Composite adaptive backstepping control considering computational complexity and relaxation of persistent excitation

A new composite adaptive backstepping control is proposed in this paper, which achieves parameter estimation convergence without persistent excitation and reduces estimation problem dimension for less computational complexity. A composite adaptation law is utilized to improve estimation and tracking performance. Relaxation of the persistent excitation requirement for parameter convergence is accomplished by making information matrix full rank only with finite excitation. The adaptation law for the proposed composite adaptive backstepping control algorithm estimates parameters in each loop separately by taking an advantage from a cascade control structure of backstepping control. Comparing to the adaptation laws which estimate whole parameters of the dynamic system at once, the designed adaptation law deals with smaller estimation problems, resulting in reduced computational complexity.