 
Summary: Automation and Remote Control, vol. 55, N # 3, pp. 311320
FEEDBACKCONTROLLED SADDLE GRADIENT PROCESSES 1
Revised 17 November 2003
A.S. Antipin UDC 519.714:519.853.3
Methods of control of saddle gradient dierential systems under the constraints imposed on
control functions and state variables are put forward. Asymptotic stability of the set of
equilibrium states is proved for controllable systems.
In [1] it is rightly noted that the problem of synthesis of control laws for nonlinear objects
(systems) is a principal problem. There are a large number of studies devoted to the problem
of stabilization of programmed motion. However, the solution to this problem is still far from
complete. The methods of global stabilization are worked out insuciently, while the methods
in which account is taken of the constraints on control functions and state variables are as yet
quite imperfect.
In this work we consider the synthesis of control laws for nonlinear objects whose set of equi
librium states is dened by the problems of convex programming or degenerate saddle functions.
These problems are of practical importance and pertain to the theory of multiply connected
nonlinear systems [2].
The stabilization algorithms presented in the paper are inherently global and what is impor
tant is that they use the projection operator to account for the presence of constraints imposed
on the control functions and state variables.
