Method of passification in adaptive control, estimation, and synchronization

The main results of the method of passification which are based on applying the Yakubovich–Kalman frequency theorem to the design of the feedback systems and examples of its use in the problems of adaptive control, state estimation, and synchronization were presented. Various types of the adaptive control algorithms with implicit reference model such as the algorithms of stabilization and tracking with the prescribed dynamics, algorithms with adaptive tuning of the standard control laws, and combined signal-parametric algorithm of adaptive control were described. Brief information about the shunting method in the adaptive control problem was given. The experimental results with the adaptive control on the “Helicopter” benchmark were described. Consideration was given to the problem of adaptive control of the nonlinear plants. Examples of applying the method of passification and adaptive observers to the problems of synchronization of the nonlinear oscillators and message transmission by chaotic signals were presented.