Adaptive Neural Control of MIMO Nonlinear Systems in Block-triangular Pure-feedback Form

Abstract In this paper, an adaptive neural control scheme is proposed for a class of MIMO nonlinear systems in block-triangular pure-feedback form. The MIMO system is composed of interconnected subsystems. Each subsystem is in the pure-feedback form with all the nonlinearities unknown. Firstly, we design for each subsystem an adaptive neural controller by using backstepping methodology. With the help of NN approximation, there is no need to solve the implicit functions for the explicit virtual controls to cancel the unknown functions in backstepping design. Secondly, by exploiting the structure properties of the MIMO system, we conclude the stability of the whole closed-loop MIMO system by stability analysis of all the signals in the closed-loop in a nested iterative manner. Semi-global uniform ultimate boundedness of all the signals in the closed-loop of MIMO nonlinear systems is guaranteed. The outputs of the systems are proven to converge to small neighborhoods of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.