DOI 10.17586/0021-3454-2017-60-7-603-611
UDC 62.50
ENSURING DYNAMIC SYSTEM STABILITY UNDER CONSTRAINED PERTURBATIONS IMPACT
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate Professor
V. Y. Tertychny-Dauri
ITMO University, Saint Petersburg, 197101, Russian Federation; Professor
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Abstract. The problem of ensuring asymptotic stability of nonlinear dynamic system by means of tuning its parameters is considered for the case when the system is subject to constrained external perturbations. A solution to the problem is found with the use of a robust finitely convergent algorithm of parameters setting. An estimate of attraction domain proportional to the perturbation level is derived.
Keywords: dynamic system, constrained perturbation, target inequality, finitely convergent algorithm
References:
References:
- Rouche N., Habets P., Laloy М. Stability Theory by Liapunov's Direct Method. Applied Mathematical Sciences 22,New York,Heidelberg,Berlin, Springer-Verlag, 1977.
- Bellman R. Stability theory of differential equations, McGraw-Hill Book Company, 1953, 179 p.
- Alfutov N.A., Kolesnikov K.S.Ustoychivost' dvizheniya i ravnovesiya (Stability of the Movement and Balance), Moscow, 2003. (in Russ.)
- Zadeh L.A., Desoer C.A. Linear System Theory: the State Space Approach, NY, Dover Publications, 2008.
- Liu J., Teel A. IEEE Trans. on Automat. Control, 2016, no. 4(61), рp. 1057–1062.
- Clarke F.H., Stern R.J. Systems & Control Letters, 2005, no. 8(54), рp. 747–752.
- Fomin V.N., Fradkov A.L., Yakubovich V.A.Adaptivnoe upravlenie dinamicheskimi ob"ektami (Adaptive Control of Dynamic Objects), Moscow, 1981. (in Russ.)
- Krasovskiy A.A., ed., Spravochnik po teorii avtomaticheskogo upravleniya (Handbook of Automatic Control Theory), Moscow, 1987. (in Russ.)
- Fradkov A.L.Adaptivnoe upravlenie v slozhnykh sistemakh (Adaptive Control in Complex Systems), Moscow, 1990. (in Russ.)
- Anderson B.D.O., Bitmead R.R., Johnson C.R., Kokotovic P.V., Kosut R.L., Mareels I.M.Y., Praly L., Riedle B.D. Stability of Adaptive Systems: Passivity and Averaging Analysis, NY, M.I.T. Press, 1986.
- Miroshnik I.V., Nikiforov V.O., Fradkov A.L. Nelineynoe i adaptivnoe upravlenie slozhnymi dinamicheskimi sistemami (Nonlinear and Adaptive Control of Complex Dynamic Systems), St. Petersburg, 2000. (in Russ.).
- Marino R., Tomei P. Nonlinear Control Design: Geometric, Adaptive and Robust, Englewood Cliffs, NJ, Prentice Hall, 1995.
- Isidori A. Nonlinear Control System, London, Springer, 1995.
- Ioannou P.A., Sun J. Robust Adaptive Control. Engewood Cliffs, NJ, Prentice Hall, 1996.
- Narendra K.S., Annaswamy A.M. Stable Adaptive Systems, NY, Dover Publication, 2012.
- Raissi T., Ramdani N., Candau Y. Automatica, 2004, no. 10(40), рp. 1771–1777.
- Grip H., Johansen T., Imsland L., Kaasa G.-O.Automatica, 2010, no. 1(46), рp. 19–28.
- Tertychnyy-Dauri V.Yu. Adaptivnaya mekhanika (Adaptive Mechanics), Moscow, 1998. (in Russ.)
- Vedyakov A.A., Tertychnyy-Dauri V.Yu. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2016, no. 4(16), рp. 620–626. (in Russ.)
