Backstepping and ADAR Method in the Problems of Synthesis of the Nonlinear Control Systems

Abstract

In this paper the authors explore comparison of the famous method of analytical design of the aggregated regulators (ADAR), developed in the works of the scientific school of the Southern Federal University (Russia), and the method of back-stepping. In a well-known review of P. Kokotović, the method of backstepping was mentioned as a milestone innovation in the control theory of the last decade of the 20th century. For the simplest nonlinear objects, which are derived to the structure of the serially connected integrators looped with feedbacks, the ADAR method and the backstepping method are formally deduced to the same results. But any variation of this structure, as well as an increase of the dimension and complexity of the control object model, leads to major difficulties for deriving of the analytical expression of the control law. The ADAR method of the Synergetic Control Theory is a way of forming and resonance exciting of the internal forces of co-interaction. These forces emerge in the desired structures, i.e. attractors, in a phase space of the designed systems, which are confirmed with a physical essence of the above system. In the paper the comparison of ADAR method with the backstepping method is presented with well-known examples of the nonlinear control systems' design problems. The provided numerical examples and computer simulation results clearly demonstrate the explicit advantages of ADAR method in comparison with the backstepping method by the following criteria: (i) the nonlinear regulators of the analytical design procedure and regulators of the physical validity; (ii) regulator settings of the selection validity and its value; and (iii) provision of the closed-loop system's asymptotic stability.