In this paper, a computationally efficient robust predictive control method is proposed for continuous-time under-actuated SISO systems in the presence of actuator saturation and state-dependent uncertainties. The proposition of this research is to employ the idea of model prediction together with the Adaptive Fuzzy Sliding-Mode Control (AFSMC) for tuning the sliding surface parameters by predicting the anticipated effects of uncertainties. In the proposed scheme, only after the trigger conditions are met, the coefficients of the sliding surface are updated and the AFSMC is applied. Hence, computational complexity can be controlled by adjusting the switching rule. In the AFSMC, a fuzzy system is used to approximate a nonlinear function, and a robust term to compensate for any possible mismatches. An adaptively tuned gain is also applied to the control signal to prevent instability caused by the actuator saturation. Based on the updating sliding surface, fuzzy singletons, the upper bound of the fuzzy approximation error, and the saturation gain are adaptively tuned. Closed-loop stability is shown to be guaranteed using the multiple Lyapunov functions theorem and the Barbalat’s lemma. Finally, the method is applied for the depth control of an Autonomous Underwater Vehicle (AUV), depicting the excellent performance of the proposed method.

本文提出了一种在执行器饱和和状态相关的不确定性存在的情况下，对于连续时间欠驱动的SISO系统的一种计算有效的鲁棒预测控制方法。这项研究的目的是将模型预测的思想与自适应模糊滑模控制（AFSMC）一起用于通过预测不确定性的预期影响来调整滑动表面参数。在提出的方案中，只有在满足触发条件之后，才更新滑动表面的系数并应用AFSMC。因此，可以通过调整切换规则来控制计算复杂度。在AFSMC中，模糊系统用于近似非线性函数，鲁棒项用于补偿任何可能的失配。自适应调谐的增益也应用于控制信号，以防止执行器饱和引起的不稳定。基于更新后的滑动面，对模糊单调，模糊逼近误差的上限和饱和增益进行自适应调整。使用多个Lyapunov函数定理和Barbalat引理证明可以保证闭环稳定性。最后，将该方法应用于水下机器人的深度控制，说明了该方法的优越性能。使用多个Lyapunov函数定理和Barbalat引理证明可以保证闭环稳定性。最后，将该方法应用于水下机器人的深度控制，说明了该方法的优越性能。使用多个Lyapunov函数定理和Barbalat引理证明可以保证闭环稳定性。最后，将该方法应用于水下自动航行器的深度控制，说明了该方法的优越性能。