The problem of transferring a non-linear dynamical system, subject to perturbations, to the null equilibrium position in a finite time by means of a botmded control is considered. Only the levels of uncontrollable perturbations are known, and are not assumed to be small. Sufficient conditions are obtained which ensure that the problem has a guaranteed solution for the given domain of initial conditions. Axt estimate of the guaranteed control time is obtained. The construction of the control can be reduced to the construction of game strategies for auxiliary linear game-theoretic problems. To estimate the "auxiliary noise" in the resulting linear system, the principle of "prescribing and subsequent confirmation" of noise levels is put forward. On the basis of this principle, these estimates are checked on the set of states of the au,~liary linear systems, where the control is also subsequently estimated. As a result, an iterative algorithm for solving the original non-linear problem is obtained. Within the framework of the method proposed a ]~'w solution of the game-theoretic problem of the reorientation of an asymmetric rigid body in the presence of noise is given. O 19gq Elsevier Science Ltd. All rights reserved.
This paper develops the approach presented in [1-4] and touches on the study of decomposition [5][6][7] as well as the partial stabilization and controllability [8--11] of non-linear controlled systems.
1. FORMULATION OF THE PROBLEM
Suppose that the motion of the controlled object can be described by a non-linear system of ordinary differential equations