๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Controllability and observability in the problem of stabilizing steady motions of non-holonomic mechanical systems with cyclic coordinatest

โœ Scribed by V.I. Kalenova; V.M. Morozov; Ye.N. Sheveleva

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
653 KB
Volume
65
Category
Article
ISSN
0021-8928

No coin nor oath required. For personal study only.

โœฆ Synopsis

The approach to the solution of stabilization problems for steady motions of holonomic mechanical systems [ 1,2] based on linear control theory, combined with the theory of critical cases of stability theory, is used to solve the analogous problems for nonholonomic systems. It is assumed that the control forces may affect both cyclic and positional coordinates, where the number r of independent control inputs may be considerably less than the number n of degrees of freedom of the system, unlike in many other studies (see, e.g., [3--5]), in which as a rule r = n. Several effective new criteria of controllability and observability are formulated, based on reducing the problem to a problem of less dimension. Stability analysis is carried out for the trivial solution of the complete non-linear system, closed by a selected control. This analysis is a necessary step in solving the stabilization problem for steady motion of a non-holonomic system (unlike holonomic systems), since in most cases such a system is not completely controllable.

๐Ÿ“œ SIMILAR VOLUMES

The stability and stabilization of the s
The stability and stabilization of the steady motions of a class of non-holonomic mechanical systems
โœ V.I. Kalenova; V.M. Morozov; M.A. Salmina ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 611 KB

The stability of the steady motions and the controllability of a class of non-holonomic mechanical systems under the action of potential and control forces are investigated. A problem of the stability of the steady motion of a three-wheeled vehicle, taking into account the inertia of the wheels, whi

Stabilization of the motions of mechanic
Stabilization of the motions of mechanical systems with non-holonomic constraints
โœ V.I. Matyukhin ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 605 KB

Mechanical systems possibly containing non-holonomic constraints are considered. The problem of stabilizing the motion of the system along a given manifold of its phase space is solved. A control law which does not involve the dynamical parameters of the system is constructed. The law is universal,

The influence of dissipative and constan
The influence of dissipative and constant forces on the form and stability of steady motions of mechanical systems with cyclic coordinates
โœ A.V Karapetyan; I.S Lagutina ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 534 KB

Mechanical systems with cyclic coordinates subject to dissipative forces with complete dissipation and constant forces applied only to the cyclic variables are considered. Problems of the existence of steady motions in such systems and the conditions for their stability are discussed. It is shown, i

The relation between problems of pursuit
The relation between problems of pursuit, controllability and stability in the large in linear systems with different types of constraints
โœ A.A. Azamov; A.Sh. Kuchkarov; B. Samatov ๐Ÿ“‚ Article ๐Ÿ“… 2007 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 166 KB

A relation is established between problems of pursuit, controllability and stability in the large in linear systems when a geometric constraint is imposed on the control vector of the pursuer and an integral constraint is imposed on the control function of the evader.