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An adaptive cerebellar-model-articulation-controller (CMAC)-based supervisory control system is developed for uncertain nonlinear systems. This adaptive CMAC-based supervisory control system consists of an adaptive CMAC and a supervisory controller. In the adaptive CMAC, a CMAC is used to mimic an ideal control law and a compensated controller is designed to recover the residual of the approximation error. The supervisory controller is appended to the adaptive CMAC to force the system states within a predefined constraint set. In this design, if the adaptive CMAC can maintain the system states within the constraint set, the supervisory controller will be idle. Otherwise, the supervisory controller starts working to pull the states back to the constraint set. In addition, the adaptive laws of the control system are derived in the sense of Lyapunov function, so that the stability of the system can be guaranteed. Furthermore, to relax the requirement of approximation error bound, an estimation law is derived to estimate the error bound. Finally, the proposed control system is applied to control a robotic manipulator, a chaotic circuit and a linear piezoelectric ceramic motor (LPCM). Simulation and experimental results demonstrate the effectiveness of the proposed control scheme for uncertain nonlinear systems.

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Underwater vehicles (UVs) are subjected to various environmental disturbances due to ocean currents, propulsion systems, and un-modeled disturbances. In practice, it is very challenging to design a control system to maintain UVs stayed at the desired static position permanently under these conditions. Therefore, in this study, a nonlinear dynamics and robust positioning control of the over-actuated autonomous underwater vehicle (AUV) under the effects of ocean current and model uncertainties are presented. First, a motion equation of the over-actuated AUV under the effects of ocean current disturbances is established, and a trajectory generation of the over-actuated AUV heading angle is constructed based on the line of sight (LOS) algorithm. Second, a dynamic positioning (DP) control system based on motion control and an allocation control is proposed. For this, motion control of the over-actuated AUV based on the dynamic sliding mode control (DSMC) theory is adopted to improve the system robustness under the effects of the ocean current and model uncertainties. In addition, the stability of the system is proved based on Lyapunov criteria. Then, using the generalized forces generated from the motion control module, two different methods for optimal allocation control module: the least square (LS) method and quadratic programming (QP) method are developed to distribute a proper thrust to each thruster of the over-actuated AUV. Simulation studies are conducted to examine the effectiveness and robustness of the proposed DP controller. The results show that the proposed DP controller using the QP algorithm provides higher stability with smaller steady-state error and stronger robustness.