Stability of a class of adaptive nonlinear systems

• Autorzy: Dzieliński A.
• Języki publikacji: EN

Abstrakty

EN

This paper presents a research effort focused on the problem of robust stability of the closed-loop adaptive system. It is aimed at providing a general framework for the investigation of continuous-time, state-space systems required to track a (stable) reference model. This is motivated by the model reference adaptive control (MRAC) scheme, traditionally considered in such a setting. The application of differential inequlities results to the analysis of the Lyapunov stability for a class of nonlinear systems is investigated and it is shown how the problem of model following control may be tackled using this methodology.

Słowa kluczowe

EN

nonlinear systems; Lyapunov stability; adaptive systems

PL

system nieliniowy; stabilność Lapunova; układ adaptacyjny

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2005
• Tom: Vol. 15, no 4
• Strony: 455--462
• Opis fizyczny: Bibliogr. 20 poz., wykr.

Twórcy

autor

Dzieliński A.

• Institute of Control and Industrial Electronics Warsaw University of Technology 00–662 Warsaw, Poland,

Bibliografia

• [1] Corduneanu C. (1960): Application of differential inequalities to stability theory.—Analele Ştiinţifice ale Universităţii “Al.I. Cuza“ din Iaşi (Serie Nouă). Secţiunea I (Matematică, Fizică, Chimie), Vol. VI, No. 1, pp. 47–58, (in Russian).
• [2] Corduneanu C. (1961): Addendum to the paper Application of differential inequalities to stability theory. — Analele Ştiinţifice ale Universităţii “Al. I. Cuza” din Iaşi (Serie Nouă). Secţiunea I (Matematică, Fizică, Chimie), Vol. VII(2), pp. 247–252, (in Russian).
• [3] Corduneanu C. (1964): On partial stability.—Revue Roumaine de Mathématiques Pures et Appliquées, Vol. IX(3), pp. 229–236, (in French).
• [4] Dzieliński A. (2002a): Neural networks based NARX models in nonlinear adaptive control. — App. Math. Comput. Sci., Vol. 12, No. 2, pp. 101–106.
• [5] Dzieliński A. (2002b): Difference inequalities and BIBO stability of approximate NARX models. — Bull. Polish Acad. Sci., Techn. Sci., Vol. 50, No. 4, pp. 295–311.
• [6] Hahn W.(1963): Theory and Application of Liapunov’s Direct Method. —Englewood Cliffs, NJ: Prentice-Hall.
• [7] Hahn W. (1967): Stability of Motion. —New York: Springer.
• [8] Hatvany L.(1975): On the application of differential inequalities to stability theory. — Vestnik Moskovskogo Universiteta, Vol. I30, No. 3, pp. 83–89, (in Russian).
• [9] Lakshmikantham V.(1962a): Differential systems and extension of Lyapunov’s method.—MichiganMath. J., Vol. 9, No. 4, pp. 311–320.
• [10] Lakshmikantham V. (1962b): Notes on variety of problems of differential systems. — Arch. Rat. Mech. Anal., Vol. 10, No. 2, pp. 119–126.
• [11] Lakshmikantham V. and Leela S. (1969a): Differential and Integral Inequalities. Theory and Applications, Vol. I: Ordinary Differential Equations. — New York: Academic Press.
• [12] Lakshmikantham V. and Leela S. (1969b): Differential and Integral Inequalities. Theory and Applications, Vol. II: Functional, Partial, Abstract, and Complex Differential Equations. —New York: Academic Press.
• [13] Liu X. and Siegel D., editors. (1994): Comparison Method in Stability Theory. — Amsterdam: Marcel Dekker.
• [14] Luzin N. N. (1951): On the method of approximate integration due to academician S. A. Chaplygin. — Uspekhi matematicheskikh nauk, Vol. 6, No. 6, pp. 3–27, (in Russian).
• [15] Makarov S. M. (1938): A generalisation of fundamental Lyapunov’s theorems on stability of motion. — Izvestiya fiziko-matematicheskogo obshchestva pri Kazanskom gosudarstvennom universitete (Seriya 3), Vol. 10, No. 3, pp. 139–159, (in Russian).
• [16] Narendra K. S. and Annaswamy A. M. (1989): Stable Adaptive Systems. — Eglewood Cliffs, NJ: Prentice-Hall.
• [17] Pachpatte B. G. (1971): Finite-difference inequalities and an extension of Lyapunov’s method. — Michigan Math. J., Vol. 18, No. 4, pp. 385–391.
• [18] Rabczuk R. (1976): Elements of Differential Inequalities. — Warsaw: Polish Scientific Publishers, (in Polish).
• [19] Szarski J. (1967): Differential Inequalities, 2nd Ed.. —Warsaw: Polish Scientific Publishers, (in Polish).
• [20] Walter W. (1970): Differential and Integral Inequalities. — Berlin: Springer.