Adaptive control of recurrent trajectories based on linearization of Poincare map

The problem of adaptive output feedback control aimed at stabilization of a (periodic or chaotic) goal trajectory is considered. Advantages and drawba cks of chaos control method based on linearization of Poincare map (first p roposed by Ott, Grebogi and Yorke in 1990) are discussed. It is suggested t hat the recurrence of the goal trajectory is the key property for applicabi lity of approach. Algorithms of adaptive control based on linearization of controlled Poincare map and method of goal inequalities are proposed. It is shown that stabilization of recurrent trajectories is possible under addit ional controllability-like and observability-like conditions. Examples of s tabilization of periodic and chaotic trajectories for forced brusselator an d Rossler systems are studied by computer simulations.