Optimal stabilization of motion with respect to some of the variables / Vorotnikov V.I. // Journal of Applied Mathematics and Mechanics. - 1990. - V. 54, l. 5. - P. 597-605.

ISSN:

00218928

Type:

Article

Abstract:

The use of non-linear transformations of variables and the theory of implicit functions yield sufficient conditions for the stabilization of the unperturbed motion of a certain class of non-linear control systems. Upon stabilization one can achieve Lyapunov stability and asymptotic stability with respect to some of the variables. Closed formulae are obtained which make it possible to organize an iterative process which will determine the most satisfactory (optimal) stabilization law from the practical point of view. A technique is worked out by which the construction of control laws in the original non-linear system can be reduced to the construction of control laws for an auxiliary linear control system of a simpler type. This technique is very similar to a principle that has become quite popular in the modern applied theory of automatic control - the iterative construction of optimal control laws. As an application, the technique is used to stabilize the equilibrium position of a rigid body by means of Cardan-suspended gyroscopes and motors in which the tractive force is continuously regulated. © 1991.

Author keywords:

Index keywords:

Control Systems--Stability; Gyroscopes; Asymptotic Stability; Linear Control System; Lyapunov Stability; Nonlinear Systems; Stabilization Law; Tractive Force; Mechanics

DOI:

10.1016/0021-8928(90)90104-I

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References	Krasovskii, Problems of the stabilization of controllable motions (1966) Theory of the Stability of Motion, , I.G. Malkin, Nauka, Moscow, Appendix 4; Rumyantsev, On optimal stabilization of controllable systems (1970) Prikl. Mat. Mekh., 34 (3); Krasovskii, (1973) Systems of Automatic Flight Control and their Analytical Design, , Nauka, Moscow; Krasovskii, (1987) Handbook of Automatic Control Theory, , Nauka, Moscow; Chernous'ko, Banichuk, (1973) Variational Problems of Mechanics and Control: Numerical Methods, , Nauka, Moscow; Zubov, (1975) Lectures in Control Theory, , Nauka, Moscow; Vorotnikov, On the complete controllability and stabilization of motion with respect to some of the variables (1982) Avtomatika i Telemekhanika, 3; Vorotnikov, On optimal stabilization of control (1988) Mekh. Tverd. Tela, 2. , Izv. Akad. Nauk SSSR; Bellman, (1972) Dynamic Programming, , Princeton University Press, Princeton, N.Y; Malkin, (1966) Theory of the Stability of Control, , Nauka, Moscow; Krementulo, (1977) Stabilization of Stationary Motions of a Rigid Body with the help of Rotating Masses, , Nauka, Moscow; Rumyantsev, On the stability of motion of a Cardan-suspended gyroscope (1958) I, II. Prikl. Mat. Mekh., 22 (4); Lur'ye, (1961) Analytical Mechanics, , Fizmatgiz, Moscow; Raushenbakh, Tokar, (1974) Control of Spacecraft Orientation, , Nauka, Moscow; Vorotnikov, On the stabilization of the orientation of a gyrostat in a circular orbit in a Newtonian force field (1986) Akad. Nauk SSSR. Mekh. Tverd. Tela, 3; Vorotnikov, On the control of the angular motion of a rigid body (1986) Mekh. Tverd. Tela, 6. , Izv. Akad. Nauk SSSR
CODEN	JAMMA
Language of Original Document	English
Abbreviated Source Title	J. Appl. Math. Mech.
Source	Scopus