniya (XII All-Russian Meeting on Control Problems), Moscow, Russia, 2014, pp. 901–910.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © M.M. Tchaikovsky, V.N. Timin, A.Yu. Kustov, A.P. Kurdyukov, 2018, published in Avtomatika i Telemekhanika, 2018, No. 1, pp. 162–182.
This paper was recommended for publication by A.I. Kibzun, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Tchaikovsky, M.M., Timin, V.N., Kustov, A.Y. et al. Numerical Procedures for Anisotropic Analysis of Time-Invariant Systems and Synthesis of Suboptimal Anisotropic Controllers and Filters. Autom Remote Control 79, 128–144 (2018). https://doi.org/10.1134/S0005117918010113
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117918010113