Adaptive Neural Control for MIMO Pure-Feedback Nonlinear Systems With Periodic Disturbances

In this paper, an adaptive neural control design method is presented for a class of multiple-input-multiple-output (MIMO) pure-feedback nonlinear systems with periodically time-varying disturbances appearing nonlinearly in unknown nonaffine functions. The nonaffine functions do not need to be differentiable, and the bounded condition of unknown nonaffine functions is relaxed such that only a more general semibounded assumption is required as the controllability condition of the considered MIMO pure-feedback system. To facilitate the control design, the gain functions are designed to he continuous and positive with the bounds being unknown functions. Furthermore, for handling with the difficulty caused by these unknown bounds, several appropriate compact sets are defined to obtain the bounds of gain functions. By utilizing Lyapunov analysis, all the variables of the resulting closed-loop system are proven to be semiglobally uniformly ultimately bounded, and the tracking error can converge to an arbitrarily' small neighborhood around zero by choosing design parameters appropriately. The effectiveness of the proposed control algorithm is demonstrated by two simulations.