Direct Adaptive NN Control of MIMO Nonlinear Discrete-Time Systems Using Discrete Nussbaum Gain

In this paper, direct adaptive neural network (NN) control is developed for a class of multi-input and multi-output (MIMO) nonlinear systems in discrete-time. To solve the difficulty of nonaffine appearance of control, implicit function theorem is exploited to assert the existence of an ideal desired feedback control (IDFC). Then, high-order-neural-network (HONN) is employed to approximate the IDFC. Under the assumption that the inverse control gain matrix has an either positive definite or negative definite symmetric part, the obstacle in NN weights tuning for the MIMO systems is transformed to as similar as unknown control direction problem for SISO system. Then, the difficulty in NN weights tuning is overcame by exploiting the discrete Nussbaum gain, which is combined with deadzone method to treat with external disturbance with unknown upper bound. All signals in the closed-loop system are guaranteed to be semi-globally-uniformly-ultimately-bounded (SGUUB). The effectiveness of the proposed control is demonstrated in the simulation.