In contemporary control theory, self-adaptive methodologies are highly esteemed for their inherent flexibility and robustness in managing modeling uncertainties. Particularly, robust adaptive control stands out owing to its potent capability of leveraging robust optimization algorithms to approximate cost functions and relax the stringent constraints often associated with conventional self-adaptive control paradigms. Deep learning methods, characterized by their extensive layered architecture, offer significantly enhanced approximation prowess. Notwithstanding, the implementation of deep learning is replete with challenges, particularly the phenomena of vanishing and exploding gradients encountered during the training process. This paper introduces a self-adaptive control scheme integrating a deep MPC, governed by an innovative weight update law designed to mitigate the vanishing and exploding gradient predicament by employing the gradient sign exclusively. The proffered controller is a self-adaptive dynamic inversion mechanism, integrating an augmented state observer within an auxiliary estimation circuit to enhance the training phase. This approach enables the deep MPC to learn the entire plant model in real-time and the efficacy of the controller is demonstrated through simulations involving a high-DoF robot manipulator, wherein the controller adeptly learns the nonlinear plant dynamics expeditiously and exhibits commendable performance in the motion planning task.

翻译：在现代控制理论中，自适应方法因其在处理建模不确定性方面固有的灵活性和鲁棒性而备受推崇。其中，鲁棒自适应控制尤为突出，它能够利用强大的鲁棒优化算法来逼近成本函数，并放宽传统自适应控制范式通常所需的严格约束。深度学习方法以其广泛的分层架构为特征，提供了显著增强的逼近能力。然而，深度学习的实施充满挑战，尤其是在训练过程中遇到的梯度消失和梯度爆炸现象。本文提出了一种集成深度模型预测控制的自适应控制方案，该方案由一种创新的权重更新律所主导，该更新律旨在通过仅使用梯度符号来缓解梯度消失和爆炸的困境。所提出的控制器是一种自适应动态逆机制，它在辅助估计回路中集成了一个增广状态观测器以增强训练阶段。这种方法使得深度模型预测控制能够实时学习整个被控对象模型，控制器的有效性通过涉及高自由度机器人机械臂的仿真得到了验证，其中控制器能够快速学习非线性被控对象动力学，并在运动规划任务中表现出值得称赞的性能。