Adaptive Predictive Control of a Class of Strict-feedback Discrete-time Systems using Discrete Nussbaum Gain

In this paper, novel adaptive control is proposed for a class of second order nonlinear discrete-time systems in strict-feedback form with unknown control directions. The system is transformed into a two steps ahead predictor form, in which the adaptive control can be easily designed by the certainty equivalence principle with the employment of one step ahead predicted state. The resultant control law is of simple structure and the design method avoids complicated backstepping design. For the unknown control directions, the discrete Nussbaum gain is exploited in the parameter adaptation law in great contrast to continuous counterpart where Nussbaum gain is directly used in the control law. All the closed-loop signals are guaranteed to be uniformly bounded and the output tracking error is made to converge to zero. The effectiveness of the proposed control law is demonstrated in the simulation.