Abstract
A new strategy for stabilization of one-dimensional dynamic objects with a priori unknown mathematical model is presented. For a given control law, the stabilization strategy consists in determination of the times when the control law changes and its reversal at these times, on the basis of a fuzzy knowledge base that takes into account the nature of the variation of the “distance” relative to an equilibrium point. The derivatives of the “distance” and such concepts as “approach” and “departure” are also used. Aggregation of the input phase variables and the use of generalized concepts of the theory of Lyapunov stability make it possible to construct a sufficiently general and, at the same time, simple fuzzy regulator with two aggregated inputs and piecewise-continuous output signals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Krasovskii, A.A., Ed., Spravochnik po teorii avtomaticheskogo upravleniya (Handbook on the Theory of Optimal Control), Moscow: Nauka, 1987, pp. 401–435.
Wu, Q., Sepehri, N., and Thornton-Trump, A.B., Lyapunov Stability of an Inverted Pendulum Model (ISIAC 017.1-5), Albuquerque: TSI Press, 1998.
Kim, A.V., Pimenov, V.G., and Kwon, O.B., Lyapunov-Krasovskii Functional Instability and Control Problems of Time-Delay Systems (ISIAC 029.1-5), Albuquerque: TSI Press, 1998.
Yong, Y., Robust Observer-Regulator Design for Nonlinear Systems with Uncertainty (ISIAC 015.1-6), Albuquerque: TSI Press, 1998.
Kolomeytseva, M.B. and Kho, L.D., Synthesis of an Optimal Fuzzy Regulator for a Nonlinear Dynamic System, Tr. Zaporozh. National. Univ. Radiotekhnika, informatika, upravlenie, 2001, no. 2, pp. 153–155.
Ho, H.F., Wong, Y.K., and Rad, A.B., Adaptive Fuzzy Sliding Mode Control Design; Lyapunov Approach, in IEEE Intern. Conf. Fuzzy Systems, 2001.
Lagrat, I., Ouakka, H., and Boumhidi, I., Fuzzy Sliding Mode PI Regulator for Nonlinear Systems, Proc. 6th WSEAS Intern. Conf. Simulation, Modeling and Optimization, Lisbon, September 22–24, 2006, p. 534–539.
Rustamov, G.A., Namazov, M.B., and Misrikhanov, L.M., Synthesis of a Relay Regulator with Fuzzy Switching Times on the Basis of a Macrovariable, Avtom. Vychisl. Tekh. (Riga), 2007, no. 3, pp. 56–62 [Autom. Control Comput. Sci. (Engl. Transl.), no. 3].
Rustamov, G.A. and Namazov, M.B., Approach to the Synthesis of Fuzzy Stabilization Systems with a priori Unknown Model of the Object, Avtom. Vychisl. Tekh. (Riga), 2007, no. 5, pp. 32–39 [Autom. Control Comput. Sci. (Engl. Transl.), no. 5].
Shtoba, S.D., Proektirovanie nechetkikh sistem sredstvami Matlab (Design of Fuzzy Systems by means of Matlab), Moscow: Goryachaya liniya. Telecom, 2007.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © G.A. Rustamov, 2008, published in Avtomatika i Vychislitel’naya Tekhnika, 2008, No. 2, pp. 65–73.
About this article
Cite this article
Rustamov, G.A. Universal Lyapunov-type fuzzy controllers. Aut. Conrol Comp. Sci. 42, 102–108 (2008). https://doi.org/10.3103/S0146411608020089
Received:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0146411608020089