Recurrent wavelet neural network (RWNN) has the advantages such as fast learning property, good generalization capability and information storing ability. With these advantages, this paper proposes an RWNN-based adaptive control (RBAC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The RBAC system is composed of a neural controller and a bounding compensator. The neural controller uses an RWNN to online mimic an ideal controller, and the bounding compensator can provide smooth and chattering-free stability compensation. From the Lyapunov stability analysis, it is shown that all signals in the closed-loop RBAC system are uniformly ultimately bounded. Finally, the proposed RBAC system is applied to the MIMO uncertain nonlinear systems such as a mass-spring-damper mechanical system and a two-link robotic manipulator system. Simulation results verify that the proposed RBAC system can achieve favorable tracking performance with desired robustness without any chattering phenomenon in the control effort.

This study presents a robust self-learning proportional-integral-derivative (RSPID) control system design for nonlinear systems. This RSPID control system comprises a self-learning PID (SPID) controller and a robust controller. The gradient descent method is utilized to derive the on-line tuning laws of SPID controller; and the H 1 control technique is applied for the robust controller design so as to achieve robust tracking performance. Moreover, in order to achieve fast learning of PID controller, a particle swarm optimization (PSO) algorithm is adopted to search the optimal learning-rates of PID adaptive gains. Finally, two nonlinear systems, a two-link manipulator and a chaotic system are examined to illustrate the effectiveness of the proposed control algorithm. Simulation results show that the proposed control system can achieve favorable control performance for these nonlinear systems.

In this study, a robust adaptive control (RAC) system is developed for a class of nonlinear systems. The RAC system is comprised of a computation controller and a robust compensator. The computation controller containing a radial basis function (RBF) neural network is the principal controller, and the robust compensator can provide the smooth and chattering-free stability compensation. The RBF neural network is used to approximate the system dynamics, and the adaptive laws are derived to on-line tune the parameters of the neural network so as to achieve favorable estimation performance. From the Lyapunov stability analysis, it is shown that all signals in the closedloop RBAC system are uniformly ultimately bounded. To investigate the effectiveness of the RAC system, the design methodology is applied to control two nonlinear systems: a wing rock motion system and a Chua's chaotic circuit system. Simulation results demonstrate that the proposed RAC system can achieve favorable tracking performance with unknown of the system dynamics.