THE CONSTRUCTION OF BOUNDED GAME-THEORETIC CONTROLS FOR NONLINEAR DYNAMICAL-SYSTEMS

The problem of transferring a non-linear dynamical;system, subject to perturbations, to the null equilibrium position in a finite time by me ans of a bounded control is considered. Only the levels of uncontrolla ble perturbations are known, and are not assumed to be small. Sufficie nt conditions are obtained which ensure that the problem has a guarant eed solution for the given domain of initial conditions. An estimate o f the guaranteed control time is obtained. The construction of the con trol can be reduced to the construction of game strategies for auxilia ry linear game-theoretic problems. To estimate the ''auxiliary noise'' in the resulting linear system, the principle of ''prescribing and su bsequent confirmation'' of noise levels is put forward. On the basis o f this principle, these estimates are checked on the set of states of the auxiliary linear systems, where the control is also subsequently e stimated. As a result, an iterative algorithm for solving the original non-linear problem is obtained. Within the framework of the method pr oposed a new solution of the game-theoretic problem of the reorientati on of an asymmetric rigid body in the presence of noise is given. (C) 1997 Elsevier Science Ltd. All rights reserved.