Sampled-Data Adaptive NN Tracking Control of Uncertain Nonlinear Systems

In this paper, for a class of single-input-single-output (SISO) uncertain nonlinear systems, adaptive neural tracking controllers designed for digital computer implementation are proposed. The overall scheme can be considered as a sampled-data adaptive neural control system. As an intermediate result, it is proven that, for a sufficiently small sampling period, the emulated adaptive neural controller i.e., the discrete implementation of the continuous-time adaptive neural network controller ensures semiglobal uniformly ultimate boundedness of the closed-loop system. Then, based on the exact discrete-time model, a controller redesign is proposed that performs efficiently for sampling periods for which the emulation controller fails. The redesigned controller consists of two terms: the emulated control law and an extra robustness term designed to increase the order of the perturbation (with respect to the sampling period) in the Lyapunov difference. In all cases, high-order neural networks are employed to approximate the unknown nonlinearities. Using Lyapunov techniques, it is proven that, for a sufficiently small sampling period, the proposed redesigned controller ensures the (semiglobal) boundedness of all the signals in the closed-loop while the output of the system converges to a small neighborhood of the desired trajectory. Simulation results illustrate the superiority of the proposed scheme with respect to the emulation controller and verify the theoretical analysis.