Modification of chaotic systems limit sets by multiparametrical optimal correction
In the paper we investigate the problem when the aim of control is the modification of the system limit set (chaotic attractor) into the stable invariant set. This problem is on a joint of chaos control and bifurcation control methods, and the complete understanding of stabilization peculiarities requires the development of means of multiparametrical analysis. Hence the dynamic correction technique of parametric space of chaotic systems is offered. Thus the demand of small parametric changes naturally allows formulating the problem of optimal correction. Based on Pontryagin's maximum principle the corrective functions and necessary conditions of achievement of the invariant stable set are found. The efficiency of correction for chaos suppression is demonstrated on Lorenz system.