Speed bi-gradient algorithms for nonlinear cascade systems with the modified reference model of the output subsystem

The control design of nonlinear affine cascade systems with parametric uncertainties is considered. Control objectives are boundedness of all trajectories of the system and desired trajectory of the output subsystem. The desired trajectory is assigned by BIBO stable reference model with bounded input. The reference model modification ensures both reduction of energy costs and the estimation of the controller parameters. Both smooth and relay speed bi-gradient control laws as well as applicability, stability and limiting properties analysis are presented.