The speed bi-gradient method for model reference adaptive control of affine cascade systems

The model reference adaptive control synthesis problem for affine systems consisting of two subsystems is considered. The reference model specifies the desired state of output subsystem. The speed bi-gradient method to design continuous or sliding mode control algorithms with tunable manifold is proposed. The control law ensures both the boundedness of the closed loop system for bounded initial conditions and desired motion of the output subsystem under parameter uncertainty. The conditions of applicability and stability analysis of proposed algorithm are presented.