Adaptive feedforward and feedback control of non-linear time-varying uncertain systems

An adaptive regulation scheme is proposed for a class of non-linear time-varying systems with parametric uncertainties. The proposed approach is based upon a combination of the adaptive backstepping design method and a feedforward control scheme to design a non-linear adaptive feedforward and feedback controller, such that robust output tracking can be achieved even in the presence of structured uncertainties, as well as time-varying, measurable disturbances. Although the systematic design procedure does not a priori satisfy the feedback linearizable system with triangular structures, however, the constructed condition must be satisfied to ensure that the control scheme has a stable inversion. Under the feasibility condition, the states of the resulting closed-loop system would be guaranteed boundedness and converge to a bounded set. Finally, the proposed methodology is illustrated by a chemical reactor example.